Question-by-question working
Read the prompt, attempt it, then check each step
Every exercise subpart and table row is a separate item. Shared figures and table headings are repeated whenever they are needed to understand the question.
Detailed worked answers
Textbook page 42
Textbook page 42 · solved item 1

In puzzle (a), interchange the least number of pairs to make both group sums equal.
Show detailed solution
- Step 1: The left group totals 19 and the right group totals 21, so the left side needs to gain 1 while the right side loses 1.
- Step 2: Interchange 2 from the left with 3 from the right. The two totals become 19-2+3=20 and 21-3+2=20.
- Answer: Interchange 2 and 3. Both groups then have sum 20.
Textbook page 42 · solved item 2

In puzzle (b), interchange the least number of pairs to make both group sums equal.
Show detailed solution
- Step 1: The left group totals 39 and the right group totals 47, so each final group must total 43.
- Step 2: Interchange 5 from the left with 9 from the right. The left gains 4 and the right loses 4.
- Answer: Interchange 5 and 9. Both groups then have sum 43.
Textbook page 42 · solved item 3

In puzzle (c), interchange the least number of pairs to make both group sums equal.
Show detailed solution
- Step 1: The two sums are 68 and 76, so both must become 72.
- Step 2: Interchange 11 with 13 and 15 with 17. Together, these moves add 4 to the left and remove 4 from the right.
- Answer: Two pair interchanges work: 11\leftrightarrow13 and 15\leftrightarrow17. Both sums become 72.
Textbook page 42 · solved item 4

In puzzle (d), interchange the least number of pairs to make both group sums equal.
Show detailed solution
- Step 1: The two sums are 314 and 330, so both must become 322.
- Step 2: Interchange 77 with 81 and 78 with 82. Each interchange adds 4 to the left, for a total gain of 8.
- Answer: These two pair interchanges make both group sums 322.
Detailed worked answers
Textbook page 43
Textbook page 43 · solved item 5

A lorry has 28 litres of fuel and 75 more litres are filled. How much fuel is there now?
Show detailed solution
- Step 1: Add the ones: 8+5=13. Write 3 ones and regroup 10 ones as 1 ten.
- Step 2: Add the tens: 2+7+1=10 tens, which is 1 hundred and 0 tens.
- Answer: 28+75=103. The lorry has 103 litres of fuel.
Textbook page 43 · solved item 6

Find the sum of 49 and 89.
Show detailed solution
- Step 1: Add the ones: 9+9=18. Write 8 and regroup 1 ten.
- Step 2: Add the tens: 4+8+1=13 tens.
- Answer: 49+89=138.
Textbook page 43 · solved item 7

Find the sum: 15+79.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add 5 and 9 to get 14; write 4, regroup 1 ten, then add the tens to get 9 tens.
- Answer: 15+79=94.
Textbook page 43 · solved item 8

Find the sum: 46+99.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Use 99=100-1: 46+100=146, then take away 1 to get 145.
- Answer: 46+99=145.
Textbook page 43 · solved item 9

Find the sum: 38+35.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add the ones to get 13, regroup 1 ten, and then add 3+3+1=7 tens.
- Answer: 38+35=73.
Textbook page 43 · solved item 10

Find the sum: 5+89.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add 5 to the 9 ones: 14 ones are 1 ten and 4 ones, making 94.
- Answer: 5+89=94.
Textbook page 43 · solved item 11

Find the sum: 76+28.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add the ones to get 14, then add 7+2+1=10 tens.
- Answer: 76+28=104.
Textbook page 43 · solved item 12

Find the sum: 69+20.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Adding 20 increases the tens by 2 while the 9 ones stay unchanged.
- Answer: 69+20=89.
Detailed worked answers
Textbook page 44
Textbook page 44 · solved item 13

Fill both blanks in relationship (a).
Show detailed solution
- Step 1: Addition joins two parts to make a total; subtraction removes one part from that total.
- Step 2: Since 46+21=67, subtracting either part from 67 leaves the other part.
- Answer: 67-21=46 and 67-46=21.
Textbook page 44 · solved item 14

Fill both blanks in relationship (b).
Show detailed solution
- Step 1: Addition joins two parts to make a total; subtraction removes one part from that total.
- Step 2: Since 198-98=100, adding the removed part back gives 198.
- Answer: 100+98=198 and 198-100=98.
Textbook page 44 · solved item 15

Fill both blanks in relationship (c).
Show detailed solution
- Step 1: Addition joins two parts to make a total; subtraction removes one part from that total.
- Step 2: Since 189+98=287, subtracting one part from 287 leaves the other.
- Answer: 287-98=189 and 287-189=98.
Textbook page 44 · solved item 16

Fill both blanks in relationship (d).
Show detailed solution
- Step 1: Addition joins two parts to make a total; subtraction removes one part from that total.
- Step 2: Since 872-672=200, adding 672 back gives 872.
- Answer: 200+672=872 and 872-200=672.
Textbook page 44 · solved item 17

