Multiply Mixed Numbers

How Can You Find the Product Question of Mixed Numbers? 

Multiplying mixed numbers is similar to multiplying fractions.  

• When we see a mixed fraction, we may be confused as to how we can multiply the mixed number by a whole number, fraction, or mixed number. 
•  When you add or subtract mixed fractions, we separate the whole number from the fraction.  
• We treat both parts as two separate things. When we multiply fractions, we do not do this. The whole number and fraction become an improper fraction. 
• An improper fraction is a fraction where the numerator is bigger than the denominator. 
• An example of an improper fraction: 15/2    
• 15/2 improper fraction into mixed fraction = Quotient Remainder/Divisor = 7 1/2  

 You can change a mixed number to an improper fraction by following these steps: 

7 1/2 = 2 X 7+1/2 = 14+1/2 = 15/2

Multiplying fractions 

• Unlike addition and subtraction, where the denominators have to match, when we multiply fractions we do not need to change the initial values. 
• To understand how to multiply fractions you should already have a basic  
• understanding of what a fraction looks like. You need to know that the top number is called the numerator while the bottom number is called the denominator.  
• To multiply the fractions together you will be multiplying the numerators together and the denominators together to get the correct answer. 

The steps to multiplying fractions are as follows: 

1. Multiply the numerators. 
2. Multiply the denominators. 
3. Check to make sure the fraction is in lowest terms. 

Multiplying mixed numbers and fractions follows these steps: 

1. Convert all mixed numbers or whole numbers to improper fractions. 
2. Multiply the numerators. 
3. Multiply the denominators. 
4. Reduce your answer and convert back to a mixed number, if necessary. 
5. When you have a whole number, and want to change it to a fraction, write the whole number as the numerator and a 1 as the denominator. 
6. For example, 5 as an improper fraction is written as ⁵⁄₁. All whole numbers have 1 as a denominator when changed into a fraction. 
7. Use the diagram below to help you visualize what the question is asking. If the puppy walks 2½ miles each day and repeats that for 5 days, we have 5 equal groups of 2½. 

Example:

The new puppy walks 2½ miles a day. If he walks 5 days a week, how far does the puppy walk in 5 days? 

Solution: 

Use the diagram below to help you visualize what the question is asking. If the puppy walks 2½ miles each day and repeats that for 5 days, we have 5 equal groups of 2½. 

Since multiplication is repeated addition, instead of adding the mixed numbers, you want to multiply them. 

5 X 2 1/2

Step 1: Convert all mixed numbers or whole numbers to improper fractions. 

5/1 X 5/2

Step 2: Multiply the numerators. 

25/?

Step 3: Multiply the denominators.  

25/2

Step 4: Reduce your answer and convert back to a mixed number, if necessary.  

Divide 25 by 2 and you get 12½. The puppy walked a total of 12½ miles in 5 days. 

Multiply two mixed fractions by models 

Example 2 : A clothing factory has machines that make jackets .The machines operate for 7 1/2 hours a day. How many jackets can the machine A make in one day? 

Solution: 

One way 

14 + 1 + 5 1/4 + 3/8 = 14 + 1 + 5 2/8 + 3/8

=15 + 5 5/8

= 20 5/8

Another way: 

You can also use an equation to find the product . Rename the mixed, then multiply. 

7 1/2 x 2

3/4 = 15/2 x 11/4

= 165/8

= 20 5/8

∴Machine A can make 20 jackets each day. 

Example 3:  

A rectangular field of crops is 4 2/3 by 2 3/4 miles. Calculate 4 2/3 x 2 3/4 to find the area.? 

Solution: 

Estimate 4 2/3 x 2 3/4 is about 5 x 3 = 15 

Use an area model to find the partial products . 

Add partial products . 

