Multiplying fractions - Definition with Examples

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Multiplying Fractions

A fraction is a part of a whole.

Multiplying Fraction

An apple pie cut into 4 equal slices and one slice is kept apart as shown.

 

Here, the apple pie is cut into 4 equal parts and each part represents one-fourth of the pie. How much apple pie would be there in 5 such pieces?

It would be the product of 5 × 1 4 . We can evaluate the multiplication as repeated addition also, and it is easier. 

5 × 1 4 = 1 4 + 1 4 + 1 4 + 1 4 + 1 4 = 5 4  

We can also convert this into a mixed number, 5 4  = 1 1 4 . Therefore, 5 pieces of the pie will have one and a quarter of apple pie.

But the repeated addition is not always an easier method, especially when the multiplier is also a fraction.

Consider the product 2 5 × 3 4 .

The fraction 3 4 can be represented as shown:

Represent Fraction

 

Now, the required product is the two-fifth of this shaded part.

To find that, you need to divide these three shaded part into 5 equal parts. An easier way to do this is to divide each of these 4 parts into 5 equal parts.

Represent Fraction 1

 

Now, the two-fifths of the three-fourths are the two shaded parts from each of these three parts, that is, 6 shaded parts out of 20 as shown.

Represent Fraction 2

 

Another way of representing this geometrically is:

Multiplying Fraction 1

In the fraction representing the product, the whole is divided into 20 equal parts and the shaded parts common to both the factors is the denominator, and 6 represents the numerator of the product.

 

Algebraically the rule to multiply two fractions is:

Step 1: Multiply the numerators of the factor fractions.

Step 2: Multiply the denominators.

Step 3: Simplify the product if required.

 

Example: 

5 6 x 3 8 = 5 × 3 6 × 8 = 15 48

 

Here, 3 is a common factor of the numerator and the denominator. So, to simplify the fraction, divide both numerator and denominator by 3.

15 ÷ 3 48 ÷ 3 = 5 6

Thus, 5 6 x 3 8 = 5 16 .

The rule is:

If a b and c d are fractions with b, d ≠ 0, then a b x c d = ac bd

 

  Fun Facts

  • The word fraction comes from the Latin word ‘fractio’ which means to break.

  • When two fractions are multiplied, if one of the fractions is greater than 1, it will increase the size of the second fraction as the product. If it is less than 1, it will decrease the size of the second fraction as the product.

 

Frequently Asked Questions

  • How to multiply two fractions?

    Follow these three simple steps to multiply two fractions: Step 1: Multiply the numerators. Step 2: Multiply the denominators. Step 3: Simplify the product if required.

  • Can the product of two proper fractions be greater than 1?

    No. The product of two proper fractions can never be greater than 1 since both the fractions are less than 1.

  • How to multiply mixed numbers?

    Follow these four simple steps to multiply two mixed numbers: Step 1: Convert the mixed numbers into an improper fraction. Step 2: Multiply the numerators. Step 3: Multiply the denominators. Step 4: Rewrite the product as a mixed number if needed.

  • Can we multiply a fraction and a whole number?

    Yes. Every whole number (e.g., 3) can be written as a fraction (3/1). So we can multiply it just the way we multiply two fractions, i.e., multiplying the numerator by the numerator and the denominator by the denominator.

Practice Problems on Multiplying Fractions

Pick the correct answer
1.   1/9 × 1/9 = ?
2.   Find the simplified product of 3/5 × 5/3.
3.   There was 3/8 of a pizza left. If you ate 1/4 of the leftover pizza, how much of the pizza did you eat?
4.   Find the simplified product of 3/4 × 20.
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