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

14×12= \frac{1}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we will multiply the two fractions given: 14 \frac{1}{4} and 12 \frac{1}{2} .

  • Step 1: Multiply the numerators: 1×1=1 1 \times 1 = 1 .
  • Step 2: Multiply the denominators: 4×2=8 4 \times 2 = 8 .
  • Step 3: Combine these results into a new fraction: 18 \frac{1}{8} .

Therefore, the product of the fractions 14 \frac{1}{4} and 12 \frac{1}{2} is 18 \frac{1}{8} . This matches choice 3 from the provided answer choices.

Answer

18 \frac{1}{8}

Exercise #2

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: The fractions are given as 34 \frac{3}{4} and 12 \frac{1}{2} . Multiplying the numerators, we get:

3×1=3 3 \times 1 = 3

Step 2: Next, multiply the denominators:

4×2=8 4 \times 2 = 8

Step 3: Combine these results to write the product of the fractions:

34×12=3×14×2=38\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}

The resulting fraction 38 \frac{3}{8} is already in its simplest form, so no further simplification is necessary.

Therefore, the solution to the problem is 38 \frac{3}{8} .

Answer

38 \frac{3}{8}

Exercise #3

16×13= \frac{1}{6}\times\frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying two fractions 16 \frac{1}{6} and 13 \frac{1}{3} , we'll follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if necessary.

Let's apply these steps to our problem:

Step 1: Multiply the numerators: 1×1=1 1 \times 1 = 1 .
Step 2: Multiply the denominators: 6×3=18 6 \times 3 = 18 .

Therefore, the product of 16 \frac{1}{6} and 13 \frac{1}{3} is 118 \frac{1}{18} .

The solution to the problem is 118 \frac{1}{18} , which corresponds to choice 4.

Answer

118 \frac{1}{18}

Exercise #4

14×32= \frac{1}{4}\times\frac{3}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 14\frac{1}{4} and 32\frac{3}{2}, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Write the result as a fraction and simplify if needed.

Now, let's work through each step:

Step 1: Multiply the numerators:
The numerators are 11 and 33. Thus, 1×3=31 \times 3 = 3.

Step 2: Multiply the denominators:
The denominators are 44 and 22. Thus, 4×2=84 \times 2 = 8.

Step 3: Write the result as a fraction and simplify:
The resulting fraction is 38\frac{3}{8}. This fraction is already in simplest form.

Therefore, the solution to the problem is 38\frac{3}{8}.

Among the choices provided, the correct answer is choice 3: 38\frac{3}{8}.

Answer

38 \frac{3}{8}

Exercise #5

23×57= \frac{2}{3}\times\frac{5}{7}=

Video Solution

Step-by-Step Solution

Let us solve the problem of multiplying the two fractions 23\frac{2}{3} and 57\frac{5}{7}.

  • Step 1: Identify the numerators and denominators. Here, the numerators are 22 and 55, and the denominators are 33 and 77.
  • Step 2: Multiply the numerators: 2×5=102 \times 5 = 10.
  • Step 3: Multiply the denominators: 3×7=213 \times 7 = 21.
  • Step 4: Put the results together in a new fraction: 1021\frac{10}{21}.
  • Step 5: Simplify the fraction if needed. In this case, 1021\frac{10}{21} is already in its simplest form as 1010 and 2121 have no common factors besides 11.

Therefore, the solution to the problem 23×57 \frac{2}{3} \times \frac{5}{7} is 1021\frac{10}{21}.

Answer

1021 \frac{10}{21}

Exercise #6

35×12= \frac{3}{5}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, we need to multiply the fractions 35 \frac{3}{5} and 12 \frac{1}{2} .

  • Step 1: Multiply the numerators of the fractions. The numerators are 33 and 11, so 3×1=33 \times 1 = 3.
  • Step 2: Multiply the denominators of the fractions. The denominators are 55 and 22, so 5×2=105 \times 2 = 10.
  • Step 3: Combine the results from steps 1 and 2 to form the new fraction. The fraction becomes 310\frac{3}{10}.
  • Step 4: Simplify the fraction, if possible. In this case, 310\frac{3}{10} is already in its simplest form.

Therefore, the solution to 35×12\frac{3}{5} \times \frac{1}{2} is 310\frac{3}{10}.

Answer

310 \frac{3}{10}

Exercise #7

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 #8

34×12= \frac{3}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 34 \frac{3}{4} and 12 \frac{1}{2} , follow these steps:

  • Step 1: Multiply the numerators.
    Multiply 3 3 and 1 1 , which gives 3 3 .
  • Step 2: Multiply the denominators.
    Multiply 4 4 and 2 2 , which gives 8 8 .
  • Step 3: Combine the results to form a new fraction.
    This results in 38 \frac{3}{8} .

The fraction 38 \frac{3}{8} is already in its simplest form, so we do not need to simplify further.

Therefore, the solution to the problem is 38 \frac{3}{8} .