Write the related addition and subtraction sentences for (a): 78 + 164 = 242.
Show detailed solution
- Step 1: Identify the whole and the two parts in the given fact.
- Step 2: Subtract either part from the whole to find the other part; for a subtraction fact, add the difference and removed part to rebuild the whole.
- Answer: 242-78=164 and 242-164=78.
Textbook page 44 · solved item 18

Write the related addition and subtraction sentences for (b): 462 + 839 = 1,301.
Show detailed solution
- Step 1: Identify the whole and the two parts in the given fact.
- Step 2: Subtract either part from the whole to find the other part; for a subtraction fact, add the difference and removed part to rebuild the whole.
- Answer: 1,301-462=839 and 1,301-839=462.
Textbook page 44 · solved item 19

Write the related addition and subtraction sentences for (c): 921 - 137 = 784.
Show detailed solution
- Step 1: Identify the whole and the two parts in the given fact.
- Step 2: Subtract either part from the whole to find the other part; for a subtraction fact, add the difference and removed part to rebuild the whole.
- Answer: 784+137=921 and 921-784=137.
Textbook page 44 · solved item 20

Write the related addition and subtraction sentences for (d): 824 - 234 = 590.
Show detailed solution
- Step 1: Identify the whole and the two parts in the given fact.
- Step 2: Subtract either part from the whole to find the other part; for a subtraction fact, add the difference and removed part to rebuild the whole.
- Answer: 590+234=824 and 824-590=234.
Textbook page 44 · solved item 21

A minibus had 18 litres of fuel and shows 65 litres after refuelling. How much fuel was added?
Show detailed solution
- Step 1: Subtract the fuel already present from the final amount: 65-18.
- Step 2: Regroup 65 as 5 tens and 15 ones. Then 15-8=7 and 5-1=4.
- Step 3: Check by adding: 18+47=65.
- Answer: 47 litres of fuel were added.
Detailed worked answers
Textbook page 45
Textbook page 45 · solved item 22

What is the difference between 82 and 37?
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 82 as 7 tens and 12 ones; 12-7=5 and 7-3=4. Check that 37+45=82.
- Answer: 82-37=45.
Textbook page 45 · solved item 23

Subtract: 57-11.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract 1 one and then 1 ten.
- Answer: 57-11=46.
Textbook page 45 · solved item 24

Subtract: 23-19.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 23 as 1 ten and 13 ones; 13-9=4 and 1-1=0.
- Answer: 23-19=4.
Textbook page 45 · solved item 25

Subtract: 49-21.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract 1 one to get 8 ones and 2 tens to get 2 tens.
- Answer: 49-21=28.
Textbook page 45 · solved item 26

Subtract: 56-18.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 56 as 4 tens and 16 ones; 16-8=8 and 4-1=3.
- Answer: 56-18=38.
Textbook page 45 · solved item 27

Subtract: 93-35.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 93 as 8 tens and 13 ones; 13-5=8 and 8-3=5.
- Answer: 93-35=58.
Textbook page 45 · solved item 28

Subtract: 84-23.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract 3 ones from 4 and 2 tens from 8.
- Answer: 84-23=61.
Textbook page 45 · solved item 29

Subtract: 70-43.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 70 as 6 tens and 10 ones; 10-3=7 and 6-4=2.
- Answer: 70-43=27.
Textbook page 45 · solved item 30

Subtract: 65-47.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 65 as 5 tens and 15 ones; 15-7=8 and 5-4=1.
- Answer: 65-47=18.
Textbook page 45 · solved item 31

State whether the displayed sums of 2 consecutive numbers are even or odd, and explain.
Show detailed solution
- Step 1: Check all four sums in the matching green box.
- Step 2: One number is even and the next is odd. An even number plus an odd number is odd.
- Answer: The sums are odd.
Textbook page 45 · solved item 32

State whether the displayed sums of 3 consecutive numbers are even or odd, and explain.
Show detailed solution
- Step 1: Check all four sums in the matching green box.
- Step 2: Each new sum is 3 more than the last. Adding an odd number changes even to odd and odd to even.
- Answer: The sums are alternately even and odd.
Textbook page 45 · solved item 33

State whether the displayed sums of 4 consecutive numbers are even or odd, and explain.
Show detailed solution
- Step 1: Check all four sums in the matching green box.
- Step 2: Every group has two even and two odd numbers. The two odd numbers make an even sum, so the total is even.
- Answer: The sums are even.
Textbook page 45 · solved item 34

What is the difference between successive displayed sums of 2 consecutive numbers?
Show detailed solution
- Step 1: Read the sums in order: 3, 5, 7, 9.
- Step 2: Subtract each sum from the next. Every difference is 2.
- Answer: The difference stays the same throughout and is 2.
Textbook page 45 · solved item 35

What is the difference between successive displayed sums of 3 consecutive numbers?
Show detailed solution
- Step 1: Read the sums in order: 6, 9, 12, 15.
- Step 2: Subtract each sum from the next. Every difference is 3.
- Answer: The difference stays the same throughout and is 3.
Textbook page 45 · solved item 36

