The ability to multiply fractions is very useful in everyday life, especially for people whose activities are closely related to fractions. To multiply two fractions, start by multiplying the numerator by the numerator and then multiplying the denominator by the denominator. After that, simplify the product if possible. Everyone can multiply fractions like a mathematician by following these instructions.
Step
Method 1 of 2: Multiply Before Simplifying
Step 1. Write down the fraction you want to multiply
First of all, write down the fractional number with the numerator position the same height (as in the picture above) or according to the following example:
2/4 x 2/4
Step 2. Multiply the numerator by the numerator
Since the numerator of both fractions is 2, multiply 2 by 2 and the result is 4.
Step 3. Multiply the denominator by the denominator
Since the denominator of both fractions is 4, multiply 4 by 4 and the result is 16.
The product you just multiplied is a fraction with a new numerator and denominator, which is 4/16
Step 4. Simplify the product
To simplify fractions, divide the numerator and denominator by the largest number that divides the two numbers evenly. To divide 4/16 in the above example, 4 is the largest divisor. So you have to divide the numerator and denominator by 4 according to the following steps:
- 4/4 = 1
- 16/4 = 4
- The end result is a new fractional number, which is 1/4.
Method 2 of 2: Simplifying Fractions Before Multiplication
Step 1. Write down the fraction you want to multiply
First of all, write down the fractional number with the numerator position the same height (as in the picture above) or according to the following example:
2/4 x 2/4
Step 2. Simplify the first fraction
To simplify the first number, which is 2/4, divide the numerator and denominator by the largest number that divides both numbers evenly. To divide 2/4 in the above example, 2 is the largest divisor. So you have to divide 2 and 4 by 2 according to the following steps:
- 2/2 = 1
- 4/2 = 2
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The first fraction is simplified to 1/2 which is equivalent or its value is equal to 2/4.
- Another way: find the greatest common factor (GCF) of the numerator and denominator. For that, write down all the divisors of the numerator and denominator and select the largest and the same factor. For example:
- Divisors 2: 1, 2.
- Divisors 4:1, 2, 4.
- 2 is the largest and the largest divisor of the numbers 2 and 4.
Step 3. Simplify the second fraction
The next step is to simplify the second fraction in the same way. Since the second fraction is the same as the first, which is 2/4, you'll get the same result.
2/4 = 1/2
Step 4. Multiply the numerator of the two simplified fractions
Multiply the numerator of the first 1/2 by the second, 1 and 1.
1 x 1 = 1
Step 5. Multiply the denominators of both fractions
Multiply the first 1/2 denominator by the second 1/2, which is 2 and 2.
2 x 2 = 4
Step 6. Write the new numerator over the new denominator
Since you've simplified both fractions before multiplying, your answer is the final result.
1/2 x 1/2 = 1/4
Tips
- If you want to multiply a fraction by an integer, write the number as a fraction. For example: to multiply a fraction by 36, write 36/1 and then do the multiplication according to the instructions above.
- In general, the first step in multiplying fractions is to multiply the numerator by the numerator and then to multiply the denominator by the denominator. However, you can multiply the denominator first, then multiply the numerator because the result is the same.
- The result of multiplying a natural number by a positive number less than one is a number that is smaller than the number being multiplied.
