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# Mixed Numbers

A mixed number is expressed as the sum of a whole number and a fraction (ex. $5\frac{1}{3}$ ). Mixed numbers give a good idea of the size of a number. But when it comes to making calculations, improper fractions are usually easier to work with. If you encounter a mixed number, you'll want to know how to convert it into an improper fraction, and vice versa. Let's go over these steps.

## Writing a mixed number as an improper fraction

Improper fractions are alternate expressions of mixed numbers. For example, the mixed number $2\frac{4}{5}$ can also be written as $\frac{14}{5}$ . But what steps should you take to turn a mixed number into an improper fraction? Let's find out.

Write the mixed number $3\frac{1}{4}$ as an improper fraction.

First, we'll write the mixed number as a sum of a whole number and a proper fraction:

$3+\frac{1}{4}$

Then, we'll write the two parts with a common denominator.

$\frac{12}{4}+\frac{1}{4}$

$\frac{12}{4}+\frac{1}{4}=\frac{13}{4}$

$\frac{13}{4}$ is the improper fraction equivalent of $3\frac{1}{4}$ .

## Writing a mixed number as an improper fraction using the shortcut method

Now that you've learned how to write a mixed number as an improper fraction, let's go over the shortcut method, which can give you the same answer much faster.

Write $3\frac{1}{4}$ as an improper fraction.

First, multiply the whole part by the denominator of the fractional part.

$3×4=12$

Next, add the numerator of the fractional part. This is the numerator of the improper fraction.

$12+1=13$

Another way to find the numerator is to write the following: $3\left(4\right)+1=13$ .

Keep the same denominator, 4, and you have the improper fraction $\frac{13}{4}$ .

## Writing an improper fraction as a mixed number

Now, let's try writing the improper fraction $\frac{27}{5}$ as a mixed number.

First, divide the numerator by the denominator.

$27÷5=5R2$

We have a quotient of 5, and a remainder of 2.

We'll use the quotient as the whole part of the mixed number and the remainder as the numerator of the fractional part. Keep the denominator the same.

$\frac{27}{5}=\frac{25}{5}+\frac{2}{5}=5\frac{2}{5}$

## Practice questions on mixed numbers

a. Write $5\frac{5}{6}$ as an improper fraction.

$5+\frac{5}{6}=\frac{30}{6}+\frac{5}{6}$

Answer: $\frac{35}{6}$

b. Write $7\frac{1}{8}$ as an improper fraction.

$7+\frac{1}{8}=\frac{56}{8}+\frac{1}{8}$

Answer: $\frac{57}{8}$

c. Write $2\frac{6}{7}$ as an improper fraction using the shortcut method.

Numerator: $2\left(7\right)+6=20$ . Denominator: 7.

Answer: $\frac{20}{7}$

d. Write $\frac{14}{3}$ as a mixed number.

To write $\frac{14}{3}$ as a mixed number, we perform the division:

$14÷3=4R2$

The quotient is 4 and the remainder is 2. The denominator remains as 3.

So, $\frac{14}{3}$ can be expressed as the sum of the whole number quotient and the fraction with the same denominator:

$\frac{14}{3}=\frac{12}{3}+\frac{2}{3}$

Therefore, the answer is $4\frac{2}{3}$ .

e. Write $\frac{47}{7}$ as a mixed number.

$47÷7=6R5$

Quotient: 6. Remainder: 5. Denominator: 7.

$\frac{47}{7}=\frac{42}{7}+\frac{5}{7}$

Answer: $6\frac{5}{7}$

## Get a better understanding of mixed numbers

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