NCERT Solutions for Class 6th Maths Chapter 3 In-text Questions — Mental Math
Book page 65 & 66 Updated on2026-09-19
Q1.
Observe the figure below. What can you say about the numbers and the lines drawn? Draw arrows from the middle to the numbers on the sides to obtain the desired sums.
The figure on page 65. The arrows already drawn are the two worked examples, for 38,800 and for 3,400.
Answer
Each number on the side is built by adding numbers from the middle column, using any of them as many times as you like. The lines show which middle numbers were used.
Side number
How to make it from the middle column
Check
38,800
25,000 + 400 × 2 + 13,000
25,000 + 800 + 13,000 = 38,800 ✓
28,000
25,000 + 1,500 × 2
25,000 + 3,000 = 28,000 ✓
61,600
60,000 + 400 × 4
60,000 + 1,600 = 61,600 ✓
31,000
25,000 + 1,500 × 4
25,000 + 6,000 = 31,000 ✓
3,400
1,500 + 1,500 + 400
3,000 + 400 = 3,400 ✓
63,000
60,000 + 1,500 × 2
60,000 + 3,000 = 63,000 ✓
19,500
13,000 + 1,500 × 3 + 400 × 5
13,000 + 4,500 + 2,000 = 19,500 ✓
20,900
13,000 + 1,500 × 5 + 400
13,000 + 7,500 + 400 = 20,900 ✓
Tip: start from the biggest middle number that is not more than your target, then fill the gap. For 61,600 begin with 60,000; only 1,600 is left, and 1,600 = 400 × 4.
Q2.
Can we make 1,000 using the numbers in the middle? Why not? What about 14,000, 15,000 and 16,000? Yes, it is possible. Explore how. What thousands cannot be made?
Answer
1,000 cannot be made.
Why not: the only middle number smaller than 1,000 is 400, and adding 400s gives 400, 800, 1200, 1600 … — it skips right over 1000. Every other middle number (1,500, 13,000, 25,000, 60,000) is already bigger than 1,000.
Which thousands cannot be made? Only 1,000. Every other whole thousand can be built:
Target
One way to make it
Target
One way to make it
2,000
400 × 5
7,000
1,500 × 2 + 400 × 10
3,000
1,500 × 2
8,000
400 × 20
4,000
400 × 10
9,000
1,500 × 6
5,000
1,500 × 2 + 400 × 5
10,000
1,500 × 4 + 400 × 10
6,000
1,500 × 4
11,000
1,500 × 6 + 400 × 5
Math Talk: notice that 400 × 5 = 2,000 and 1,500 × 2 = 3,000. Once you can make 2,000 and 3,000, you can make every thousand from 2,000 upwards just by combining them.
Q3.
Adding and Subtracting. Here, using the numbers in the boxes, we are allowed to use both addition and subtraction to get the required number. An example is shown: 39,800 = 40,000 – 800 + 300 + 300. Find 45,000 = , 5,900 = , 17,500 = , 21,400 = The six boxes printed with this question on page 66.
Answer
Now subtraction is allowed too, which makes the target much easier to hit.
Target
One correct way
Check
45,000
40,000 + 12,000 − 7,000
52,000 − 7,000 = 45,000 ✓
5,900
7,000 − 800 − 300
6,200 − 300 = 5,900 ✓
17,500
12,000 + 7,000 − 1,500
19,000 − 1,500 = 17,500 ✓
21,400
40,000 − 12,000 − 7,000 + 1,500 − 300 − 800
21,000 + 1,500 − 1,100 = 21,400 ✓
The last one uses every box exactly once. Step by step: