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Now that we’ve learned how to add and subtract fractions, we will learn how to multiply fractions. Multiplying fractions is a lot simpler than adding or subtracting fractions because we don’t need to find a common denominator, instead we just multiply across numerators and denominators. The following video will explain why this works and show a few examples.
Video Source (05:48 mins) | Transcript
When multiplying fractions we simply multiply the numerators together and the denominators together. Remember, any whole number can be represented as a fraction by putting it over 1.
Example: \(3=\frac{3}{1}\)
Reduce when needed.
Example when reducing is not needed: \(\frac{2}{5}\cdot\frac{2}{3}=\frac{2\cdot2}{5\cdot3}=\frac{4}{15}\)
Example when reducing is needed: \(\frac{2}{5}\cdot\frac{3}{4}=\frac{2\cdot3}{5\cdot2\cdot2}=\frac{2}{2}\cdot\frac{3}{5\cdot2}=1\cdot\frac{3}{10}=\frac{3}{10}\)
You might have been in fifth grade the last time you thought about multiplying fractions. But if you're trying to cut a recipe in half or calculate the new price of a sale sweater using fractions, you might need to dig around in the back of your memory for how to do it. Let's refresh:
In every fraction, there's a top number and a bottom number, separated by a short horizontal line. In a proper fraction, the smaller number — called the numerator — will always be on top, while the larger number — the denominator — will be on the bottom. The numerator tells us how many units we have of a whole and the denominator tells us how many units make up the whole. So, in the fraction 1/2, 1 is the numerator and 2 is the denominator — there are two units in the whole, but this fraction tells us that we only have one of these units.
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Unlike when you are adding or subtracting fractions, you can multiply fractions with different denominators. For instance, it's not a problem to multiply 3/4 x 2/5.
Each worksheet has a variety of fractions all with a common (same) denominator. When multiplying fractions, simply multiply the numerator (top number) then multiply the denominator (bottom number) and reduce to its lowest term if needed.
- Example 1: 1/4 x 3/4 = 3/16 (1 x 3 on top and 3 x 4 on bottom) in this example the fraction cannot be reduced further.
- Example 2: 1/3 x 2/3 = 2/9 This cannot be reduced further.
- Example 3: 1/6 x 2/6 = 2/36 In this case, the fraction can be reduce further. Both numbers can be divided by 2 which gives us 1/18 which is the reduced answer.
Worksheets like these provide exercises for students to enhance their understanding.
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Worksheet #2 (Answers on 2nd Page of PDF)
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Multiply the Improper Fractions, Worksheet #3 (Answers on 2nd Page of PDF)
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Worksheet #4 (Answers on 2nd Page of PDF)
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Worksheet #5 (Answers on 2nd Page of PDF)
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Worksheet #6 (Answers on 2nd Page of PDF)
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Worksheet #7 (Answers on 2nd Page of PDF)
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Worksheet #8 (Answers on 2nd Page of PDF)
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Worksheet #9 (Answers on 2nd Page of PDF)
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Worksheet #10 (Answers on 2nd Page of PDF)
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Russell, Deb. "Multiply Fractions With Common Denominators Worksheets." ThoughtCo. //www.thoughtco.com/multiplying-with-common-denominators-fraction-worksheets-2312280 (accessed December 14, 2022).