Let's Review
Multiplying fractions is a simpler process than adding or subtracting fractions. The steps are shown below.
- Set up the multiplication problem.
- Use cross-cancelation to reduce the fractions before multiplying.
- Multiply the numerators and then multiply the denominators.
- Make sure that your answer is in simplest form.
Sometimes the product of the multiplication of fractions is a whole number. Remember that the fraction bar represents division. For example:
What is the product of \( \frac{4}{3} \) and \( \frac{18}{4} \)?
Set up the multiplication problem. |
\( \frac{4}{3} \cdot \frac{18}{4} \) |
Use cross-cancelation to reduce the fractions before multiplying. |
\( \frac{\overset{1}{\cancel{4}}}{\underset{1}{\cancel{3}}} \cdot \frac{\overset{6}{\cancel{18}}}{\underset{1}{\cancel{4}}} \) |
Multiply the numerators and then multiply the denominators. |
\( \frac{1}{1} \cdot \frac{6}{1} = \frac{6}{1} \) |
Make sure that your answer is in simplest form. |
The fraction \( \frac{6}{1} \) can be further simplified. The fraction bar represents division, so \( \frac{6}{1} = 6 \ \div\ 1 = 6. \) |
Give it a shot!
How well can you multiply fractions? Use the activity below to practice. Answer the question on each tab and check your answer.
What is the product of 15, \( \frac{8}{5} \), and \( \frac{14}{4} \)?
84
If you need help arriving at this answer, click the solution button.
Set up the multiplication problem. Place the whole number over 1 to make it a fraction. |
\( \frac{15}{1} \cdot \frac{8}{5} \cdot \frac{14}{4} \) |
Use cross-cancelation to reduce the fractions before multiplying. |
\( \frac{\overset{3}{\cancel{15}}}{1} \cdot \frac{\overset{2}{\cancel{8}}}{\underset{1}{\cancel{5}}} \cdot \frac{14}{\underset{1}{\cancel{4}}} \) |
Multiply the numerators and then multiply the denominators. |
\( \frac{3}{1} \cdot \frac{2}{1} \cdot \frac{14}{1} = \frac{84}{1} \) |
Make sure that your answer is in simplest form. |
\( \frac{84}{1} = 84 \ \div\ 1 = 84 \) |
A zoo has a carousel ride for park visitors. Both adults and children pay the same fee to ride the carousel. On an average day, the zoo earns $420 from carousel rides and \( \frac{3}{4} \) of the riders are children.
In a 7-day period, how much does the zoo earn from children riding the carousel?
$2,205
If you need help arriving at this answer, click the solution button.
Set up the multiplication problem. You are asked to find the part of the carousel earnings that were collected from children's ride fees over 7 days. Remember that by the commutative property of multiplication, you can multiply in any order you choose. |
\( \frac{420}{1} \cdot \frac{7}{1} \cdot \frac{3}{4} \) |
Use cross-cancelation to reduce the fractions before multiplying. |
\( \frac{\overset{105}{\cancel{420}}}{1} \cdot \frac{7}{1} \cdot \frac{3\phantom{0}}{\underset{1}{\cancel{4\phantom{0}}}} \) |
Multiply the numerators and then multiply the denominators. |
\( \frac{105}{1} \cdot \frac{7}{1} \cdot \frac{3}{1} = \frac{2205}{1} \) |
Make sure that your answer is in simplest form. |
\( \frac{2205}{1} = 2205 \ \div\ 1 = 2205 \) |
The emperor tamarin monkey troop eats a breakfast that consists of \( \frac{1}{8} \) cup of dried insects, \( \frac{1}{2} \) cup of mixed fruits, \( \frac{1}{4} \) cup of green beans, and \( \frac{1}{8} \) cup of edible flowers.
If the monkey troop has 13 members and each member receives their own breakfast, how many cups of each ingredient does the zookeeper need to make this breakfast mixture for seven days?
Dried Insects: \( \frac{91}{8} \) cups or \( 11\frac{3}{8} \) cups
Mixed Fruits: \( \frac{91}{2} \) cups or \( 45\frac{1}{2} \) cups
Green Beans: \( \frac{91}{4} \) cups or \( 22\frac{3}{4} \) cups
Edible Flowers: \( \frac{91}{8} \) cups or \( 11\frac{3}{8} \) cups
If you need help arriving at this answer, click the solution button.
To solve this problem, you need to set up three multiplication problems. |
Dried Insects/Edible Flowers: \( \frac{1}{8} \cdot \frac{13}{1} \cdot \frac{7}{1} \) Mixed Fruits: \( \frac{1}{2} \cdot \frac{13}{1} \cdot \frac{7}{1} \) Green Beans: \( \frac{1}{4} \cdot \frac{13}{1} \cdot \frac{7}{1} \) |
There is no cross-canceling to be done within any of these multiplication problems. Multiply the numerators and then multiply the denominators. These fractions are all in simplest form. You can leave them as improper fractions, or you can divide them out. |
Dried Insects/Edible Flowers: \( \frac{1}{8} \cdot \frac{13}{1} \cdot \frac{7}{1} = \frac{91}{8} \) Mixed Fruits: \( \frac{1}{2} \cdot \frac{13}{1} \cdot \frac{7}{1} = \frac{91}{2} \) Green Beans: \( \frac{1}{4} \cdot \frac{13}{1} \cdot \frac{7}{1} = \frac{91}{4} \) |
These fractions are all in simplest form. You can leave them as improper fractions, or you can divide them out to convert the improper fractions to mixed numbers. |
Dried Insects/Edible Flowers: \( \frac{91}{8} = 91 \ \div\ 8 = 11 \textsf{ R}3 = 11\frac{3}{8} \) cups Mixed Fruits: \( \frac{91}{2} = 91 \ \div\ 2 = 45 \textsf{ R}1 = 45\frac{1}{2} \) cups Green Beans: \( \frac{91}{4} = 91 \ \div\ 4 = 22 \textsf{ R}3 = 22\frac{3}{4} \) cups |
