Multiplying fractions review (article)

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Course: Arithmetic (all content)>Unit 5

Lesson 21: Multiplying fractions

Intro to multiplying 2 fractions
Multiplying 2 fractions: fraction model
Multiplying 2 fractions: number line
Multiplying fractions with visuals
Multiplying 2 fractions: 5/6 x 2/3
Multiplying fractions
Finding area with fractional sides 1
Finding area with fractional sides 2
Area of rectangles with fraction side lengths
Multiplying fractions review

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Arithmetic (all content)>

Fractions>

Multiplying fractions

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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

$\frac{5}{6} \times \frac{5}{7}$ ‍

$= \frac{5 \times 5}{6 \times 7}$ ‍

$= \frac{25}{42}$ ‍

Example 2: Mixed numbers

Before multiplying, we need to write the mixed numbers as improper fractions.

$2 \frac{2}{3} \times 1 \frac{3}{5}$ ‍

$= \frac{8}{3} \times \frac{8}{5}$ ‍ ‍

Here is how we rewrite $2 \frac{2}{3}$ ‍ as $\frac{8}{3}$ ‍ :

$2 \frac{2}{3} = 1 + 1 + \frac{2}{3}$ ‍

$= \frac{3}{3} + \frac{3}{3} + \frac{2}{3}$ ‍

$= \frac{3 + 3 + 2}{3}$ ‍

$= \frac{8}{3}$ ‍

Here is how we rewrite $1 \frac{3}{5}$ ‍ as $\frac{8}{5}$ ‍ :

$1 \frac{3}{5} = 1 + \frac{3}{5}$ ‍

$= \frac{5}{5} + \frac{3}{5}$ ‍

$= \frac{5 + 3}{5}$ ‍

$= \frac{8}{5}$ ‍

$= \frac{8 \times 8}{3 \times 5}$ ‍

$= \frac{64}{15}$ ‍

We can also write this as $4 \frac{4}{15}$ ‍ .

Want to learn more about multiplying fractions? Check out this video.

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

$\frac{3}{10} \times \frac{1}{6}$ ‍

$= \frac{3 \times 1}{10 \times 6}$ ‍

$= \frac{\overset{1}{3} \times 1}{10 \times \underset{2}{6}}$ ‍

Instead of simplifying our answer at the end, we can divide the numerator and denominator by a common factor before multiplying. This makes multiplying easier!

We can divide the $3$ ‍ in the numerator and the $6$ ‍ in the denominator by their common factor of $3$ ‍:

$\frac{\overset{1}{3 \div 3} \times 1}{10 \times \underset{2}{6 \div 3}}$ ‍

$= \frac{1}{20}$ ‍

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

$\frac{5}{8} \times \frac{7}{8}$ ‍

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

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🐼 Nylah🐼
7 years agoPosted 7 years ago. Direct link to 🐼 Nylah🐼's post “How do you do Cross redus...”
How do you do Cross redusucing?
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(34 votes)
- dave
  4 years agoPosted 4 years ago. Direct link to dave's post “Good explanation here : h...”
  Good explanation here : https://www.youtube.com/watch?v=psWT_2QiAVc
  Button navigates to signup page
  (4 votes)
Blake Mcgill
7 years agoPosted 7 years ago. Direct link to Blake Mcgill's post “how do you multiply negat...”
how do you multiply negative
fractions
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(29 votes)
- Anthony Fritz
  7 years agoPosted 7 years ago. Direct link to Anthony Fritz's post “Multiply the fractions no...”
  $Multiplying fractions review (article) | Khan Academy (8)$
  See Also
  3.3: Multiply 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.)
  Comment on Anthony Fritz's post “Multiply the fractions no...”
  (23 votes)
SG
6 years agoPosted 6 years ago. Direct link to SG's post “Why do you always have to...”
Why do you always have to simplify?
Button navigates to signup page•Comment on SG's post “Why do you always have to...”
(16 votes)
- ckovell
  6 years agoPosted 6 years ago. Direct link to ckovell's post “So the fraction reduced t...”
  $Multiplying fractions review (article) | Khan Academy (12)$
  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.
  Button navigates to signup page
  (12 votes)
Mustafa
6 years agoPosted 6 years ago. Direct link to Mustafa's post “What is GCD? thanks to wh...”
What is GCD? thanks to whoever answers it
Button navigates to signup page•Button navigates to signup page
(11 votes)
- Swift
  a year agoPosted a year ago. Direct link to Swift's post “greatest common denominat...”
  greatest common denominator= GCD
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  (2 votes)
ealphonse1
6 years agoPosted 6 years ago. Direct link to ealphonse1's post “What is the difference be...”
What is the difference between LCD and LCM.
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(8 votes)
- Kalabi
  2 years agoPosted 2 years ago. Direct link to Kalabi's post “The mathematical approach...”
  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.
  Button navigates to signup page
  (1 vote)
daphne_hartman
6 years agoPosted 6 years ago. Direct link to daphne_hartman's post “How do you multiply the s...”
How do you multiply the single number with the mixed number?
Button navigates to signup page•Comment on daphne_hartman's post “How do you multiply the s...”
(5 votes)
- Emma Villescas
  5 years agoPosted 5 years ago. Direct link to Emma Villescas's post “You multiply a single num...”
  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.
  Comment on Emma Villescas's post “You multiply a single num...”
  (6 votes)
emily_prickett
6 years agoPosted 6 years ago. Direct link to emily_prickett's post “how do you get the top nu...”
how do you get the top number on the top like 3 times 2 2/5 how do you get 7 1/5
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(10 votes)
Mae Niemie
6 years agoPosted 6 years ago. Direct link to Mae Niemie's post “In the Multiplying Fracti...”
In the Multiplying Fractions Review, why is 5/6 x 5/7 clumped together as 5 x 5 with a single line below both and then 6 x 7 also brought together. It seems like an unnecessary step or is there a special meaning to doing this?
Button navigates to signup page•Comment on Mae Niemie's post “In the Multiplying Fracti...”
(5 votes)
- Kim Seidel
  6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “It's just a reminder that...”
  $Multiplying fractions review (article) | Khan Academy (27)$
  It's just a reminder that when multiplying fractions, we multiply numerator to numerator and denominator to denominator.
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  (14 votes)
Nathalie Figueroa
5 years agoPosted 5 years ago. Direct link to Nathalie Figueroa's post “same what's a LCD? can yo...”
same what's a LCD? can you comment it pls or explan it better.
Button navigates to signup page•Comment on Nathalie Figueroa's post “same what's a LCD? can yo...”
(5 votes)
- Jae Chung
  4 years agoPosted 4 years ago. Direct link to Jae Chung's post “If LCD means least common...”
  If LCD means least common denominator. What does LCM mean?
  Comment on Jae Chung's post “If LCD means least common...”
  (1 vote)
Lauren
6 years agoPosted 6 years ago. Direct link to Lauren's post “I'm realy confused when i...”
I'm realy confused when it comes to math in general.
Button navigates to signup page•Comment on Lauren's post “I'm realy confused when i...”
(5 votes)

Multiplying fractions review (article) | Khan Academy (2024)

Course: Arithmetic (all content)>Unit 5

Multiplying fractions

Cross-reducing

Practice

Want to join the conversation?

References