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## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 5

Lesson 21: Multiplying fractions

# Multiplying fractions review

Review the basics of multiplying fractions, and try some practice problems.

## Multiplying fractions

To multiply fractions, we multiply the numerators and then multiply the denominators.
Example 1: Fractions
empty space, start fraction, 5, divided by, 6, end fraction, times, start fraction, 5, divided by, 7, end fraction
equals, start fraction, 5, times, 5, divided by, 6, times, 7, end fraction
equals, start fraction, 25, divided by, 42, end fraction
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
2, start fraction, 2, divided by, 3, end fraction, times, 1, start fraction, 3, divided by, 5, end fraction
equals, space, start fraction, 8, divided by, 3, end fraction, times, start fraction, 8, divided by, 5, end fraction $\qquad$
equals, start fraction, 8, times, 8, divided by, 3, times, 5, end fraction
equals, start fraction, 64, divided by, 15, end fraction
We can also write this as 4, start fraction, 4, divided by, 15, end fraction .

### Cross-reducing

Cross-reducing is a way to simplify before we multiply. This can save us from dealing with large numbers in our product.
Example
empty space, start fraction, 3, divided by, 10, end fraction, times, start fraction, 1, divided by, 6, end fraction
equals, start fraction, 3, times, 1, divided by, 10, times, 6, end fraction
equals, start fraction, start cancel, 3, end cancel, start superscript, 1, end superscript, times, space, 1, divided by, 10, times, start cancel, 6, end cancel, start subscript, 2, end subscript, end fraction
equals, start fraction, 1, divided by, 20, end fraction
Prefer a visual understanding of fraction multiplication? Check out one of these videos:
Multiplying 2 fractions: fraction model
Multiplying 2 fractions: number line

## Practice

Problem 1
• Current
start fraction, 5, divided by, 8, end fraction, times, start fraction, 7, divided by, 8, end fraction

Want to try more problems like this? Check out these exercises:
Multiply fractions
Multiply mixed numbers

## Want to join the conversation?

• How do you do Cross redusucing?
• how do you multiply negative
fractions
• Multiply the fractions normally, and ensure that the product has the correct sign.

1/2 * 1/2 = 1/4 (Two positives equal a positive.)
-1/2 * -1/2 = 1/4 (Two negatives equal a positive.)

-1/3 * 1/3 = -1/9 (A negative times a positive produces a negative .)
1/3 * -1/3 = -1/9 (The product will be negative, whether the negative number comes first or second.)
• Why do you always have to simplify?
• So the fraction reduced to lowest terms. When we reduce or simplify the fraction, we are writing a fraction in an equivalent form that may be easier to work with.
• What is GCD? thanks to whoever answers it
• Greatest common divisor of two or more integers which are not all 0
(1 vote)
• What is the difference between LCD and LCM.
• The mathematical approach to finding the LCM and LCD is the same. For both, we need to find the least common multiple of two or more numbers. The least common denominator (LCD) is actually the least common multiple (LCM) of the denominators.
(1 vote)
• How do you multiply the single number with the mixed number?
• You multiply a single number by a mixed number by putting a 1 under the single number.For example 2 + 3 1/2 your new equation would be 2/1 + 3 1/2. This is because 2/1 is the SAME exact thing a 2.