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NCERT Solutions for Class 5th Maths Chapter 9 Each division done twice: with partial quotients and with place value — Let Us Divide

Book page 130–131 Updated on2026-09-19

Q1.
(a) 7,032 ÷ 6 — complete both solutions: 6) 7,032 (1,000 + ____ + 70 + ____ , and the place value method.
Answer

7,032 ÷ 6 = 1,172, with no remainder. The blanks are 100 and 2.

First way — partial quotients (take away chunks).

6) 7032 ( 1,000 + 100 + 70 + 2
 −6000 → 1032   (6 × 1000)
  −600 →  432   (6 × 100)
  −420 →   12   (6 × 70)
   −12 →    0   (6 × 2)

1000 + 100 + 70 + 2 = 1,172

Second way — place value (Thousands, Hundreds, Tens, Ones).

        Th H T O
6) 7032 (  1  1  7  2
  −6  (Thousands) → 1 Th left
  10  (Hundreds: 1 Th regrouped = 10 H, plus 0 H)
 −6 → 4 H left
  43  (Tens: 4 H = 40 T, plus 3 T)
 −42 → 1 T left
  12  (Ones: 1 T = 10 O, plus 2 O)
 −12 → 0
  1. 7 Thousands ÷ 6 = 1 Thousand, 1 Thousand left.
  2. Regroup: 1 Th = 10 Hundreds. 10 Hundreds ÷ 6 = 1 Hundred, 4 Hundreds left.
  3. Regroup: 4 H = 40 Tens, plus the 3 Tens = 43 Tens. 43 ÷ 6 = 7 Tens, 1 Ten left.
  4. Regroup: 1 Ten = 10 Ones, plus the 2 Ones = 12 Ones. 12 ÷ 6 = 2 Ones, nothing left.
Check by a second route: 6 × 1,172 = 6 × 1,000 + 6 × 100 + 6 × 72 = 6,000 + 600 + 432 = 7,032 ✓
Both methods gave 1,172 — that is the point of doing it twice.
Q2.
(b) 3,005 ÷ 5 — complete both solutions: 5) 3,005 (____ + ____ , and the place value method. Discuss why we have to write this 0 here.
Answer

3,005 ÷ 5 = 601, with no remainder. The blanks are 600 and 1.

First way — partial quotients.

5) 3005 ( 600 + 1
 −3000 → 5   (5 × 600)
    −5 → 0   (5 × 1)

600 + 1 = 601

Second way — place value.

        Th H T O
5) 3005 (  0  6  0  1
  3 Thousands ÷ 5 → not possible, so 0 Th
 −30  (Hundreds: 3 Th = 30 H) → 0 H left
  00  (Tens) − 00 → 0
   5  (Ones) − 5 → 0
  1. 3 Thousands cannot be shared among 5. Write 0 in the Thousands place of the quotient.
  2. Regroup: 3 Th = 30 Hundreds. 30 ÷ 5 = 6 Hundreds, nothing left.
  3. There are 0 Tens to share. 0 ÷ 5 = 0 Tens. Write the 0.
  4. 5 Ones ÷ 5 = 1 One, nothing left.
  5. Quotient = 0 Th, 6 H, 0 T, 1 O = 601.

Discuss why we have to write this 0 here — sample answer:

The 0 in the Tens place says "each part gets no tens". It keeps the 6 sitting in the Hundreds column and the 1 sitting in the Ones column. If we skipped it, the digits would slide together and we would write 61 — but 5 × 61 is only 305, nowhere near 3,005. The zero is what makes 601 mean six hundred and one instead of sixty-one.
Check by a second route: 5 × 601 = 3,005 ✓  Also 601 × 5 = 600 × 5 + 1 × 5 = 3,000 + 5 = 3,005 ✓
Q3.
(c) 2,874 ÷ 14 — complete both solutions: 14) 2,874 (____ + ____ , and the place value method.
Answer

2,874 ÷ 14 = 205 with remainder 4. The blanks are 200 and 5.

First way — partial quotients.

14) 2874 ( 200 + 5
 −2800 → 74   (14 × 200 = 2800)
   −70 →  4   (14 × 5 = 70)

Quotient = 200 + 5 = 205, Remainder = 4

Second way — place value.

         Th H T O
14) 2874 (  0  2  0  5
 2 Thousands ÷ 14 → not possible, so 0 Th
 −28  (Hundreds: 2 Th = 20 H, plus 8 H = 28 H) → 0 H left
   7  (Tens) − 0 → 7 Tens left, so 0 Tens in the quotient
  74  (Ones: 7 T = 70 O, plus 4 O)
 −70 →  4  (remainder)
  1. 2 Thousands cannot be shared among 14. Write 0 in the Thousands place.
  2. 28 Hundreds ÷ 14 = 2 Hundreds, nothing left.
  3. 7 Tens ÷ 14 — not possible, so 0 Tens. Write the 0.
  4. Regroup: 7 Tens = 70 Ones, plus 4 Ones = 74 Ones. 74 ÷ 14 = 5, with 4 left over.
Check by a second route: N = D × Q + R → 14 × 205 + 4 = 2,870 + 4 = 2,874 ✓  And 4 is smaller than 14, so the remainder is right.
Q4.
(d) 9,805 ÷ 32 — complete both solutions: 32) 9,805 (____ + ____ , and the place value method. Compare both solutions. Also, remember to put 0 in the right places.
Answer

9,805 ÷ 32 = 306 with remainder 13. The blanks are 300 and 6.

First way — partial quotients.

32) 9805 ( 300 + 6
 −9600 → 205   (32 × 300 = 9600)
  −192 →  13   (32 × 6 = 192)

Quotient = 300 + 6 = 306, Remainder = 13

Why 300 and not 400? 32 × 400 = 12,800, which is bigger than 9,805. Why 6 and not 7? 32 × 7 = 224, bigger than 205.

Second way — place value.

         Th H T O
32) 9805 (  0  3  0  6
 9 Thousands ÷ 32 → not possible, so 0 Th
 −96  (Hundreds: 98 H) → 2 H left
  20  (Tens: 2 H = 20 T, plus 0 T) − 0 → 0 Tens in the quotient
  205  (Ones: 20 T = 200 O, plus 5 O)
 −192 → 13  (remainder)

Compare both solutions — sample answer:

Partial quotientsPlace value
What you take awaywhole chunks like 32 × 300one place value at a time
Number of steps24 (Th, H, T, O)
Chance of a zero mistakelow — you add the chunks uphigher — the 0 in the Tens place is easy to forget
Answer306 R 13306 R 13 — the same
The zero warning: In the place value method, 20 Tens shared among 32 gives 0 Tens. That 0 must be written. Drop it and the answer becomes 36 instead of 306 — ten times too small.
Check: 32 × 306 + 13 = 9,792 + 13 = 9,805 ✓
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