What is the difference between successive displayed sums of 4 consecutive numbers?
Show detailed solution
- Step 1: Read the sums in order: 10, 14, 18, 22.
- Step 2: Subtract each sum from the next. Every difference is 4.
- Answer: The difference stays the same throughout and is 4.
Textbook page 45 · solved item 37

What is the difference between successive sums of 5 consecutive numbers?
Show detailed solution
- Step 1: Moving to the next group removes the first number and adds a number 5 greater than it.
- Step 2: The new sum therefore increases by 5.
- Answer: The difference is 5.
Textbook page 45 · solved item 38

What is the difference between successive sums of 6 consecutive numbers?
Show detailed solution
- Step 1: Moving to the next group removes the first number and adds a number 6 greater than it.
- Step 2: The new sum therefore increases by 6.
- Answer: The difference is 6.
Detailed worked answers
Textbook page 46
Textbook page 46 · solved item 39

Find 67+68+69 without adding every number one by one.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: 68 is the middle number, so the total is three groups of 68: 68+68+68=204.
- Answer: 67+68+69=204.
Textbook page 46 · solved item 40

Find 24+25+26+27 without adding every number one by one.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Pair the ends: 24+27=51 and 25+26=51; then 51+51=102.
- Answer: 24+25+26+27=102.
Textbook page 46 · solved item 41

Find 48+49+50+51+52 without adding every number one by one.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: 50 is the middle number, so five balanced numbers total 5\times50=250.
- Answer: 48+49+50+51+52=250.
Textbook page 46 · solved item 42

Find 237+238+239+240+241+242 without adding every number one by one.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Pair the ends. Each pair totals 479, and 479+479+479=1,437.
- Answer: 237+238+239+240+241+242=1,437.
Textbook page 46 · solved item 43

A point on the North-South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the corridor's total length?
Show detailed solution
- Step 1: The two distances meet at the same point, so add them: 1,855+1,862.
- Step 2: Add by place value: ones give 7, tens give 11 tens, hundreds give 17 hundreds after regrouping, and thousands give 3.
- Step 3: Check the size: two distances a little under 1,900 km should total a little under 3,800 km.
- Answer: The North-South Corridor was 3,717 km long in 2019.
Detailed worked answers
Textbook page 47
Textbook page 47 · solved item 44

Mahesh spends ₹21,880 on fuel and tolls and ₹38,900 on other expenses. How much does he spend in total?
Show detailed solution
- Step 1: Add the two amounts: 21,880+38,900.
- Step 2: Add by place value, regrouping 10 hundreds as 1 thousand and 10 thousands as 1 ten-thousand.
- Step 3: The sum is 60,780, which is sensible because ₹22,000 and ₹39,000 are about ₹61,000.
- Answer: Mahesh spends ₹60,780 in total.
Detailed worked answers
Textbook page 48
Textbook page 48 · solved item 45

Find the sum: 238+367.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: The ones make 15, the tens make 10 after regrouping, and the hundreds make 6.
- Answer: 238+367=605.
Textbook page 48 · solved item 46

Find the sum: 1,234+12,345.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add each place from ones to ten-thousands; no place is skipped.
- Answer: 1,234+12,345=13,579.
Textbook page 48 · solved item 47

Find the sum: 12+123.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Write 12 under the tens and ones of 123, then add each place.
- Answer: 12+123=135.
Textbook page 48 · solved item 48

Find the sum: 46,120+12,890.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: The ones are 0; the tens make 11 tens, and regrouping continues into the thousands.
- Answer: 46,120+12,890=59,010.
Textbook page 48 · solved item 49

Find the sum: 878+8,789.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Place 878 under the last three digits of 8,789 and regroup from ones through hundreds.
- Answer: 878+8,789=9,667.
Textbook page 48 · solved item 50

Find the sum: 1,749+17,490.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Align the 1,749 with the ones place of 17,490 and add from right to left.
- Answer: 1,749+17,490=19,239.
Textbook page 48 · solved item 51

Find the total distance of the Delhi-Mumbai-Goa-Hyderabad-Puri road trip shown on the map.
Show detailed solution
- Step 1: Read the four marked distances: 1,600 km, 590 km, 670 km, and 1,055 km.
- Step 2: Add in friendly groups: 1,600+590=2,190 and 670+1,055=1,725.
- Step 3: Add the two subtotals: 2,190+1,725=3,915.
- Answer: The total road-trip distance is 3,915 km.
Textbook page 48 · solved item 52

Which two listed numbers have a sum closest to 10,000?
Show detailed solution
- Step 1: Add likely pairs and compare each sum with the target.
- Step 2: Their sum is 10,045, only 45 away from 10,000.
- Answer: Choose 5,205 and 4,840.
Textbook page 48 · solved item 53

Which two listed numbers have a sum closest to 15,000?
Show detailed solution
- Step 1: Add likely pairs and compare each sum with the target.
- Step 2: Their sum is 14,675, which is 325 away from 15,000.
- Answer: Choose 6,220 and 8,455.
Textbook page 48 · solved item 54