8 + 1 1/3 + 3 + 1/2 = 8 + 1 2/6+ 3 + 3/6  

= 8+ 3+ 1 2/6 + 3/6 

= 12 5/6

So, 4 2/3 x  2 3/4 = 12 5/6

The area of the field is 12 5/6 square miles . The product is close to the estimate of 15, 

So the answer is reasonable. 

Practice

1. Find the value of 2 𝟏/𝟔 x 4 𝟏/𝟐. 

Solution: 

2 1/6 x 4 1/2 is about 2 times 4. so , the answer should be about 8. 

2 1/6 x 4 1/2 = 13/6 x 9/2

= 117/12

= 9 9/12

Since 8 is close to estimate of 9, the answer is reasonable  

∴ 2 1/6 x 4 1/2 = 9 9/12

2. Find the value of 418𝟏𝟖 x 512𝟏𝟐. 

Solution: 

4 1/8 x 5 1/2 is about 4 times 5 .so the answer should be about 20 . 

4 1/8 x 5 1/2 = 33/8 x 11/2

= 33×11/8×2

= 363/16

= 363/16

= 22 11/16

Since 20 is close to estimate of 22, the answer is reasonable.  

3. Find the value of (𝟏/𝟔 + 2 𝟐/𝟑) x (𝟏/𝟒 – 𝟏/𝟐). 

Solution: 

First change all the mixed fraction into improper fractions 

(1/6 + 2 2/3) x (1/4 – 1/2) = (1/6 + 8/3) x (1/4 + 1/2) 

= (1×1 + 8×2/6) x (1×1 + 1×2/4) 

= (1+16/6) x (1+2/4) 

= 17/6 x 3/4

= 51/24

= 17/8

∴(1/6 + 2 2/3) x (1/4 + 1/2) = 17/8 = 2 1/8

4. Find the value of (2 𝟒/𝟗 + 𝟏/𝟑) x (1 𝟏/𝟒 – 𝟏/𝟖). 

Solution: 

First change all the mixed fractions into improper fractions 

(2 4/9 + 1/3) x (1 1/4 – 1/8) = (22/9 + 1/3) x (5/4 . 1/8) 

= (22×1 +1×3/9) x (5×2 −1×1/8) 

= (22+3/9) x (10 −1/8)  

= 25/9 x 9/8

= 25/8

∴ (2 4/9 + 1/3) x (1 1/4 – 1/8) = 25/8 = 3 1/8

5. Find the value of (178𝟕𝟖 + 212𝟏𝟐) x (115𝟏𝟓 – 110𝟏𝟏𝟎). 

Solution: 

First change all the mixed fractions into improper fractions 

(1 7/8 + 2 1/2) x (1 1/5 – 1/10) = (15/8 + 5/2) x (6/5 – 1/10) 

= (15×1 + 5×4/8) x (6×2 −1×1/10) 

= (15+20/8) x (12 −1/10) 

= (25/8) x (11/10) 

= 275/80 = 55/16
∴ (1 7/8 + 2 1/2) x (1 1/5 – 1/10) = 55/16 = 3 7/16

6. The world’s smallest gecko is 𝟑/𝟒 inch long. An adult male Western Banded Gecko is 7 𝟏/𝟑  times as long. How long is a Western Banded Gecko? 

Solution: 

Given that, 

Size of smallest Gecko= 3/4 inch long 

Size of male western banded gecko = 7 1/3 times the Size of smallest Gecko 

Then , 

Size of male western banded gecko = 7 1/3 x 3/4

= 22/3 x 3/4

= 22×3/3 x 4

= 66/12 = 22/4

∴Size of male western banded gecko = 22/4 = 5 1/2

7. How can you use multiplication to find 3 𝟑/𝟓 + 3 𝟑/𝟓 + 3 𝟑/𝟓 . 

We know that, 

Repeated addition is called multiplication. 

3 3/5 + 3 3/5 + 3 3/5 = 3 x 3 3/5

= 3 x 18/5

= 54/5

=10 4/5

∴ 3 3/5 + 3 3/5 + 3 3/5

= 10 4/5