Fundamental operation with fractions: Division — lesson. Mathematics CBSE, Class 7.

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Dividing a fraction by another fraction:

To divide a fractional number with another fractional number, follow the steps below:

Step 1: Take the reciprocal of the divisor.

Step 2: Multiply the reciprocal of the divisor with the dividend to get the new numerator and denominator of the fraction.

Reciprocal of a fraction: The reciprocal of a fraction can be obtained by interchanging the numerator and denominator of the fraction. For example, reciprocal of

\frac{1}{2} is \frac{2}{1}

. The non-zero numbers whose product with each other is \(1\) are called the reciprocals of each other that is,

\frac{1}{2} \times \frac{2}{1} = 1

. Hence,

\frac{1}{2} and \frac{2}{1}

are reciprocals of each other.

Example:

\begin{array}{l} \frac{\frac{- 1}{2}}{\frac{5}{6}} = ? \\ Step 1 : Take the reciprocal of divisor (\frac{5}{6}) = \frac{6}{5} \\ Step 2 : Multiply the dividend (\frac{- 1}{2}) by \frac{6}{5} = \frac{- 1}{2} \times \frac{6}{5} = \frac{- 3}{5} \\ \frac{New numerator}{New denominator} = \frac{- 3}{5} \end{array}

Number of negative fractions	Sign of new fraction
Even	\(+\)
Odd	\(-\)

Division of the whole number by a fraction:

Dividing a whole number by a fraction will follow the same procedure as dividing a fraction by another fraction.

Example:

\begin{array}{l} Let us find 1 \div \frac{1}{4} \\ Step 1 : Reciprocal of the divisor, \frac{1}{4} is \frac{4}{1} \\ Step 2 : Multiply the dividend (1) by \frac{4}{1} = 1 \times 4 = 4 \end{array}

Division of a fraction by a whole number:

Dividing a fractional number by a whole number will follow the same procedure as dividing a fraction by another fraction.

Example:

\begin{array}{l} Let us find \frac{1}{4} \div 1 \\ Step 1 : Reciprocal of the divisor, 1 is 1 \\ Step 2 : Multiply the dividend \frac{1}{4} by 1 = \frac{1}{4} \end{array}

Division of mixed fractions:

First, convert the mixed fractions to improper fractions and divide the fractions.

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4. Fundamental operation with fractions: Division

Theory: