# Multiplying Fractions & Mixed Numbers

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Multiplying Fractions & Mixed Numbers
5.NF.B.6

Multiplying Fractions & Mixed Numbers
6 2 3 8 3 2 = 2 3 3 5 24 15 2 × = Here is 2-2/3 x 3/5. To find the product, we need to multiply a mixed number by a fraction. To solve this problem, we first need to convert the mixed number to an improper fraction. Let’s write the mixed number where we can have some space to work with it. There is a denominator of 3 alongside the whole number 2. 3 x 2 = 6. The whole number 2 is equal to 6/3. And, here are 2 more thirds. 6/3 + 2/3 = 8/3 2-2/3 = 8/3 Now, we will multiply this by 3/5. What is 8 x 3? 24 And, what is 3 x 5? 15 8/3 x 3/5 = 24/15 So, 2-2/3 x 3/5 = 24/15. 8 3 3 5 24 × = 15 And, what is 3 x 5? 24 15 8/3 x 3/5 = 24/15 What is 8 x 3? So, 2-2/3 x 3/5 = 24/15. To find the product, we need to multiply a mixed number by a fraction. Let’s write the mixed number where we can have some space to work with it. To solve this problem, we first need to convert the mixed number to an improper fraction. Here is 2-2/3 x 3/5. There is a denominator of 3 alongside the whole number 2. 3 x 2 = 6. The whole number 2 is equal to 6/3. 2-2/3 = 8/3 6/3 + 2/3 = 8/3 And, here are 2 more thirds. Now, we will multiply this by 3/5.

8 40 4 5 44 5 = Multiplying Fractions & Mixed Numbers 44/5 5 x 8 = ?
Before we continue multiplying, let’s convert some more mixed numbers to improper fractions. Here is 8 and 4/5. 5 x 8 = ? 40. That means the whole number 8 is equal to 40/5. Here are 4 more fifths. 40/5 + 4/5 = ? 44/5 44/5 5 x 8 = ? 40. That means the whole number 8 is equal to 40/5. Before we continue multiplying, let’s convert some more mixed numbers to improper fractions. Here are 4 more fifths. 40/5 + 4/5 = ? Here is 8 and 4/5.

7 63 5 9 68 9 = Multiplying Fractions & Mixed Numbers 68/9 9 x 7 = ?
Here is 7 and 5/9. 9 x 7 = ? 63. That means the whole number 7 is equal to 63/9. Here are 5 more ninths. 63/9 + 5/9 = ? 68/9 68/9 9 x 7 = ? Here are 5 more ninths. 63. That means the whole number 7 is equal to 63/9. 63/9 + 5/9 = ? Here is 7 and 5/9.

2 8 3 4 11 4 = Multiplying Fractions & Mixed Numbers 11/4 4 x 2 = ?
Here is 2 and 3/4. 4 x 2 = ? 8. That means the whole number 2 is equal to 8/4. Here are 3 more fourths. 8/4 + 3/4 = ? 11/4 11/4 4 x 2 = ? Here are 3 more fourths. 8. That means the whole number 2 is equal to 8/4. 8/4 + 3/4 = ? Here is 2 and 3/4.

Multiplying Fractions & Mixed Numbers
Lightning Round

Convert the mixed number to an improper fraction.
Multiplying Fractions & Mixed Numbers Convert the mixed number to an improper fraction. 2 3 17 3 5 =

Convert the mixed number to an improper fraction.
Multiplying Fractions & Mixed Numbers Convert the mixed number to an improper fraction. 1 2 9 2 4 =

Convert the mixed number to an improper fraction.
Multiplying Fractions & Mixed Numbers Convert the mixed number to an improper fraction. 3 7 59 7 8 =

Convert the mixed number to an improper fraction.
Multiplying Fractions & Mixed Numbers Convert the mixed number to an improper fraction. 3 4 27 4 6 =

Multiplying Fractions & Mixed Numbers
9 2 3 11 3 3 = 2 3 7 8 77 24 3 × = Now, let’s multiply again. Here is 3-2/3 x 7/8. To find the product, we need to multiply a mixed number by a fraction. To solve this problem, we first need to convert the mixed number to an improper fraction. Let’s write the mixed number where we can have some space to work with it. 3 x 3 = ? 9. The whole number 3 is equal to 9/3. Add 2 more thirds ... … to get 11/3. 3-2/3 = 11/3 Now, we will multiply this by 7/8. What is 11 x 7? 77 And, what is 3 x 8? 24 11/3 x 7/8 = 77/24 So, 3-2/3 x 7/8 = 77/24. 11 3 7 8 77 × = 24 24 And, what is 3 x 8? 11/3 x 7/8 = 77/24 So, 3-2/3 x 7/8 = 77/24. 9. The whole number 3 is equal to 9/3. 77 To find the product, we need to multiply a mixed number by a fraction. Let’s write the mixed number where we can have some space to work with it. To solve this problem, we first need to convert the mixed number to an improper fraction. Now, let’s multiply again. Here is 3-2/3 x 7/8. 3 x 3 = ? Add 2 more thirds ... Now, we will multiply this by 7/8. 3-2/3 = 11/3 … to get 11/3. What is 11 x 7?

Multiplying Fractions & Mixed Numbers
28 2 7 30 7 4 = 4 5 2 7 120 35 4 × = Here is 4/5 x 4-2/7. Let’s convert the mixed number to an improper fraction. Here is 4 and 2/7. 7 x 4 = ? 28. The whole number 4 is equal to 28/7. Add 2 more sevenths ... … to get 30/7. 4-2/7 = 30/7 And, that is what we will multiply by 4/5. What is 4 x 30? 120 And, what is 5 x 7? 35 4/5 x 30/7 = 120/35 So, 4/5 x 4-2/7 = 120/35. 4 5 30 7 120 × = 35 35 4/5 x 30/7 = 120/35 And, what is 5 x 7? 28. The whole number 4 is equal to 28/7. So, 4/5 x 4-2/7 = 120/35. Let’s convert the mixed number to an improper fraction. 7 x 4 = ? Here is 4 and 2/7. Here is 4/5 x 4-2/7. Add 2 more sevenths ... … to get 30/7. What is 4 x 30? And, that is what we will multiply by 4/5. 4-2/7 = 30/7 120

Multiplying Fractions & Mixed Numbers
45 8 9 53 9 5 = 1 8 8 9 53 72 5 × = Here is 1/8 x 5-8/9. Let’s convert the mixed number to an improper fraction. Here is 5 and 8/9. 9 x 5 = ? 45. The whole number 5 is equal to 45/9. Add 8 more ninths ... … to get 53/9. 5-8/9 = 53/9 Now, we will multiply this by 1/8. What is 1 x 53? 53 And, what is 8 x 9? 72 1/8 x 53/9 = 53/72 So, 1/8 x 5-8/9 = 53/72. 1 8 53 9 53 × = 72 72 1/8 x 53/9 = 53/72 And, what is 8 x 9? 45. The whole number 5 is equal to 45/9. So, 1/8 x 5-8/9 = 53/72. Let’s convert the mixed number to an improper fraction. 9 x 5 = ? Here is 5 and 8/9. Here is 1/8 x 5-8/9. Add 8 more ninths ... … to get 53/9. What is 1 x 53? Now, we will multiply this by 1/8. 5-8/9 = 53/9 53

Multiplying Fractions & Mixed Numbers
Closing Question

Multiplying Fractions & Mixed Numbers
18 2 3 20 3 6 = 2 3 2 7 40 21 6 × = Here is 6-2/3 x 2/7. Let’s convert the mixed number to an improper fraction. Here is 6 and 2/3. 3 x 6 = ? 18. 6 is equal to 18/3. Add 2 more thirds ... … to get 20/3. 6-2/3 = 20/3 Now, we will multiply this by 2/7. What is 20 x 2? 40 And, what is 3 x 7? 21 20/3 x 2/7 = 40/21 So, 6-2/3 x 2/7 = 40/21. 20 3 2 7 40 × = 21 21 And, what is 3 x 7? 20/3 x 2/7 = 40/21 So, 6-2/3 x 2/7 = 40/21. 18. 6 is equal to 18/3. 40 Here is 6-2/3 x 2/7. 3 x 6 = ? Here is 6 and 2/3. Let’s convert the mixed number to an improper fraction. Add 2 more thirds ... … to get 20/3. Now, we will multiply this by 2/7. 6-2/3 = 20/3 What is 20 x 2?