Answer

38 \frac{3}{8}

Exercise #9

13×47= \frac{1}{3}\times\frac{4}{7}=

Video Solution

Step-by-Step Solution

To solve this problem, we need to multiply two fractions, 13 \frac{1}{3} and 47 \frac{4}{7} , by following these steps:

  • Step 1: Multiply the numerators:
    1×4=4 1 \times 4 = 4 .
  • Step 2: Multiply the denominators:
    3×7=21 3 \times 7 = 21 .
  • Step 3: Combine the results to form a new fraction:
    Thus, 13×47=421 \frac{1}{3} \times \frac{4}{7} = \frac{4}{21} .

This fraction, 421 \frac{4}{21} , is in its simplest form since there are no common factors between 4 and 21 other than 1.

Therefore, the solution to the problem is 421 \frac{4}{21} .

Answer

421 \frac{4}{21}

Exercise #10

25×12= \frac{2}{5}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this problem, let's multiply the fractions 25 \frac{2}{5} and 12 \frac{1}{2} .

Step 1: Multiply the numerators:
2×1=2 2 \times 1 = 2

Step 2: Multiply the denominators:
5×2=10 5 \times 2 = 10

Step 3: Construct the fraction using the products from steps 1 and 2:
210 \frac{2}{10}

Step 4: Simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:
2÷210÷2=15 \frac{2 \div 2}{10 \div 2} = \frac{1}{5}

Thus, the product of 25 \frac{2}{5} and 12 \frac{1}{2} is 15 \frac{1}{5} .

Therefore, the solution to the problem is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #11

24×45= \frac{2}{4}\times\frac{4}{5}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 24\frac{2}{4} and 45\frac{4}{5}, follow these steps:

  • Step 1: Multiply the numerators. We have the numerators 22 and 44, so we calculate 2×4=82 \times 4 = 8.
  • Step 2: Multiply the denominators. We have the denominators 44 and 55, so we calculate 4×5=204 \times 5 = 20.
  • Step 3: Form the new fraction using the results from Steps 1 and 2. This gives us 820\frac{8}{20}.
  • Step 4: Simplify the fraction 820\frac{8}{20}. The greatest common divisor (GCD) of 88 and 2020 is 44.
  • Step 5: Divide both the numerator and the denominator by their GCD, 44: 8÷420÷4=25 \frac{8 \div 4}{20 \div 4} = \frac{2}{5}.

Therefore, the simplified product of 24\frac{2}{4} and 45\frac{4}{5} is 25\frac{2}{5}.

Answer

25 \frac{2}{5}

Exercise #12

23×14= \frac{2}{3}\times\frac{1}{4}=

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the fractions 23\frac{2}{3} and 14\frac{1}{4}, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction if necessary.

Let's begin solving the problem:

Step 1: Multiply the numerators:
2×1=22 \times 1 = 2.

Step 2: Multiply the denominators:
3×4=123 \times 4 = 12.

Putting these together, the product of the fractions is:
212\frac{2}{12}.

Step 3: Simplify the fraction 212\frac{2}{12}. Both the numerator and the denominator are divisible by 2:
Divide the numerator and denominator by 2:
2÷212÷2=16 \frac{2 \div 2}{12 \div 2} = \frac{1}{6} .

Therefore, the product of 23\frac{2}{3} and 14\frac{1}{4} simplifies to 16\frac{1}{6}.

From the given choices, the correct answer is choice 3: 16 \frac{1}{6} .

Answer

16 \frac{1}{6}

Exercise #13

24×12= \frac{2}{4}\times\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve this multiplication of fractions problem, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Simplify the resulting fraction, if possible.

Now, let's carry out these steps:
Step 1: Multiply the numerators: 2×1=2 2 \times 1 = 2 .
Step 2: Multiply the denominators: 4×2=8 4 \times 2 = 8 .
Step 3: The resulting fraction is 28 \frac{2}{8} . We simplify by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, 28=2÷28÷2=14\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}.

Therefore, the solution to the problem is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #14

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 #15

23×34= \frac{2}{3}\times\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Multiply the numerators of the fractions. The numerators are 2 2 and 3 3 .
  • Step 2: Multiply the denominators of the fractions. The denominators are 3 3 and 4 4 .
  • Step 3: Simplify the resulting fraction if necessary.

Now, let us perform the multiplication:

Step 1: Multiply the numerators:

2×3=6 2 \times 3 = 6

Step 2: Multiply the denominators:

3×4=12 3 \times 4 = 12

So, the product of the fractions is:

612 \frac{6}{12}

Step 3: Simplify the fraction. To simplify, find the greatest common divisor (GCD) of 6 and 12, which is 6. Divide both numerator and denominator by 6:

6÷612÷6=12 \frac{6 \div 6}{12 \div 6} = \frac{1}{2}

Therefore, the simplified product of the fractions 23×34 \frac{2}{3} \times \frac{3}{4} is 12 \frac{1}{2} .

This matches choice 4, which is 12 \frac{1}{2} .

Answer

12 \frac{1}{2}