Which two listed numbers have a sum closest to 13,000?
Show detailed solution
- Step 1: Add likely pairs and compare each sum with the target.
- Step 2: Their sum is 13,295, which is 295 away from 13,000 and closer than the other pair sums.
- Answer: Choose 8,455 and 4,840.
Textbook page 48 · solved item 55

Which two listed numbers have a sum closest to 16,000?
Show detailed solution
- Step 1: Add likely pairs and compare each sum with the target.
- Step 2: Their sum is 15,550, only 450 away from 16,000.
- Answer: Choose 7,095 and 8,455.
Detailed worked answers
Textbook page 49
Textbook page 49 · solved item 56

A ship travels 1,083 km from Mumbai to Cochin on a 2,700 km route to Chennai. How much farther must it travel?
Show detailed solution
- Step 1: Subtract the completed part from the full route: 2,700-1,083.
- Step 2: Regroup across the zeroes. The ones give 7, tens give 1, hundreds give 6, and thousands give 1.
- Step 3: Check by addition: 1,083+1,617=2,700.
- Answer: The ship must travel 1,617 km more.
Detailed worked answers
Textbook page 50
Textbook page 50 · solved item 57

How much longer is the 15,150 km Talon-Sagres route than the 10,228 km Cairo-Cape Town highway?
Show detailed solution
- Step 1: Find the difference: 15,150-10,228.
- Step 2: Regroup where needed and subtract from ones through ten-thousands.
- Step 3: Check by adding the difference back: 10,228+4,922=15,150.
- Answer: The Talon-Sagres route is 4,922 km longer.
Textbook page 50 · solved item 58

Subtract: 4,578-2,222.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract each place directly: 8-2, 7-2, 5-2, and 4-2.
- Answer: 4,578-2,222=2,356.
Textbook page 50 · solved item 59

Subtract: 15,324-11,780.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup in the tens and hundreds places, then continue to the thousands.
- Answer: 15,324-11,780=3,544.
Textbook page 50 · solved item 60

Subtract: 5,423-423.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: The last three digits cancel exactly, leaving 5 thousands.
- Answer: 5,423-423=5,000.
Textbook page 50 · solved item 61

Subtract: 123-12.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align 12 under the tens and ones before subtracting.
- Answer: 123-12=111.
Textbook page 50 · solved item 62

Subtract: 77,777-777.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align 777 under the final three digits; those three places cancel.
- Answer: 77,777-777=77,000.
Textbook page 50 · solved item 63

Subtract: 826-752.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup 826 as 7 hundreds, 11 tens, and 16 ones before subtracting.
- Answer: 826-752=74.
Detailed worked answers
Textbook page 51
Textbook page 51 · solved item 64

Mary starts with ₹12,540, spends ₹3,275, receives ₹4,900, then spends ₹2,645 and ₹1,275. How much is left?
Show detailed solution
- Step 1: After the first expense, she has 12,540-3,275=9,265.
- Step 2: Add the gift: 9,265+4,900=14,165.
- Step 3: After the ticket she has 14,165-2,645=11,520, and after souvenirs she has 11,520-1,275=10,245.
- Answer: Mary has ₹10,245 left.
Textbook page 51 · solved item 65

Estimate whether ₹70,500 is enough for purchases costing ₹39,785, ₹9,545, and ₹19,548.
Show detailed solution
- Step 1: Round the costs to easy nearby amounts: about ₹40,000, ₹10,000, and ₹20,000.
- Step 2: Their estimated total is about ₹70,000.
- Answer: ₹70,500 should be enough, but only by a small amount. We should calculate exactly to check.
Textbook page 51 · solved item 66

Check exactly whether the school council's ₹70,500 is enough for all three purchases.
Show detailed solution
- Step 1: Add the purchases: 39,785+9,545=49,330.
- Step 2: Add sports equipment: 49,330+19,548=68,878.
- Step 3: Compare with the amount raised: 70,500-68,878=1,622.
- Answer: Yes. The council has ₹1,622 left.
Textbook page 51 · solved item 67

What total weight is loaded when a truck carries 3,675 kg of cement and 2,850 kg of steel?
Show detailed solution
- Step 1: Add the two loads: 3,675+2,850.
- Step 2: Add by place value and regroup to get 6,525.
- Answer: The truck is carrying 6,525 kg.
Textbook page 51 · solved item 68

How much more can the 8,250 kg truck carry after 6,525 kg has been loaded?
Show detailed solution
- Step 1: Subtract the current load from the capacity: 8,250-6,525.
- Step 2: Regroup where needed and subtract to get 1,725.
- Answer: The truck can carry 1,725 kg more.
Textbook page 51 · solved item 69

Fill the blank: 32 + ___ = 100.
Show detailed solution
- Step 1: Count from 32 to 100 or subtract 100-32.
- Step 2: From 32 to 40 is 8, and from 40 to 100 is 60; 8+60=68.
- Answer: 32+68=100, so the missing number is 68.
Detailed worked answers
Textbook page 52
Textbook page 52 · solved item 70

