Table of Contents

## What Are Whole Numbers?

solid numbers are the plant of numbers that includes all natural numbers along with 0. For exemplar, 10, 18, 200, etc .

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## What Is a Fraction?

Fractions are frequently referred to as a number between numbers. Fractions are numeric values that represent a part or a share of a whole. For exemplar, search at the pizza below .

This pizza has been cut into 4 peer parts. sol each slice of the pizza represents 1 out of 4 equal parts. indeed, mathematically, we can represent each part as $ \frac { 1 } { 4 } $. This phone number is called a divide.

In general, when a whole is divided into adequate parts, each part represents a fraction of the whole and we write fractions as $ \frac { a } { bel } $, where a and b are very numbers and b can not be zero .

The number below the cake, which represents the full number of equal parts that the whole is divided into, is called the denominator. And the total on the top, which represents the number of peer parts we are considering, is called the numerator .

## Multiplying Fractions with Whole Numbers

Multiplying two numbers is the same as repeat addition. For example,

2 times 4 or $ 2 \times 4 $ is the same as adding the issue “ 4 ” 2 times .

so, multiplying fractions with unharmed numbers is the like as perennial accession, where we add the fraction the same number of times as the solid number .

For exemplar : Let ’ s try on multiplying 3 and $ \frac { 1 } { 4 } $ .

3 times $ \frac { 1 } { 4 } $ means adding the fraction $ \frac { 1 } { 4 } 3 $ times.

algebraically this means ,

We can solve this formula visually ,

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And our answer will be :

But nowadays, let ’ s see how we can generalize this without having to make a model every time we want to multiply a unharmed act and a divide .

## Multiplying Fractions with Whole Numbers

Let ’ s do this with the aid of an example ,

Let ’ s multiply 5 and $ \frac { 3 } { 4 } $ .

step 1 : change 5 into its divide form by applying 1 in the denominator .

step 2 : Multiply the numerator with the numerator and the denominator with the denominator .

And voila, we have our answer.

As an extra tone, if you get an improper fraction you can convert this into a mix number .

## Multiplying Mixed Fractions with Whole Numbers

Multiplying interracial numbers and whole numbers follows the lapp procedure, only with an supernumerary pace .

Let ’ s do this with the aid of an model .

How do we multiply 3 and $ 2\frac { 1 } { 5 } $ ?

step 1 : Convert the mix phone number into an improper divide .

step 2 : convert 3 into its divide form by applying 1 in the denominator .

step 2 : Multiply the numerator with the numerator and the denominator with the denominator .

And after converting this into an improper fraction ,

We have our answer :

## Solved Examples

**Example 1: ** **Catherine is making a cake, for which she needs to use three-fourths of a cup of butter. If she decides to make three cakes, what would be the amount of butter required?**

**Solution** :

Number of cakes $ = 3 $

butter required for 1 cake $ = \frac { 3 } { 4 } $ ** ** cup

full sum of butter required $ = 3 \times { 3 } { 4 } = \frac { 9 } { 4 } = 2\frac { 1 } { 4 } $ cups

**Example 2: Find the product of the whole number 10 and the mixed fraction ** 523. **Solution** : $ 10\times 5\frac { 2 } { 3 } = 10 \times \frac { 17 } { 3 } = \frac { 170 } { 3 } = 56\frac { 2 } { 3 } $

## Practice Problems

## Multiplying Fraction With Whole Numbers

Attend this quiz & Test your cognition.

1

### In a party, each person drink $\frac{3}{5}$$l$ of the juice. If you invite 15 people to your party, how much juice will you need?

$ 8 $ $ liter $ $ 10 $ $ fifty $ $ 9 $ $ fifty $ $ 15 $ $ fifty $

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Correct

Incorrect

Correct answer is: $9$$l$

Quantity of juice required $= 15 \times \frac{3}{5} = \frac{45}{5} = $$9$$l$

2

### Clove cycles $\frac{1}{4}$ miles every day. How much will she cycle in 10 days?

$ 2\frac { 2 } { 4 } $ miles $ \frac { 2 } { 5 } $ miles $ 2 $ miles $ 1\frac { 1 } { 4 } $ miles

Correct

Incorrect

Correct answer is: $2\frac{2}{4}$ miles

Distance traveled in 10 days $= 10 \times$ distance traveled in one day

$= 10 \times \frac{1}{4} = \frac{10}{4} = 2\frac{2}{4}$ miles

3

### Jane purchased 20 apples at the store, out of which $\frac{1}{5}$ of the apples were rotten. How many apples were rotten?

5 10 2 4

Correct

Incorrect

Correct answer is: 4

Total numbers of apples $= 20$

Fraction of apples rotten $= \frac{1}{5}$

Number of apples rotten $= 20 \times \frac{1}{5} = \frac{20}{5} = 4 apples

## Frequently Asked Questions

**How do we multiply a fraction by a whole number using a number line?**

We first mark the divide on the number line and then, in order to multiply it with a whole number, we add on the like fraction as many times as the multiplication requires it .

**What is the product of multiplying a whole number and a mixed fraction?**

The product of multiplying a whole number and a shuffle divide can be a shuffle fraction, improper divide, proper fraction or a solid numeral .

**Which whole number gives the same product as the original fraction?**

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The act “ 1 ”, when multiplied by any fraction, gives the like fraction as the solution. For exemplar, $ 1 \times \frac { 3 } { 5 } = \frac { 3 } { 5 } $ .