NCERT Solutions for Class 7th Maths Chapter 4 Figure it Out — Decimal Division

Book page 83 Updated on2026-09-19

Q1.

Find the quotient by converting the denominator into 1, 10, 100 or 1000 and verify the solution by the long division method (division by place value). (a) 18/5 (b) 415/4 (c) 1217/2 (d) 4827/8

Answer

Find the number that turns the denominator into 10, 100 or 1000, then multiply the top by the same number.

(a) 5 × 2 = 10
18/5 = (18 × 2)/(5 × 2) = 36/10 = 3.6

(b) 4 × 25 = 100
415/4 = (415 × 25)/(4 × 25) = 10375/100 = 103.75

(c) 2 × 5 = 10
1217/2 = (1217 × 5)/(2 × 5) = 6085/10 = 608.5

(d) 8 × 125 = 1000
4827/8 = (4827 × 125)/(8 × 125) = 603375/1000 = 603.375

Verification by long division (the last steps only):

Division	Whole part	Regrouping	Quotient
18 ÷ 5	3, remainder 3	3 Ones → 30 Tenths; 30 ÷ 5 = 6 Tenths	3.6
415 ÷ 4	103, remainder 3	30 Tenths → 7 Tenths r 2; 20 Hundredths → 5	103.75
1217 ÷ 2	608, remainder 1	10 Tenths ÷ 2 = 5 Tenths	608.5
4827 ÷ 8	603, remainder 3	30 Tenths → 3 r 6; 60 Hund. → 7 r 4; 40 Thou. → 5	603.375

Why it happens: 5, 4, 2 and 8 are all built only from 2s and 5s, so each of them divides some power of ten exactly. That is why all four quotients stop after a few decimal places.

Q2.

Choose the correct answer: (a) 1526/4 = (i) 38.15 (ii) 380.15 (iii) 381.5 (iv) 381.05 ; (b) 3567/8 = (i) 4458.75 (ii) 44.5875 (iii) 445.875 (iv) 4458.75

Answer

(a) (iii) 381.5 (b) (iii) 445.875

(a) 1526/4 = (1526 × 25)/100 = 38150/100 = 381.5

(b) 3567/8 = (3567 × 125)/1000 = 445875/1000 = 445.875

Why it happens: you can pick the answer without dividing fully, by estimating. For (a), 4 × 400 = 1600, which is a bit more than 1526, so the quotient is a little under 400 — only 381.5 fits. For (b), 8 × 450 = 3600, a little more than 3567, so the quotient is a little under 450 — only 445.875 fits.

Note: in the book, options (i) and (iv) of part (b) are both printed as 4458.75. It is a printing slip; neither is correct, since both are ten times too big.

Q3.

What is the quotient? (a) 132 ÷ 4 = (b) 13.2 ÷ 4 = (c) 1.32 ÷ 4 = (d) 0.132 ÷ 4 =

Answer

Only the dividend's point moves, so only the quotient's point moves.

	Division	Quotient
(a)	132 ÷ 4	33
(b)	13.2 ÷ 4	3.3
(c)	1.32 ÷ 4	0.33
(d)	0.132 ÷ 4	0.033

Why it happens: each dividend is one-tenth of the one above it, and the divisor never changes. Sharing one-tenth as much among the same 4 people gives each person one-tenth as much. So the quotient's point slides one place left each time, exactly as the dividend's did.

Q4.

What is the quotient? (a) 126 ÷ 8 = (b) 12.6 ÷ 8 = (c) 1.26 ÷ 8 = (d) 0.126 ÷ 8 = (e) 0.0126 ÷ 8 =

Answer

Divide 126 by 8 once, then slide the point.

126 ÷ 8: 8 × 15 = 120, remainder 6
60 Tenths ÷ 8 → 7 Tenths, 4 Tenths remain
40 Hundredths ÷ 8 → 5 Hundredths, nothing remains
So 126 ÷ 8 = 15.75

	Division	Quotient
(a)	126 ÷ 8	15.75
(b)	12.6 ÷ 8	1.575
(c)	1.26 ÷ 8	0.1575
(d)	0.126 ÷ 8	0.01575
(e)	0.0126 ÷ 8	0.001575

Why it happens: dividing the dividend by 10 divides the quotient by 10 as well, because the divisor is untouched. The digits 1575 stay put; only their place value drops one step each row.

Check it yourself: 0.001575 × 8 = 0.0126. ✓

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