Use Piku's method to fill the blank: 59 + ___ = 100.
Show detailed solution
- Step 1: First reach 99. The number needed is 40 because 59+40=99.
- Step 2: Add 1 more to reach 100, so the full missing number is 40+1=41.
- Answer: 59+41=100.
Textbook page 52 · solved item 71

Fill the blank: 877 + ___ = 1,000.
Show detailed solution
- Step 1: Use Piku's idea: first find the amount needed to reach the number made entirely of 9s just before the target.
- Step 2: 877+122=999, then one more makes 1,000.
- Answer: The missing number is 123.
Textbook page 52 · solved item 72

Fill the blank: 666 + ___ = 1,000.
Show detailed solution
- Step 1: Use Piku's idea: first find the amount needed to reach the number made entirely of 9s just before the target.
- Step 2: 666+333=999, then one more makes 1,000.
- Answer: The missing number is 334.
Textbook page 52 · solved item 73

Fill the blank: 4,103 + ___ = 10,000.
Show detailed solution
- Step 1: Use Piku's idea: first find the amount needed to reach the number made entirely of 9s just before the target.
- Step 2: 4,103+5,896=9,999, then one more makes 10,000.
- Answer: The missing number is 5,897.
Textbook page 52 · solved item 74

Fill the blank: 5,555 + ___ = 10,000.
Show detailed solution
- Step 1: Use Piku's idea: first find the amount needed to reach the number made entirely of 9s just before the target.
- Step 2: 5,555+4,444=9,999, then one more makes 10,000.
- Answer: The missing number is 4,445.
Textbook page 52 · solved item 75

Does Piku's missing-addend method work when the units digit is 0? What other method can be used?
Show detailed solution
- Step 1: Yes. For example, 60+39=99, and one more gives 60+40=100.
- Step 2: Another method is to count up to the next ten and then to the target, or subtract the starting number from the target.
- Answer: The method still works for a units digit of 0; counting up and subtraction also work.
Textbook page 52 · solved item 76

Fill the blank: 180 + ___ = 1,000.
Show detailed solution
- Step 1: Find how far the starting number is from 1,000.
- Step 2: Check by addition: 180+820=1,000.
- Answer: The missing number is 820.
Textbook page 52 · solved item 77

Fill the blank: 760 + ___ = 1,000.
Show detailed solution
- Step 1: Find how far the starting number is from 1,000.
- Step 2: Check by addition: 760+240=1,000.
- Answer: The missing number is 240.
Textbook page 52 · solved item 78

Fill the blank: 400 + ___ = 1,000.
Show detailed solution
- Step 1: Find how far the starting number is from 1,000.
- Step 2: Check by addition: 400+600=1,000.
- Answer: The missing number is 600.
Textbook page 52 · solved item 79

Subtract: 67-9.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 67 to get 68, then subtract 10: 68-10=58.
- Answer: 67-9=58.
Textbook page 52 · solved item 80

Subtract: 83-9.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 83 to get 84, then subtract 10: 84-10=74.
- Answer: 83-9=74.
Textbook page 52 · solved item 81

Subtract: 144-9.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 144 to get 145, then subtract 10: 145-10=135.
- Answer: 144-9=135.
Textbook page 52 · solved item 82

Subtract: 187-99.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 187 to get 188, then subtract 100: 188-100=88.
- Answer: 187-99=88.
Textbook page 52 · solved item 83

Subtract: 247-99.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 247 to get 248, then subtract 100: 248-100=148.
- Answer: 247-99=148.
Textbook page 52 · solved item 84

Subtract: 763-99.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Add 1 to 763 to get 764, then subtract 100: 764-100=664.
- Answer: 763-99=664.
Textbook page 52 · solved item 85

Fill the blank: 32 - ___ = 9.
Show detailed solution
- Step 1: The missing number is the part removed from the starting number.
- Step 2: Subtract the desired answer from the starting number: 32-9=23.
- Answer: The missing number is 23.
Textbook page 52 · solved item 86

Fill the blank: 56 - ___ = 9.
Show detailed solution
- Step 1: The missing number is the part removed from the starting number.
- Step 2: Subtract the desired answer from the starting number: 56-9=47.
- Answer: The missing number is 47.
Textbook page 52 · solved item 87

Fill the blank: 877 - ___ = 99.
Show detailed solution
- Step 1: The missing number is the part removed from the starting number.
- Step 2: Subtract the desired answer from the starting number: 877-99=778.
- Answer: The missing number is 778.
Textbook page 52 · solved item 88

Fill the blank: 666 - ___ = 99.
Show detailed solution
- Step 1: The missing number is the part removed from the starting number.
- Step 2: Subtract the desired answer from the starting number: 666-99=567.
- Answer: The missing number is 567.
Detailed worked answers
Textbook page 53
Textbook page 53 · solved item 89

