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

Multiplying Decimals With Fractions

Multiply decimals by writing them as fractions over 10, 100 or 1000: the cost of pens, petrol mileage, a week's walk and an area.

6 micro-lessons

Preview · progress not saved — Chapter 1 is free

Decimals Are Fractions in Disguise

Rewrite each decimal as a fraction, multiply, then turn it back.

Repeated addition (Textbook p. 69)

$9.5 \times 5$ means adding 9.5 five times: $9.5 + 9.5 + 9.5 + 9.5 + 9.5 = 47.5$ .

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Pens and Petrol

Examples 1 and 2: the cost of 5 pens and the distance on 7.5 litres.

Problem 1. One pen costs ₹9.5 (9 rupees 50 paise). How much do 5 pens cost? (Textbook p. 69, Example 1)

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Ajay's Walk and a Rectangle

Examples 3 and 4: kilometres walked in a week, and an area.

Problem 1. Ajay's school is 827 m from home. He walks there and back, 6 days a week. How far does he walk in a week, in km? (Textbook p. 70, Example 3)

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Fraction Method Card

Decimal to fraction, multiply, back to decimal.

Multiplying decimals with fractions

\frac{a}{1 0 ^{?}} \times \frac{b}{1 0 ^{?}} = \frac{a \times b}{product of the denominators}

What each part means

one place

— over 10

two places

— over 100

three places

— over 1000

When it works

Multiply the numerators, multiply the denominators, then write the answer back as a decimal.

Example

5.7 \times 13.3 = \frac{57}{10} \times \frac{133}{10} = \frac{7581}{100} = 75.81

Can the Product Be Whole?

Math Talk questions about decimal products.

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Math Talk (p. 70): can the product of two decimals be a natural number?

Multiply Using Fractions

Fill the fraction steps for two products.

0 of 4 blanks filled

3.5 × 4 = 35/10 × 4 = /10 =

2.4 × 1.5 = 24/10 × 15/10 = /100 =

← previousDecimals Recap: Tenths, Hundredths And T...next →The Decimal Places Rule

Decimals Are Fractions in Disguise

Rewrite each decimal as a fraction, multiply, then turn it back.

Repeated addition (Textbook p. 69)

$9.5 \times 5$ means adding 9.5 five times: $9.5 + 9.5 + 9.5 + 9.5 + 9.5 = 47.5$ .

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