Back to Ganita Prakash: Class 7 Mathematics, Par...BackConcept

Dividing By A Decimal

Make a decimal divisor whole by multiplying both numbers by 10, 100 or 1000, then divide as usual. Ravi's scooter trip and more.

7 micro-lessons

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Scale Both Numbers

Multiply the dividend and the divisor by the same 10, 100 or 1000.

With fractions (Textbook p. 84)

Write the decimal divisor as a fraction and multiply by its reciprocal:

$126 \div 2.5 = 126 \div \frac{25}{10} = 126 \times \frac{10}{25} = \frac{1260}{25}$

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Ravi's Speed and 4.68 ÷ 1.3

Examples 12 and 13 worked in full.

Problem 1. Ravi rode his scooter from Pune to Matheran, 126 km, in 2.5 hours. What was his average speed? (Textbook p. 84, Example 12)

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Decimal Divisor Card

Make the divisor whole, then divide.

Dividing by a decimal

a \div b = (a \times 10) \div (b \times 10) = (a \times 100) \div (b \times 100) = \dots

What each part means

b

— the divisor: choose 10, 100, 1000 to make it a counting number

a

— the dividend: multiply it by the same number

When it works

The quotient stays the same, like an equivalent fraction.

Example

2.46 \div 0.15 = 246 \div 15 = 16.4

Use 156 × 12 = 1872

Write products and quotients from one known fact.

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Figure it Out, Textbook p. 87, Q3. Given 156 × 12 = 1872:

(a) 15.6 × 1.2 =

(b) 187.2 ÷ 1.2 =

(d) 0.156 × 0.12 =

Q4. (a) 25 ÷ = 0.025

(b) 25 ÷ = 250

(d) 25 ÷ 10 = 25 ×

(e) 25 ÷ 0.10 = 25 ×

(f) 25 ÷ 0.01 = 25 ×

Divide by Decimals

Quotients with decimal divisors.

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$2.46 \div 1.5 = ?$ (Textbook p. 87, Q5)

The a ÷ b Grid

Fill the missing cells when each cell is a ÷ b.

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Figure it Out, Textbook p. 94, Q9. Each cell is a ÷ b. Use 1517 ÷ 37 = 41.

b = 37: 1517 ÷ 37 = 41, 151.7 ÷ 37 = , 15.17 ÷ 37 = , 1.517 ÷ 37 = , 15170 ÷ 37 =

b = 3.7: 1517 ÷ 3.7 = , 151.7 ÷ 3.7 = , 15.17 ÷ 3.7 = 4.1, 1.517 ÷ 3.7 = , 15170 ÷ 3.7 =

b = 0.37: 1517 ÷ 0.37 = , 151.7 ÷ 0.37 = , 15.17 ÷ 0.37 = , 1.517 ÷ 0.37 = , 15170 ÷ 0.37 =

b = 0.037: 1517 ÷ 0.037 = , 151.7 ÷ 0.037 = 4100, 15.17 ÷ 0.037 = , 1.517 ÷ 0.037 = , 15170 ÷ 0.037 =

b = 370: 1517 ÷ 370 = , 151.7 ÷ 370 = , 15.17 ÷ 370 = , 1.517 ÷ 370 = , 15170 ÷ 370 =

Divisions That Don't Stop

Divide by a decimal and round when the answer keeps going.

Find the quotients

Figure it Out, Textbook p. 86, Q2 and p. 87, Q9. Make each divisor whole, then divide. These quotients do not end: give each answer to 2 decimal places, and say what you notice about the remainders.

(a) $24.86 \div 1.2$

(b) $5.728 \div 1.52$

(a) 24.86 ÷ 1.2*

Multiply both by 10 first.

(b) 5.728 ÷ 1.52*

Multiply both by 100 first.

Distance ÷ litres.

What do you notice?*

About the remainders.

← previousDividing A Decimal By A Counting Number next →Does This Ever End? Never-Ending Decimal...

Scale Both Numbers

Multiply the dividend and the divisor by the same 10, 100 or 1000.

With fractions (Textbook p. 84)

Write the decimal divisor as a fraction and multiply by its reciprocal:

$126 \div 2.5 = 126 \div \frac{25}{10} = 126 \times \frac{10}{25} = \frac{1260}{25}$

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Divide by Decimals

Quotients with decimal divisors.

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$2.46 \div 1.5 = ?$ (Textbook p. 87, Q5)

Divisions That Don't Stop

Divide by a decimal and round when the answer keeps going.

Find the quotients

(a) $24.86 \div 1.2$

(b) $5.728 \div 1.52$

(a) 24.86 ÷ 1.2*

Multiply both by 10 first.

(b) 5.728 ÷ 1.52*

Multiply both by 100 first.

Distance ÷ litres.

What do you notice?*

About the remainders.