List all palindrome numbers between 100 and 200.
Show detailed solution
- Step 1: A palindrome must read exactly the same from both ends.
- Step 2: For a three-digit palindrome beginning with 1, the last digit must also be 1. Let the middle digit run from 0 to 9.
- Answer: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191.
Textbook page 53 · solved item 90

List all palindrome numbers between 900 and 1,200.
Show detailed solution
- Step 1: A palindrome must read exactly the same from both ends.
- Step 2: List the three-digit palindromes beginning and ending in 9, then check four-digit numbers up to 1,200.
- Answer: 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1,001, 1,111.
Textbook page 53 · solved item 91

List all palindrome numbers between 25,000 and 27,000.
Show detailed solution
- Step 1: A palindrome must read exactly the same from both ends.
- Step 2: A five-digit palindrome reads 2, then 5 or 6, a middle digit, and then those first two digits in reverse.
- Answer: 25,052, 25,152, 25,252, 25,352, 25,452, 25,552, 25,652, 25,752, 25,852, 25,952, 26,062, 26,162, 26,262, 26,362, 26,462, 26,562, 26,662, 26,762, 26,862, 26,962.
Textbook page 53 · solved item 92

Fill the first 3 by 3 grid so every row and column increases.
Show detailed solution
- Step 1: Put the smallest numbers at the top-left and move to larger numbers across each row.
- Step 2: Use the rows 1, 2, 3; then 4, 5, 6; then 7, 8, 9. Every column also increases from top to bottom.
- Answer: One valid grid is \begin{matrix}1&2&3\\4&5&6\\7&8&9\end{matrix}.
Textbook page 53 · solved item 93

Fill the second 3 by 3 grid so every row and column decreases.
Show detailed solution
- Step 1: Put the largest numbers at the top-left and move to smaller numbers across each row.
- Step 2: Use the rows 9, 8, 7; then 6, 5, 4; then 3, 2, 1. Every column also decreases.
- Answer: One valid grid is \begin{matrix}9&8&7\\6&5&4\\3&2&1\end{matrix}.
Textbook page 53 · solved item 94

Fill the left mixed inc/dec grid using 1 to 9 once each.
Show detailed solution
- Step 1: Read the direction labels: Rows decrease and columns increase.
- Step 2: Place the numbers, then check every row and column. Each row moves down in value from left to right, while each column grows from top to bottom.
- Answer: One valid grid is \begin{matrix}3&2&1\\6&5&4\\9&8&7\end{matrix}.
Textbook page 53 · solved item 95

Fill the middle mixed inc/dec grid using 1 to 9 once each.
Show detailed solution
- Step 1: Read the direction labels: The first two rows and columns decrease; the last row and column increase.
- Step 2: Place the numbers, then check every row and column. Check each outside inc or dec label: 9, 7, 3 and 8, 6, 4 decrease, while 1, 2, 5 increases.
- Answer: One valid grid is \begin{matrix}9&8&1\\7&6&2\\3&4&5\end{matrix}.
Textbook page 53 · solved item 96

Fill the right mixed inc/dec grid using 1 to 9 once each.
Show detailed solution
- Step 1: Read the direction labels: The first two rows and first column increase; the last row and last two columns decrease.
- Step 2: Place the numbers, then check every row and column. The rows 1,8,9 and 2,6,7 increase; 5,4,3 decreases. The columns match their labels too.
- Answer: One valid grid is \begin{matrix}1&8&9\\2&6&7\\5&4&3\end{matrix}.
Detailed worked answers
Textbook page 54
Textbook page 54 · solved item 97

Should (a) 297 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 7, so it cannot be split into pairs with none left over.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 98

Should (b) 498 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 8, an even digit.
- Answer: It is even, so circle it.
Textbook page 54 · solved item 99

Should (c) 724 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 4, an even digit.
- Answer: It is even, so circle it.
Textbook page 54 · solved item 100

Should (d) 100 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 0, an even digit.
- Answer: It is even, so circle it.
Textbook page 54 · solved item 101

Should (e) 199 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 9, so one is left unpaired.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 102

Should (f) 789 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 9, an odd digit.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 103

Should (g) 49 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 9, an odd digit.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 104

Should (h) 6,893 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 3, an odd digit.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 105

Should (i) 846 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 6, an even digit.
- Answer: It is even, so circle it.
Textbook page 54 · solved item 106

Should (j) 111 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 1, an odd digit.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 107

Should (k) 222 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 2, an even digit.
- Answer: It is even, so circle it.
Textbook page 54 · solved item 108

Should (l) 1,023 be circled as an even number?
Show detailed solution
- Step 1: Look only at the ones digit.
- Step 2: Its ones digit is 3, an odd digit.
- Answer: It is odd, so do not circle it.
Textbook page 54 · solved item 109

Add 2 to the paired arrangement for 18. What changes and what stays the same?
Show detailed solution
- Step 1: 18 has 9 complete pairs and no unpaired dot.
- Step 2: Adding 2 makes one new pair, giving 20 with 10 complete pairs.
- Answer: The number of pairs increases by 1, and the arrangement remains even with no unpaired dot.
Textbook page 54 · solved item 110

