Arithmetic Worksheets

Practice and master arithmetic with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

Multiplying Fractions

By Michelle Arreola

When you are multiplying by a fraction you are finding part of that number. To multiply a fraction you would multiply the numerator with another numerator and the denominator with the other denominator. Then you would simply if possible.

Why is this concept useful?

This concept is used in cooking, bookkeeping, accounting, data entry, and even discounts off sales prices. This concept is useful for architects, chefs, engineers, and many others in the working community.

Where does this concept fit into the curriculum?

5th and Up

How can we use the concept:

In order to apply this concept you will need to know the steps for multiplying 2 fractions together, multiplying a whole number with a fraction, and multiplying a proper fraction with a mixed fraction.

Multiplying 2 fractions together:

  1. First, multiply the numerator with the other numerator.
  2. Next, multiply the denominator with the other denominator.
  3. Finally, write out your product and reduce it if possible by using division.

Multiplying a whole number with a fraction:

  1. First, rewrite the whole number as a fraction over 1.
  2. Next, multiply the numerator with the other numerator.
  3. Then, multiply the denominator with the other denominator.
  4. Finally, write out your product and reduce it if possible by using division.

Multiplying a proper fraction with a mixed fraction.

  1. First, convert the mixed fraction to an improper fraction.
  2. Next, multiply the numerator with the other numerator.
  3. Then, multiply the denominator with the other denominator.
  4. Finally, write out your product and reduce it if possible by using division.

*Note: You can choose to simplify before multiplying or after.2

Sample Math Problems

Question

Solve the following (Enter your answer in the lowest form):

410∗912\frac{4}{10} * \frac{9}{12}

Solution

First, you would multiply the numerator in fraction 1 with the numerator in fraction 2. 4 x 9= 36

Then, you would multiply the denominator in fraction 1 with the denominator in fraction 2. 10 x12= 120

36120\frac{36}{120}

Now, you can reduce your fraction if possible.

36 and 120 are both divisible by 12. 36 divided by 12 is 3. 120 divided by 12 is 10.

So the answer in the lowest form would be:

310\frac{3}{10}

Question

Samantha bought 248 pounds of mixed vegetables for her restaurant. Over the weekend the restaurant used ⅞ of the mixed vegetables. How many pounds did the restaurant use over the weekend?

Solution

First, you would rewrite the whole number as a fraction over 1.

2481\frac{248}{1}

Then, you would multiply the numerator from the 1st fraction with the numerator from the 2nd fraction. 248 x 7 = 1736.

After, you would multiply the denominator in the fist fraction with the denominator in the 2nd fraction. 1 x 8 = 8.

Finally, you would get:

17368\frac{1736}{8}

When you reduce you would divide both the numerator and denominator by 8. So, the answer would be 217 pounds of mixed vegetables.

Question

Solve the following (Enter your answer in the lowest form of proper or mixed fraction):

3 ⅖ x 6/7

Solution

First, you would convert the mixed fraction to an improper fraction. 17/5

Then, you would multiply the numerator in the 1st fraction with the numerator in the 3nd fraction. 17 x 6 =102

After, you would multiply the denominator in the 1st fraction with the denominator in the second fraction. 5 x 7 = 35

Finally you would reduce your fraction and convert to a mixed fraction. 102/35 = 2 32/35

So the answer in lowest form would be 2  32/35

Question

Solve the following (Enter your answer in the lowest form)

¾ x ⅑ x ⅘

Solution

First, you would multiply the numerators together. 3 x 1 x 4 =12

Then, you would multiply the denominators together. 4 x 9 x 5 =180

Finally, you would reduce your fraction to the lowest terms.

So

12180\frac{12}{180}
would reduce to
115\frac{1}{15}

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Practice Math Problems

1.) Solve the following (Enter your answer in the lowest form):

913∗1635\frac{9}{13} * \frac{16}{35}

2.) In a theater, there are 438 seats available for a show. On Thursday night ⅗ of the seats were occupied. How many seats were filled on Thursday night?

3.) Jan is making cookies. For each cookie she used ⅔ cups of chocolate chips. How many cups of chocolate chips would she use if she made 8 ½ cookies? (Enter your answer in the lowest form of proper or mixed fraction)

4.) Solve the following (Enter your answer in the lowest form): ½ x ⅔ x ⅞


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