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Math18

Multiplying fractions

Contenido

What is fraction multiplication?

The multiplication of fractions is one of the basic operations that allows obtaining a third fraction that will be the product of the previous ones, which is known as "Product" or "Result of Multiplication".

Symbol or sign of the multiplication of fractions

The multiplication of fractions is represented by the symbol of a cross or "x", it can also be represented with a middle point, the multiplication symbol is known as "by".


How do we multiply fractions?

To obtain the numerical value in the form of fractions, there is only one procedure either for multiplication of fractions with different denominator or the same denominator.

In the multiplication of fractions, the numerators of the fractions are multiplied and the denominators apart.

2 / 2
x
1 / 2
=
2 / 4
2/2
1/2
2/4

In the following example the fractions 1/3 and 2/6 are multiplied, the numerators of both fractions corresponding to 1 and 2 are identified, multiplied and the result is placed in the numerator. Now identify the denominators of both fractions corresponding to 3 and 6, multiply and place the result in the denominator.

1 / 3
x
2 / 6
=
1 x 2 / 3 x 6
=
2
/ 18

The result of 2/18 can be simplified because both numerator and denominator can be reduced by half. Thus, half of 2 is 1 and half of 18 is 9.

2
/ 18
=
1 / 9

Note: The fraction 2/18 and 1/9 are equivalent because they represent the same amount.

Example:

2 / 3
x
4 / 3
=
2 x 4 /
3 x 3
=
8 / 9
5 / 2
x
6 / 2
=
5 x 6 /
2 x 2
=
30 /
4
5 / 6
x
4 / 3
=
5 x 4 /
6 x 3
=
20 /
18
8 / 3
x
2 / 4
=
8 x 2 /
3 x 4
=
16 /
12

From the previous examples you can simplify 30/4 = 15/2, 20/18 = 10/9 and 16/12 = 4/3.

Exercise:

A)
5 / 3
x
3 / 3
= ?
B)
9 / 2
x
5 / 2
= ?
C)
6 / 5
x
4 / 3
= ?
D)
6 / 8
x
2 / 2
= ?

Multiplication of three or more fractions

The procedure is similar to having two fractions, the multiplication is done in line, numerator with numerator and denominator with denominator.

4 / 2
x
5 / 3
x
3 / 2
=
4 x 5 x 3 / 2 x 3 x 2
=
60 / 12
=
10 /
2
= 5

Example:

3 / 2
x
4 / 2
x
8 /
2
=
3 x 4 x 8 /
2 x 2 x 2
=
96 /
8
3 / 4
x
5 / 4
x
10 /
4
=
3 x 5 x 10 /
4 x 4 x 4
=
150 /
64
2 / 3
x
4 / 2
x
4 /
6
=
2 x 4 x 4 /
3 x 2 x 6
=
32 /
36
5 / 4
x
4 / 8
x
3 /
2
=
5 x 4 x 3 /
4 x 8 x 2
=
60 /
64

From the previous examples you can simplify 96/8 = 12, 32/36 = 8/9 and 60/64 = 15/18.

Exercise:

A)
4 / 3
x
7 / 2
x
3 / 2
= ?
B)
4 / 2
x
5 / 2
x
3 / 4
= ?
C)
3 / 2
x
7 / 2
x
3 / 2
= ?
D)
6 / 6
x
7 / 6
x
2 / 6
= ?

Multiplication of mixed fractions

In the multiplication of mixed fractions, it is necessary that the whole part be expressed as a fraction that has the same denominator as in the fractional part that accompanies it. For example, to perform the following mixed multiplication:

4
2 / 5
x 3
4 / 8
    1.- The entire part is multiplied by the denominator of the accompanying fraction.

    4 x 5 = 20
    3 x 8 = 24

    2.- The result of the multiplication is added with the numerator of the accompanying fraction.
    20 + 2 /
    5
    x
    24 + 4 /
    8
    3.- Once the mixed fractions are converted, multiplication can be performed.
    22 /
    5
    x
    28 /
    8
    =
    22 x 28 /
    5 x 8
    =
    616 /
    40