The class 7 maths chapter 2 Fractions and Decimals, discusses the multiplication and division of fractions and decimals. First, let us revise a few basic terminologies related to fractions before we move on to the concepts discussed in the chapter.

The three types of fractions are:

**Proper Fraction –**Fractions that represents a part of a whole. Examples, \(\frac{1}{3},\frac{2}{7}\)

**Improper Fraction –**Fraction where the numerator is greater or equal to the denominator. Example, \(\frac{4}{3},\frac{7}{7}\)

**Mixed Fraction –**Mixed fraction is the combination of a whole number and a proper fraction. Example, \(1\frac{1}{2},5\frac{2}{5}\)

## Multiplication of Fractions and Decimals

### Multiplication of Fraction

- The numerators and denominators of two fractions are multiplied separately and the product is written as \(\frac{product \; of\; numerators}{product\; of\; denominators}\). For example, \(\frac{4}{5}\times \frac{6}{5}=\frac{4\times 6}{5\times 5}=\frac{24}{25}\)
- The product of two proper fractions is lesser than each of the fractions multiplied.
- The product of two improper fractions is greater than the two fractions multiplied.
- The product obtained by multiplying a proper and an improper fraction is lesser than the multiplied improper fraction but greater than the multiplied proper fraction.

### Multiplication of Decimals

- First, multiply the two decimals numbers as whole numbers.
- Count the number of digits to the right of the decimal point in both the decimal numbers.
- Add the number of digits counted.
- Put the decimal point in the product by counting the digits from its rightmost place.
- The count should be the sum obtained earlier.

Example: \(0.30\times 5=0.15\)

While multiplying a decimal number with 10, 100 or 1000, shift the decimal point in the number to the right by as many places as there are zeros over 1. For example,

- \(0.48\times 10=4.8\)
- \(0.48\times 100=48\)
- \(0.48\times 1000=480\)

## Division of Fractions and Decimals

### Division of Fractions

- When a whole number is divided by a fraction, the whole number is multiplied with the reciprocal of the fraction.

Example: \(4\div \frac{3}{8}=4\times \frac{8}{3}=\frac{32}{3}\)

- When a fraction is divided by a whole number, the fraction is multiplied by the reciprocal of the whole number.

Example: \(\frac{1}{2}\div 5=\frac{1}{2}\times \frac{1}{5}=\frac{1}{10}\)

- When we divide one fraction by another, we multiply the first fraction with the reciprocal of the second fraction.

Example: \(\frac{1}{2}\div \frac{3}{8}=\frac{1}{2}\times\frac{8}{3}=\frac{8}{6}\)

### Division of Decimals

- When a decimal number is divided by a whole number, the whole numbers are divided first and later the decimal point is divided

For example, \(6.42\div 3.2\)

- When a decimal number is divided by 10, 100 and 100, shift the digits in the decimal

number to the left by as many places as there are zeros over 1, to obtain the quotient.

For example,

- \(45.9\div 10=4.5\)
- \(45.9\div 100=0.459\)
- \(45.9\div 1000=0.0459\)

- When a decimal number is divided by another decimal number, shift the decimal point to the right by the equal number of places in both, to convert the divisor to a whole number. Then, divide.

For example, \(3.2\div 0.8=32\div 8=4\)

## Class 7 Fractions and Decimals Important Question

- A rectangular sheet of paper is \(12\frac{1}{2}\) cm long and \(10\frac{2}{3}\) cm wide. Find its perimeter.
- Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent

saplings is \(\frac{3}{4}\) m. Find the distance between the first and the last sapling. - Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g

oranges and 4 kg 150 g bananas. Who bought more fruits? - The side of an equilateral triangle is 3.5 cm. Find its perimeter.
- Find the average of 4.2, 3.8 and 7.6.

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