NCERT Solutions for Class 5th Maths Chapter 9 Filling the partial-quotient ladders, and the rule N = D × Q + R — Let Us Learn to Divide

Book page 125 Updated on2026-09-19

Q1.

726 ÷ 4 — complete: 4) 726 (100 + ____ + ____ . Could we have written 200 here?

Answer

726 ÷ 4 = 181 with remainder 2. The blanks are 80 and 1.

4) 726 ( 100 + 80 + 1
  −400 → 326   (4 × 100 = 400)
  −320 →   6   (4 × 80 = 320)
    −4 →   2   (4 × 1 = 4)

Quotient = 100 + 80 + 1 = 181
Remainder = 2

How each blank was found:

After taking away 400, we have 326 left. Ask: how many fours in 326? 4 × 80 = 320, which fits. 4 × 90 = 360, too big. So the chunk is 80.
After taking away 320, we have 6 left. 4 × 1 = 4 fits, 4 × 2 = 8 is too big. So the chunk is 1.
Now 2 is left, and 2 is smaller than 4. We cannot take away another whole 4. So 2 is the remainder.

Could we have written 200 here? No.

4 × 200 = 800
800 is bigger than 726
So 200 is too big a chunk to take away

Check by a second route: N = D × Q + R → 4 × 181 + 2 = 724 + 2 = 726 ✓

Q2.

902 ÷ 16 — complete: 16) 902 (____ + 6. What should we write here so that we get a number close to 902 but less than it? Could we have multiplied 16 by a larger tens?

Answer

902 ÷ 16 = 56 with remainder 6. The blank is 50.

16) 902 ( 50 + 6
−800 → 102 (16 × 50 = 800)
−96 → 6 (16 × 6 = 96)

Quotient = 50 + 6 = 56
Remainder = 6

Finding the first chunk — count in tens of 16.

Try	16 × that	Is it less than 902?
40	640	Yes, but far below 902
50	800	Yes — close to 902 ✓ best choice
60	960	No, bigger than 902

Could we have multiplied 16 by a larger tens? No. The next tens up is 60, and 16 × 60 = 960, which is more than 902. So 50 is the largest tens that fits.

Check by a second route: N = D × Q + R → 16 × 56 + 6 = 896 + 6 = 902 ✓ And the remainder 6 is smaller than the divisor 16, as it always must be.

Q3.

Sometimes, the divisor (D) does not completely divide the dividend (N) and leaves a remainder (R). What is the relationship between N, D, Q and R? Is 726 = 4 × 181? Yes/No. So, 726 = 4 × 181 + ______. Is 902 = 16 × 56? Yes/No. So, 902 = 16 × 56 + ______.

Answer

The relationship is N = D × Q + R.

First one: Is 726 = 4 × 181? No.

4 × 181 = 724
724 is 2 less than 726
So 726 = 4 × 181 + 2

Second one: Is 902 = 16 × 56? No.

16 × 56 = 896
896 is 6 less than 902
So 902 = 16 × 56 + 6

The dividend is made of the part that shares out evenly plus the little bit left over.

The four names, in one sentence: the dividend (N) is what you start with, the divisor (D) is how you share it, the quotient (Q) is what each group gets, and the remainder (R) is what would not fit.

Two rules to remember:
1. N = D × Q + R — use it to check every division you do.
2. The remainder is always smaller than the divisor. If your remainder is bigger, the quotient should have been larger.

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