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# Subtracting Fractions

In mathematics, a fraction is a portion of a quantity out of the whole. The whole quantity can be any number, special value, or item. We can perform different arithmetic operations on fractions such as addition, subtraction, multiplication, and division.

A fraction consists of two parts-the numerator and the denominator. The upper part of the fraction is called the numerator and the lower part of the fraction is called the denominator. For example, $\frac{4}{9}$ is a fraction. Here, 4 is the numerator and 9 is the denominator. Based on the numerator and denominator, there are different types of fractions including proper fractions, improper fractions, mixed fractions, and more.

## What is meant by subtracting fractions?

Subtracting fractions means the process of subtraction of two fractional values. We have learned to subtract whole numbers. For example, the subtraction of 2 from 7 results in 5. We can also perform subtraction operations on fractions. We can:

• Subtract fractions with like denominators
• Subtract fractions with unlike denominators
• Subtract mixed fractions
• Subtract fractions with whole numbers

## Subtracting fractions with like denominators

To subtract fractions with like denominators, keep the denominators as they are, subtract the numerators, and write the difference over the denominator. If necessary, simplify the resulting fraction.

$\frac{5}{7}-\frac{4}{7}=\frac{1}{7}$

Example 1

Find $\frac{4}{5}-\frac{2}{5}$

Since the denominators are the same, subtract the numerators.

$=\frac{4-2}{5}$

$=\frac{2}{5}$

You may not get an answer that is in lowest terms, even if the fractions you were subtracting were. In that case, you must reduce the fraction.

Example 2

$\frac{8}{9}-\frac{2}{9}=\frac{6}{9}$

$=\frac{6÷3}{9÷3}$

$=\frac{2}{3}$

## Subtracting fractions with unlike denominators

If the denominators are not the same in the fractions you are subtracting, then you must use equivalent fractions that do have a common denominator. To do this, you have to find the least common multiple (LCM) of the two denominators.

To subtract fractions with unlike denominators, rename the fractions with a common denominator. Then subtract and simplify.

Example 3

For example, suppose you want to subtract

$\frac{6}{7}-\frac{2}{3}$

The LCM of 3 and 7 is 21. So we need to find fractions equivalent to $\frac{6}{7}$ and $\frac{2}{3}$ that have 21 in the denominator. To do this, you multiply the numerator and denominator of $\frac{6}{7}$ by 3 and multiply the numerator and denominator of $\frac{2}{3}$ by 7.

$\frac{6×3}{7×3}-\frac{2×7}{3×7}=\frac{18}{21}-\frac{14}{21}$

Now that we have like denominators, we can subtract as described above.

$\frac{18}{21}-\frac{14}{21}=\frac{4}{21}$

## Subtracting mixed fractions

While subtracting mixed fractions, use the following steps.

• Convert mixed fractions into improper fractions.
• Check the denominator values. If the fractions have like denominators, follow the instructions for subtracting fractions with like denominators. If the fractions have unlike denominators, follow the instructions for subtracting fractions with unlike denominators.
• Simplify, converting back into a mixed number if applicable.

Example 4

Subtract $8\frac{5}{6}$ from $15\frac{3}{4}$ .

Convert mixed fractions into improper fractions.

$\frac{63}{4}-\frac{53}{6}$

Next, find the LCM of 4 and 6, which is 12, and make the denominators equal.

$\frac{189}{12}-\frac{106}{12}=\frac{83}{12}$

Convert back to a mixed number.

$6\frac{11}{12}$

So $15\frac{3}{4}-8\frac{5}{6}=6\frac{11}{12}$

## Subtracting fractions with whole numbers

Follow these steps while subtracting fractions with whole numbers.

1. Convert the whole number into the fractional form. For example, 3 is a whole number, so you would convert it to 3/1.
2. Follow the procedure of subtracting fractions with unlike denominators.
3. Simplify the fraction if required.

Example 5

Subtract $2-\frac{1}{2}$ .

Convert the number 2 into the fractional form.

$\frac{2}{1}-\frac{1}{2}$

Find the LCM of 1 and 2, which is 2. Do the necessary multiplication of numerators to get

$\frac{4}{2}-\frac{1}{2}=\frac{3}{2}$

Simplify.

$1\frac{1}{2}=\frac{3}{2}$

So $2-\frac{1}{2}=1\frac{1}{2}$ .

## Get help learning about subtracting fractions

Subtracting fractions can get confusing because of the different behaviors of the numerators and denominators. If your student is having a hard time subtracting fractions, have them meet with a math tutor who can help them understand how and why the steps work. With the 1-on-1 attention a tutor provides, your student can quickly gain a thorough understanding of how to subtract fractions without distractions. Contact the Educational Directors at Varsity Tutors today to learn more about how working with a tutor can benefit your student.

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