Add 2 to the paired arrangement for 23. What changes and what stays the same?
Show detailed solution
- Step 1: 23 has 11 complete pairs and 1 unpaired dot.
- Step 2: Adding 2 makes one new pair, giving 25 with 12 pairs and still 1 unpaired dot.
- Answer: The number of pairs increases by 1, and the number remains odd.
Textbook page 54 · solved item 111

Choose five pairs of even numbers, add each pair, and describe the result.
Show detailed solution
- Step 1: Examples are 2+4=6, 6+8=14, 10+12=22, 14+16=30, and 18+20=38.
- Step 2: Every answer is even because each starting number is made of complete pairs, and joining them leaves complete pairs.
- Answer: The sum of two even numbers is always even.
Textbook page 54 · solved item 112

Choose five pairs of odd numbers, add each pair, and describe the result.
Show detailed solution
- Step 1: Examples are 1+3=4, 5+7=12, 9+11=20, 13+15=28, and 17+19=36.
- Step 2: The single unpaired dot from each odd number joins to make one more pair.
- Answer: The sum of two odd numbers is always even.
Textbook page 54 · solved item 113

Choose five odd-even pairs, add each pair, and describe the result.
Show detailed solution
- Step 1: Examples are 1+2=3, 3+4=7, 5+6=11, 7+8=15, and 9+10=19.
- Step 2: The even number has no unpaired dot, while the odd number has one, so one dot stays unpaired.
- Answer: The sum of an odd number and an even number is always odd.
Textbook page 54 · solved item 114

Jincy has eight ₹1 coins, nine ₹2 coins, and five ₹5 coins. Give one way to pay exactly ₹38.
Show detailed solution
- Step 1: Use five ₹5 coins: 5\times₹5=₹25.
- Step 2: Use six ₹2 coins: 6\times₹2=₹12, and one ₹1 coin. These are all within the available counts.
- Step 3: Check: ₹25+₹12+₹1=₹38.
- Answer: One possible combination is five ₹5 coins, six ₹2 coins, and one ₹1 coin.
Textbook page 54 · solved item 115

Will Raghu's torch be ON or OFF after the 23rd press?
Show detailed solution
- Step 1: The torch is ON after press 1, OFF after press 2, and this two-step pattern repeats.
- Step 2: Odd-numbered presses turn it ON; even-numbered presses turn it OFF.
- Step 3: 23 is odd.
- Answer: The torch will be ON after the 23rd press.
Detailed worked answers
Textbook page 55
Textbook page 55 · solved item 116

For which press numbers is the torch ON, and for which is it OFF?
Show detailed solution
- Step 1: Starting from OFF, each press changes the state.
- Step 2: Presses 1, 3, 5, and all other odd numbers leave it ON; presses 2, 4, 6, and all other even numbers leave it OFF.
- Answer: The torch is ON after odd-numbered presses and OFF after even-numbered presses.
Textbook page 55 · solved item 117

Which is the highest peak Priyanka climbed?
Show detailed solution
- Step 1: Read the needed height or year from the table.
- Step 2: Compare all heights in the table. The greatest height is 8,848 metres.
- Answer: Mount Everest is the highest peak, at 8,848 metres.
Textbook page 55 · solved item 118

What is the difference between the highest and lowest peaks in the table?
Show detailed solution
- Step 1: Read the needed height or year from the table.
- Step 2: The highest is 8,848 m and the lowest is 5,642 m. Subtract: 8,848-5,642=3,206.
- Answer: The difference is 3,206 metres.
Textbook page 55 · solved item 119

What is the difference between the heights of Mount Elbrus and Mount Kanchenjunga?
Show detailed solution
- Step 1: Read the needed height or year from the table.
- Step 2: Kanchenjunga is 8,586 m and Elbrus is 5,642 m. Subtract: 8,586-5,642=2,944.
- Answer: The difference is 2,944 metres.
Textbook page 55 · solved item 120

If Priyanka was 20 years old when she climbed Mount Everest in 2013, in which year was she born?
Show detailed solution
- Step 1: Read the needed height or year from the table.
- Step 2: Count back 20 years from 2013: 2013-20=1993.
- Answer: She was born in 1993, assuming her birthday had already occurred by the summit date.
Detailed worked answers
Textbook page 56
Textbook page 56 · solved item 121

Were the certificates sufficient for Chittoor, A.P., and by how many?
Show detailed solution
- Step 1: Compare the certificates printed with the students who attended.
- Step 2: More certificates were printed than needed. Subtract 18,225-18,104=121.
- Answer: The certificates were sufficient, with 121 extra.
Textbook page 56 · solved item 122

Were the certificates sufficient for Jaunpur, U.P., and by how many?
Show detailed solution
- Step 1: Compare the certificates printed with the students who attended.
- Step 2: More students attended than there were certificates. Subtract 19,265-19,043=222.
- Answer: The certificates were insufficient; 222 more were needed.
Textbook page 56 · solved item 123

