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NCERT Solutions for Class 5th Maths Chapter 6 Jump to a friendly number, then adjust — Nearest Multiple

Book page 76 Updated on2026-09-19

Q1.
(a) 4 × 19. Observe the picture and find why we need to subtract 4.
The picture for 4 × 19 printed on page 76. Each small square is one item.
Answer

Because the picture shows 4 rows of 20 with one column rubbed out, and that column holds 4 packets.

  1. Look at the drawing. It is 4 rows deep and 20 columns wide — that is 4 × 20 = 80 squares.
  2. Count the white column at the end. The last column is not filled. It has 4 squares, one from each row.
  3. Take that column away. 80 − 4 = 76.
  4. So 4 × 19 = 76.
4 rows of 20 = 80 this empty column holds 4 80 − 4 = 76
Nineteen columns is twenty columns minus one, and one column here is 4 packets.
4 × 19
Step 1. Go to the nearest easy number: 4 × 20 = 80
Step 2. That is one column of 4 too many.
Step 3. 80 − 4 = 76
Why we subtract 4 and not 1: The column we removed is not one square, it is one whole column. The block is 4 deep, so the column has 4 squares in it.
Q2.
(b) 14 × 21. Observe the picture and find why we need to add 14.
The picture for 14 × 21 printed on page 76. Each small square is one item.
Answer

Because 21 columns is 20 columns plus one extra, and that extra column holds 14 packets.

  1. Look at the drawing. The yellow part is 14 rows deep and 20 columns wide, so 14 × 20 = 280.
  2. Look at the green strip on the right. That is the twenty-first column, coloured green.
  3. Count the green squares. The block is 14 deep, so the green column has 14 squares.
  4. Add it on. 280 + 14 = 294.
14 × 21
Step 1. 14 × 20 = 280
Step 2. One extra column = 14
Step 3. 280 + 14 = 294
Why the extra column is 14: The number of squares in a column is always the depth of the block. Here the block is 14 rows deep, so every column — yellow or green — holds 14 squares.
The rule in one line: Go to the nearest ten or hundred, then add or take away as many whole groups as you overshot or fell short.
Q3.
(c) Give 5 examples of problems where you can use the nearest multiple to find the product easily. Find the products as well.
Answer

Sample answer: choose problems where one number is just below or just above a ten, a hundred or a nice multiple.

My exampleNearest multipleAdjustProduct
9 × 3210 × 32 = 320− 32288
99 × 7100 × 7 = 700− 7693
21 × 1520 × 15 = 300+ 15315
49 × 650 × 6 = 300− 6294
101 × 8100 × 8 = 800+ 8808
What makes a good example: One number should sit within 1 or 2 of a friendly number like 10, 20, 50, 100. Then you only have to add or take away one or two groups.
Check one: 49 × 6 = 294. Test it the long way: 40 × 6 = 240 and 9 × 6 = 54, and 240 + 54 = 294 ✓
Q4.
(d) Find the products of the following numbers by finding the nearest multiple. 1) 7 × 52 2) 12 × 28 3) 75 × 31 4) 99 × 15 5) 8 × 25 6) 22 × 42
Answer

All six, with the friendly number named each time.

ProblemNearest multipleAdjustmentAnswer
1) 7 × 527 × 50 = 350+ 7 × 2 = 14364
2) 12 × 2812 × 30 = 360− 12 × 2 = 24336
3) 75 × 3175 × 30 = 2,250+ 752,325
4) 99 × 15100 × 15 = 1,500− 151,485
5) 8 × 2510 × 25 = 250− 2 × 25 = 50200
6) 22 × 4222 × 40 = 880+ 22 × 2 = 44924
3) 75 × 31
Step 1. 31 is one more than 30.
Step 2. 75 × 30 = 75 × 3 × 10 = 225 × 10 = 2,250
Step 3. Add one more group of 75.
Step 4. 2,250 + 75 = 2,325
6) 22 × 42
Step 1. 42 is two more than 40.
Step 2. 22 × 40 = 22 × 4 × 10 = 88 × 10 = 880
Step 3. Two more groups of 22 = 44
Step 4. 880 + 44 = 924
Check 12 × 28 a second way: 12 × 28 = 12 × 20 + 12 × 8 = 240 + 96 = 336 ✓
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