Multiplication of ordinary fractions

In this publication, we will consider how an ordinary (simple) fraction can be multiplied by a number or another fraction, and how to find the product of mixed fractions. We will also analyze examples of solving problems for a better understanding and consolidation of theoretical material.

Content

Multiplication of fractions

On a number

Multiplying a fraction by a number n equal to the sum of which the given fraction is nth number of times.

Multiplication of ordinary fractions

In other words, the numerator of the fraction is multiplied by the given number. n, and the denominator remains the same.

Multiplication of ordinary fractions

Note: the fraction obtained as a result of multiplication should be checked to see if it can be .

For another fraction

As a result of multiplying one fraction by another, a new fraction is obtained, the numerator of which is equal to the product of the numerators of the original fractions, and the denominator is the product of the denominators.

a/b

c/d

=

a⋅b/c⋅d

Product of mixed fractions

To multiply mixed fractions, you must first represent them in the form, and only then perform the multiplication.

X
a/b

 ⋅ Y

c/d

 = 

X ⋅ b + a/b

  

Y ⋅ d + c/d

Examples of tasks

Task 1

Multiply a fraction 
3/15

 to the number 5.

 

Solution

3/15

⋅ 5 =

3⋅5/15

=

15/15

=1

 

Task 2

Find the product of fractions 
9/17

 и 

4/7

.

 

Solution

9/17

4/7

=

9⋅4/17⋅7

=

36/119

 

Task 3

Find the product of fractions 3

3/8

 and 7

1/9

.

Solution

Because we are dealing with mixed fractions, first we represent them as improper, then we perform the multiplication.

3
3/8

⋅7

1/9

=

3⋅8+3/8

7⋅9+1/9

=

27/8

64/9

=

27⋅64/8⋅9

=

1728/72

= 24

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