## 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:

- Multiply the numerators.
- Multiply the denominators.
- Check to make sure the fraction is in lowest terms.

**Multiplying mixed numbers and fractions follows these steps:**

- Convert all mixed numbers or whole numbers to improper fractions.
- Multiply the numerators.
- Multiply the denominators.
- Reduce your answer and convert back to a mixed number, if necessary.
- 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.
- 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. - 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 4**18𝟏𝟖** x 5**12𝟏𝟐**.**

**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 (1**78𝟕𝟖** + 2**12𝟏𝟐**) x (1**15𝟏𝟓** – **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

**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

**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

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