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Explanation of Multiplying Fractions - Succeed in Arithmetic. Also refer to mathematics, math, maths, numerator, denominator, mixed number, convert, Ron Kurtus, School for Champions. Copyright © Restrictions
Multiplying Fractions
by Ron Kurtus (11 January 2008)
Multiplying fractions simply consists of multiplying the numerators (top numbers) by each other and the denominators (bottom numbers) by each other. If you want to multiply a whole number by a fraction, you must first convert the whole number to a fraction and then proceed. When multiplying fractions and mixed numbers, you must first convert the mixed number to a fraction and then proceed.
Questions you may have include:
- How do you multiply two fractions?
- How do you multiply a fraction and whole number?
- How do you multiply a fraction and a mixed number?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Multiply two fractions
It is easy to multiple two fractions together. You just multiply the top numbers (numerators) by each other and the bottom numbers (denominators) by each other.
Example
Consider the multiplying the fractions:
2/7 × 3/5
Multiply top numbers (numerators) together and bottom numbers (denominators) together.
(2 × 3) / (7 × 5) = 6/35
You can apply this technique to multiply a series of fractions.
Multiply whole number with fraction
You can multiply a whole number and a fraction by considering the whole number as a form of fraction. For example, the number 5 can be considered the fraction 5/1 (5 divided by 1 equals 5). Thus, you follow the same technique as in multiply two fractions together.
Example
Consider the multiplying a whole number by a fraction:
5 × 3/7
Change the whole number to a fraction.
5/1 × 3/7
Multiply numerators together and denominators together.
(5 × 3)/(1 × 7) = 15/7
Note that 15/7 is considered an improper fraction. The proper form for your fraction answer is that the numerator is smaller than the denominator.
Divide 15 by 7 to reduce your answer a mixed number.
15 ÷ 7 = 2 1/7
Another example
Consider the multiplying a fraction by a whole number:
1/2 × 9
Change whole number to fraction.
1/2 × 9/1
Multiply numerators together and denominators together.
(1 × 9)/(2 × 1) = 9/2
Reduce improper fraction to a mixed number.
9 ÷ 2 = 4 1/2
Multiply with mixed numbers
When you multiply fractions and mixed numbers, you must first convert the mixed number into a fraction.
Convert mixed number
A mixed number is the sum of a whole number and a fraction: 5 1/2 = 5 + 1/2.
You can convert a mixed number into a fraction by first converting the whole number into a fraction over 1. For example: 5 = 5/1.
Then you multiply the top and bottom of that fraction by the denominator of the fraction part of the mixed number. In other words, if your mixed number is 5 1/2, you multiple 5/1 × 2/2 = 10/2. Note that 2/2 = 1, so you are just multiplying by 1.
Instead of going through those steps, you can shortcut the operation for 5 1/2 by seeing that the numerator is (5 × 2) + 1 = 11.
Likewise:
7 2/3
Change whole number to fraction over 1.
7/1 + 2/3
Multiply whole number fraction by 3/3.
7/1 × 3/3 + 2/3
21/3 + 2/3
Add fractions.
23/3
Another example
or
7 2/3 =
(Multiply whole number by denominator of fraction and add to numerator)
(7 × 3 + 2)/3 =
(21 + 3)/3 =
23/3
Multiply fraction and mixed number
It doesn't matter whether you multiply the fraction times the mixed number or the mixed number times the fraction.
3/5 × 6 2/7 =
(Change mixed number to fraction)
3/5 × (6 × 7 + 2)/7 =
3/5 × (42 + 2)/7 =
(Multiply fractions)
3/5 × 44/7 =
132/35
Multiply two mixed numbers
A similar process is followed when you multiply two mixed numbers.
2 1/2 × 3 2/3 =
(Change both mixed numbers to fractions)
5/2 × 11/3 =
55/6
Summary
Multiplying fractions consists of multiplying the numerators by each other and the denominators by each other. In multiplying a whole number by a fraction, you must first convert the whole number to a fraction and then proceed. When multiplying fractions and mixed numbers, you must first convert the mixed number to a fraction and then proceed.
Be amazed
Resources
The following resources provide information on this subject:
Websites
Books
Mini-quiz to check your understanding
1. What is 1/2 × 1/3 × 1/4?
2. What is 2/3 × 5 1/2?
3. What is 2 1/4 × 2 1/2?
If you got all three correct, you are on your way to becoming a Champion in Arithmetic. If you had problems, you had better look over the material again.
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Multiplying Fractions