Were the certificates sufficient for Raigad, Maharashtra, and by how many?
Show detailed solution
- Step 1: Compare the certificates printed with the students who attended.
- Step 2: More certificates were printed than needed. Subtract 20,863-19,974=889.
- Answer: The certificates were sufficient, with 889 extra.
Textbook page 56 · solved item 124

Find the sum: 2,009+7,388.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add by place value, regrouping 17 hundreds as 1 thousand and 7 hundreds.
- Answer: 2,009+7,388=9,397.
Textbook page 56 · solved item 125

Find the sum: 26,444+71,111.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Each place adds without regrouping: ones 5, tens 5, hundreds 5, thousands 7, ten-thousands 9.
- Answer: 26,444+71,111=97,555.
Textbook page 56 · solved item 126

Find the sum: 777+888.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Regroup in the ones, tens, and hundreds places.
- Answer: 777+888=1,665.
Textbook page 56 · solved item 127

Find the sum: 1,234+1,234.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Double each place from right to left.
- Answer: 1,234+1,234=2,468.
Textbook page 56 · solved item 128

Find the sum: 56+56,789.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Write 56 under the tens and ones of 56,789 before adding.
- Answer: 56+56,789=56,845.
Textbook page 56 · solved item 129

Find the sum: 777+77,777.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Align the three-digit number at the right and regroup through the thousands.
- Answer: 777+77,777=78,554.
Textbook page 56 · solved item 130

Add the next printed (f): 5,922+9,221.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add each place and regroup 11 thousands as 1 ten-thousand and 1 thousand.
- Answer: 5,922+9,221=15,143.
Textbook page 56 · solved item 131

Find the sum: 4,321+8,765.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Regroup from ones through thousands while keeping every place aligned.
- Answer: 4,321+8,765=13,086.
Textbook page 56 · solved item 132

Find the sum: 50,050+55,000.
Show detailed solution
- Step 1: Line up the ones, tens, hundreds, and larger places correctly.
- Step 2: Add the thousands and ten-thousands; the 50 in the final two places stays unchanged.
- Answer: 50,050+55,000=105,050.
Textbook page 56 · solved item 133

Subtract: 458-226.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract each place directly.
- Answer: 458-226=232.
Textbook page 56 · solved item 134

Subtract: 7,777-4,449.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup in the tens and hundreds places, then subtract.
- Answer: 7,777-4,449=3,328.
Textbook page 56 · solved item 135

Subtract: 65,447-47,299.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Regroup from the tens through the ten-thousands places.
- Answer: 65,447-47,299=18,148.
Textbook page 56 · solved item 136

Subtract: 1,234-123.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align 123 under the last three digits; each of those places becomes 1.
- Answer: 1,234-123=1,111.
Textbook page 56 · solved item 137

Subtract: 12,345-1,234.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align the numbers and subtract each place directly.
- Answer: 12,345-1,234=11,111.
Textbook page 56 · solved item 138

Subtract: 56,789-56.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align 56 under the tens and ones before subtracting.
- Answer: 56,789-56=56,733.
Textbook page 56 · solved item 139

Subtract the next printed (f): 87,326-11,111.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract 1 from each aligned place.
- Answer: 87,326-11,111=76,215.
Textbook page 56 · solved item 140

Subtract: 878-52.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Align 52 under the tens and ones, then subtract.
- Answer: 878-52=826.
Textbook page 56 · solved item 141

Subtract: 749-222.
Show detailed solution
- Step 1: Line up equal place values before subtracting.
- Step 2: Subtract each place directly.
- Answer: 749-222=527.
Textbook page 56 · solved item 142

Ambrish has ₹92,375. He buys a cow for ₹26,000, a goat for ₹17,000, and a milking machine for ₹19,873. Does he have enough, and how much remains?
Show detailed solution
- Step 1: Add the costs: 26,000+17,000=43,000, then 43,000+19,873=62,873.
- Step 2: Compare this with ₹92,375. The savings are greater, so he has enough.
- Step 3: Find what remains: 92,375-62,873=29,502.
- Answer: Yes. Ambrish has ₹29,502 left.
Textbook page 56 · solved item 143

A factory makes 54,000 nuts and bolts, but the order is for 85,300. How many more must it make?
Show detailed solution
- Step 1: Subtract the amount already made from the order: 85,300-54,000.
- Step 2: The difference is 31,300.
- Step 3: Check: 54,000+31,300=85,300.
- Answer: The factory must produce 31,300 more nuts and bolts.
Textbook page 56 · solved item 144

Virat Kohli has 27,599 runs, which is 6,758 fewer than Sachin Tendulkar. How many runs does Sachin have?
Show detailed solution
- Step 1: Sachin's score is greater, so add the difference to Virat's score.
- Step 2: 27,599+6,758=34,357.
- Step 3: Check: 34,357-6,758=27,599.
- Answer: Sachin Tendulkar has 34,357 runs.
