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# Subtracting Fractions Word Problems

## Introduction to Subtracting Fractions

Last updated date: 24th Mar 2023
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Subtraction of fractions is an arithmetic operation to find the difference between two fractions. To subtract two like fractions, we have to subtract their numerators and write the difference over the common denominator. To subtract two unlike fractions, we must first convert them into like fractions by taking the LCM of the denominators. We can also subtract a whole number and fraction by writing the whole number in fractional form, for example, $3 = \dfrac{3}{1}$. Let us learn more about subtracting fractions and fraction subtraction problems in detail in this article.

## How to Subtract Fractions?

Fractions are referred to as a part of a whole. A group of fractions can be classified as like fractions and unlike fractions based on the denominator value. Like fractions are those that have the same denominator. For example, $\dfrac{3}{4}$ and $\dfrac{5}{4}$. While unlike fractions are those that have different denominators, for example, $\dfrac{2}{3}$ and $\dfrac{4}{7}$. We can find the difference between two like fractions, unlike fractions and fractions and whole numbers.

The steps for subtracting fractions are listed below:

Step 1: Identify whether the given fractions have the same denominator or different denominators.

Step 2: In the case of like fractions, subtract the numerators and write their difference over the common denominator. For example, $\dfrac{5}{7} - \dfrac{2}{7} = \dfrac{5 - 2}{7} = \dfrac{3}{7}$.

On the other hand, unlike fractions, find the LCM of the denominators.

Step 3: Multiply the numerator and denominator of each fraction with a whole number to get the LCM in the denominator. It is done to convert unlike fractions to like fractions.

Step 4: Subtract their numerators and write the difference over the common denominator.

This is how we subtract two fractions.

## Subtracting Fractions with Like Denominators

Fractions with the same denominator can be easily subtracted. To subtract fractions with the same denominators, follow the given steps:

• Subtract the numerator.

• Write the common denominator as the denominator of the resulting fraction.

• Now, reduce the result to the lowest fraction, if possible.

Example: $\dfrac{4}{5}-\dfrac{2}{5}=\dfrac{2}{5}$

## Subtraction of Fractions with Unlike Denominators

Two fractions with different or unequal denominators can be subtracted by following these steps:

• First, take the LCM of the denominators.

• We convert the given fractions to like fractions with the denominator as the LCM.

• Now, subtract the numerators and write their difference over the common denominator.

• Simplify, if needed.

## Subtracting Fractions with Whole Numbers

Just like you have subtracted two fractions, you can also subtract fractions from whole numbers and vice-versa. Any integer can be written in fractional form by writing 1 as the denominator. For example, 7 can be written as $\dfrac{7}{1}$. Therefore, to subtract fractions and whole numbers, write them in the fractional form first. Then you can easily find the difference using the same rules for subtracting two unequal fractions. Consider the following example of subtracting a fraction from an integer: $2 - \dfrac{1}{4}$

• Convert the integer, 2 to fractional form, i.e. $\dfrac{2}{1}$

• We convert the given fractions to like fractions with the denominator as the LCM.

• Now, subtract the numerators and write their difference over the common denominator.

• Now, to subtract $\dfrac{2}{1} - \dfrac{1}{4}$, the least common multiple of 1 and 4 is 4. Multiply the numerator and denominator of $\dfrac{2}{1}$ by 4 to get 4 in the denominator.

$\dfrac{2}{1} - \dfrac{1}{4}$

= $\dfrac{2 \times 4}{1 \times 4} - \dfrac{1}{4}$

= $\dfrac{8}{4} - \dfrac{1}{4}$

= $\dfrac{7}{4}$

Thus, the subtraction of an integer and fraction, $2 - \dfrac{1}{4} = \dfrac{7}{4}$.

## Solved Word Problems on Fraction Subtraction

Q 1. Jack jumped $4 \dfrac{1}{7}$ m in the long jump competition. Shane jumped $3 \dfrac{2}{9}$ m. Who jumped longer, and how many meters?

Ans: Jack jumped $=4 \dfrac{1}{7} \mathrm{~m}=\dfrac{29}{7} \mathrm{~m}=\dfrac{261}{63} \mathrm{~m}$

Shane jumped $=3 \dfrac{2}{9} \mathrm{~m}=\dfrac{29}{9} \mathrm{~m}=\dfrac{203}{63} \mathrm{~m}$

Because $261>203$, Jack jumped more.

$\text { Difference }=\dfrac{261}{63} \mathrm{~m}-\dfrac{203}{63} \mathrm{~m}$

$=\dfrac{261-203}{63} \mathrm{~m}$

$=\dfrac{58}{63} \mathrm{~m}$

Therefore, Jack jumped $\dfrac{58}{63} \mathrm{~m}$ more than Shane.

Q 2. Mary gave $\dfrac{1}{8}$ part of her money to Shelly. What fraction of money is left with her?

Ans: Money given to Shelly $=\dfrac{1}{8}$

Remaining money $=1-\dfrac{1}{8}$

$=\dfrac{1}{1}-\dfrac{1}{8}$

$=\dfrac{8}{8}-\dfrac{1}{8}$

$=\dfrac{7}{8}$

Thus, the fraction of money left is $=\dfrac{7}{8}$.

## Fraction Subtraction Problems for Practice

Q 1. Sharon spent $4 \dfrac{3}{7}$ hours studying maths and playing tennis. How long did she study if she played tennis for $2 \dfrac{1}{4}$ hours?

Ans: $\dfrac{61}{28}$

Q 2. Rex had some money. He spent $\dfrac{1}{6}$ of it on Monday, $\dfrac{3}{8}$ on Thursday, and $\dfrac{1}{4}$ on Wednesday. What part of the money is still left with him?

Ans: $\dfrac{5}{24}$.

Q 3. Ron used $3 \dfrac{1}{4}$ litres of paint from a tin of $5 \dfrac{1}{2}$, to colour the walls of his room. What fraction of paint is still left in the tin?

Ans: $\dfrac{9}{4}$ litres.

## Summary

In this article, we have learned about fractions. Then we learned about the different rules of how to solve subtracting fractions word problems having like as well as unlike denominators with the help of an example. We became aware of solving, unlike denominators, by taking the help of LCM of the denominators, then multiplying with the numerator and calculating the difference. We also did numerous word problems on fraction subtraction. Kindly solve the given unsolved problems for practice.

## FAQs on Subtracting Fractions Word Problems

1. What are the rules for adding fractions?

The basic rule of adding fractions is to first ensure whether the denominators are the same. If the denominators are different, first convert them to equal fractions by taking LCM and then solve the fractions by the usual addition.

2. How to add Improper Fractions?

Improper fractions are added in the same way as proper fractions. Some steps are given below:

• If the fractions are the same, add the numerator keeping the same denominator.

• To add different fractions, take the lowest common multiple of the denominators, convert them to equivalent fractions, and then add them as equal fractions.

• When the addition is complete, and the answer is an improper fraction, convert the fraction to a mixed one and write it in its simplest form.

3. Why are addition and subtraction important?

Addition and subtraction play a very important role in our daily life activities, which involve counting, such as billing at the store, buying groceries, travelling, the speed of a vehicle, checking weight, and so on. It helps us understand situational-based problems. Hence, addition and subtraction are important in our life.