How to Multiply Fractions

The multiplication of fractions is carried out by multiplying numerator by numerator and denominator by denominator, this is the method.

  • In case there is any mixed number - We will convert it into a fraction and then solve according to the learned method.
  • In case there is any whole number - We will convert it into a fraction and then solve according to the learned method.
  • The commutative property works - We can change the order of the fractions within the exercise without altering its result.

Suggested Topics to Practice in Advance

  1. Sum of Fractions
  2. Subtraction of Fractions

Practice Multiplication of Fractions

Examples with solutions for Multiplication of Fractions

Exercise #1

14×45= \frac{1}{4}\times\frac{4}{5}=

Video Solution

Step-by-Step Solution

To multiply fractions, we multiply numerator by numerator and denominator by denominator

1*4 = 4

4*5 = 20

4/20

Note that we can simplify this fraction by 4

4/20 = 1/5

Answer

15 \frac{1}{5}

Exercise #2

44×12= \frac{4}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

When we have a multiplication of fractions, we multiply numerator by numerator and denominator by denominator:

4*1 = 4
4*2 8

We can reduce the result, so we get:

4:4 = 1
8:4 2

And thus we arrived at the result, one half.

Similarly, we can see that the first fraction (4/4) is actually 1, because when the numerator and denominator are equal it means the fraction equals 1,
and since we know that any number multiplied by 1 remains the same number, we can conclude that the solution remains one half.

Answer

12 \frac{1}{2}

Exercise #3

32×1×13= \frac{3}{2}\times1\times\frac{1}{3}=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since there are only multiplication operations:

32×1=32 \frac{3}{2}\times1=\frac{3}{2}

32×13= \frac{3}{2}\times\frac{1}{3}=

We will multiply the three by three and get:

12×1=12 \frac{1}{2}\times1=\frac{1}{2}

Answer

1\over212 1\over2

Exercise #4

14×(13+12)= \frac{1}{4}\times(\frac{1}{3}+\frac{1}{2})=

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expression in parentheses.

Note that since the denominators are not common, we will look for a number that is both divisible by 2 and 3. That is 6.

We will multiply one-third by 2 and one-half by 3, now we will get the expression:

14×(2+36)= \frac{1}{4}\times(\frac{2+3}{6})=

Let's solve the numerator of the fraction:

14×56= \frac{1}{4}\times\frac{5}{6}=

We will combine the fractions into a multiplication expression:

1×54×6=524 \frac{1\times5}{4\times6}=\frac{5}{24}

Answer

524 \frac{5}{24}

Exercise #5

14×12= \frac{1}{4}\times\frac{1}{2}=

Video Solution

Answer

18 \frac{1}{8}

Exercise #6

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Answer

38 \frac{3}{8}

Exercise #7

16×13= \frac{1}{6}\times\frac{1}{3}=

Video Solution

Answer

118 \frac{1}{18}

Exercise #8

14×32= \frac{1}{4}\times\frac{3}{2}=

Video Solution

Answer

38 \frac{3}{8}

Exercise #9

23×57= \frac{2}{3}\times\frac{5}{7}=

Video Solution

Answer

1021 \frac{10}{21}

Exercise #10

35×12= \frac{3}{5}\times\frac{1}{2}=

Video Solution

Answer

310 \frac{3}{10}

Exercise #11

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Answer

38 \frac{3}{8}

Exercise #12

16×23= \frac{1}{6}\times\frac{2}{3}=

Video Solution

Answer

19 \frac{1}{9}

Exercise #13

13×47= \frac{1}{3}\times\frac{4}{7}=

Video Solution

Answer

421 \frac{4}{21}

Exercise #14

25×12= \frac{2}{5}\times\frac{1}{2}=

Video Solution

Answer

15 \frac{1}{5}

Exercise #15

24×45= \frac{2}{4}\times\frac{4}{5}=

Video Solution

Answer

25 \frac{2}{5}

Topics learned in later sections

  1. Division of Fractions
  2. Comparing Fractions
  3. Operations with Fractions