- Fractions are important topics in Mathematics and clear understanding is important for various topics.
- We have already learned about Fraction Definition,Types of Fractions,Proper Fraction,Mixed Fraction, Improper Fraction, Mixed Fractions to Improper Fractions, Improper Fractions to Mixed Fraction, How to Represent Fraction on Number Line?, Simplest form of Fraction, Equivalent Fractions, Like and Unlike Fractions, Comparing Fractions, How to add Fractions, How to Subtract Fractions,Comparison, Addition and Subtraction of Mixed Fractions in previous class.
- In this we will learning multiplying fractions, how to multiply fractions with whole numbers, how to multiply 3 fractions and various other thing related to Multiplication

Suppose we have 2 , 1/4 piece of chocolate. So total chocolate we have,

$\frac {1}{4} + \frac {1}{4} =\frac {2}{4}= \frac {1}{2}$

or

$\frac {1}{4} + \frac {1}{4} =2 \times \frac {1}{4}$

So,

$2 \times \frac {1}{4} =\frac {2}{4}= \frac {1}{2}$

Here are the steps to multiply fractions with whole numbers

- if we have mixed fraction in the multiplication, first convert into improper fraction

- Now multiply the whole number with the numerator of the fraction, keeping the denominator same

- We can simplify the fractions if needed and if the multiplication fraction results in improper fraction, you can convert into mixed fraction if required.

$ 3 \times \frac {1}{5} = \frac {3 \times 1}{5}= \frac {3}{5}$

$ 2 \times \frac {4}{5} = \frac {2 \times 4}{5}=\frac {8}{5} = 1 \frac {3}{5} $

$ 2 \times 2\frac {1}{5} = 2 \times \frac {11}{5}=\frac {22}{5} = 4 \frac {2}{5} $

$ 2 \times \frac {1}{8} =\frac {2}{8} = \frac {1}{4} $

'of' represent multiplication .So 1/2 of 4 is represent $ \frac {1}{2} \times 4 = 2$

$ \frac {1}{5} \; of \; 20 = \frac {1}{5} \times 20= \frac {20}{5} = 4$

$\frac {4}{5} \; of \; 10= \frac {4}{5} \times 10=\frac {40}{5} = 8$

Suppose Ram have half (1/2) piece of pizza. And he want to equally share that with his Friend Suresh. So each of them would get 1/2 of 1/2 which can be written as

$\frac {1}{2} \; of \; \frac {1}{2} = \frac {1}{2} \times \frac {1}{2}$.

Now we can easily see that each of them get 1/4 piece of the whole pizza actually.So

$\frac {1}{2} \; of \; \frac {1}{2} = \frac {1}{2} \times \frac {1}{2} = \frac {1}{4}$.

Here we can see that Multiplying fraction is simply acheived by

$Multiplying \; Fractions= \frac {products \; of \; numerator}{products \; of \; denominators}$

$\frac {1}{2} \times \frac {1}{2} = \frac { 1 \times 1 }{2 \times 2} = \frac {1}{4}$

$\frac {1}{3} \times \frac {1}{2} = \frac { 1 \times 1 }{3 \times 2} = \frac {1}{6}$

$\frac {2}{3} \times \frac {1}{2} = \frac { 2 \times 1 }{3 \times 2} = \frac {2}{6} = \frac {1}{3}$

$\frac {2}{3} \times \frac {3}{4} = \frac { 2 \times 3 }{3 \times 4} = \frac {6}{12} = \frac {1}{2}$

Here are the steps for multiplying fractions

- if we have mixed fraction in the multiplication, first convert into improper fraction

- Now obtain the products of the numerator and denominators.

- We can simplify the fractions if needed and if the multiplication fraction results in improper fraction, you can convert into mixed fraction if required.

$ \frac {3}{2} \times \frac {1}{5} = \frac {3 \times 1}{2 \times 5}= \frac {3}{10}$

$ \frac {3}{7} \times \frac {4}{5} = \frac {3 \times 4}{7 \times 5}=\frac {12}{35} $

$ \frac {3}{7} \times 2\frac {1}{5} = \frac {3/7} \times \frac {11}{5}=\frac {33}{35} $

$ 2\frac {1}{5} \times 1\frac {1}{8} =\frac {11}{5} \times \frac {9}{8} = \frac {99}{40} = 2 \frac {19}{40}$

a. when two proper fractions are multiplied, the product is less than each of the fractions

b. the product of two improper fractions is greater than each of the two fractions.

Checkout Multiplying Fractions calculator

Given below are the links of some of the reference books for class 7 math.

- Mathematics for class 7 by R S Aggarwal
- Mathematics for Class 7 by R D Sharma
- Mathematics Foundation Course For JEE/IMO/Olympiad - Class 7
- IIT Foundation Physics, Chemistry & Maths for Class 7

You can use above books for extra knowledge and practicing different questions.

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Class 7 Maths Class 7 Science