Subtraction of Fractions - Examples, Exercises and Solutions

Understanding Subtraction of Fractions

Complete explanation with examples

To subtract fractions, we must find the common denominator by simplifying, expanding, or multiplying the denominators.
Then, we only need to subtract the numerators to get the result.

Detailed explanation

Practice Subtraction of Fractions

Test your knowledge with 30 quizzes

Solve the following exercise:

\( \frac{5}{7}-\frac{3}{7}=\text{?} \)

Examples with solutions for Subtraction of Fractions

Step-by-step solutions included
Exercise #1

Solve the following exercise:

3919=? \frac{3}{9}-\frac{1}{9}=\text{?}

Step-by-Step Solution

To solve this problem, we'll subtract two fractions with a common denominator. Here is the step-by-step process:

  • Step 1: Identify the numerators: The numbers on top of the fractions are 3 and 1.
  • Step 2: Subtract the numerators: Calculate 31=23 - 1 = 2.
  • Step 3: Retain the common denominator: Since the two fractions have the same denominator, 9, retain this in the result.

Thus, the result of subtracting 19\frac{1}{9} from 39\frac{3}{9} is 29\frac{2}{9}.

Therefore, the solution to the problem is 29\frac{2}{9}.

Answer:

29 \frac{2}{9}

Video Solution
Exercise #2

Solve the following exercise:

3525=? \frac{3}{5}-\frac{2}{5}=\text{?}

Step-by-Step Solution

Let's solve the subtraction of two fractions:

Step 1: Identify the fractions given:
The fractions are 35\frac{3}{5} and 25\frac{2}{5}, both having a common denominator of 5.

Step 2: Subtract the numerators while keeping the denominator the same:
The numerator result is 32=13 - 2 = 1.

Step 3: Retain the common denominator:
Thus, the result of the subtraction is 15\frac{1}{5}.

Therefore, the solution to the problem is 15\frac{1}{5}.

Answer:

15 \frac{1}{5}

Video Solution
Exercise #3

Solve the following exercise:

3313=? \frac{3}{3}-\frac{1}{3}=\text{?}

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Identify and understand the problem
  • Step 2: Analyze the structure of the fractions involved
  • Step 3: Perform subtraction of like fractions

Now, let's work through each step:

Step 1: The problem asks us to subtract two fractions: 33 \frac{3}{3} and 13 \frac{1}{3} . These fractions have the same denominator, which means they are "like" fractions.

Step 2: In subtraction of fractions with like denominators, we only need to subtract the numerators while keeping the denominator the same. Let's set up the expression:

3313 \frac{3}{3} - \frac{1}{3}

Step 3: Subtract the numerators:

31=2 3 - 1 = 2

So, the result of the subtraction is 23 \frac{2}{3} .

Therefore, the solution to the problem is 23 \frac{2}{3} .

Answer:

23 \frac{2}{3}

Video Solution
Exercise #4

Solve the following exercise:

6545=? \frac{6}{5}-\frac{4}{5}=\text{?}

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Verify that both fractions have the same denominator, which they do here — 5.
  • Step 2: Subtract the numerators while keeping the denominator the same.
  • Step 3: The numerators for each fraction are 6 and 4, so we calculate 64=2 6 - 4 = 2 .
  • Step 4: Write the result as a fraction, keeping the original denominator: 25\frac{2}{5}.

Therefore, the solution to the problem is 25\frac{2}{5}.

Answer:

25 \frac{2}{5}

Video Solution
Exercise #5

Solve the following exercise:

2414=? \frac{2}{4}-\frac{1}{4}=\text{?}

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given fractions and their denominators.
  • Step 2: Use the subtraction formula for fractions with like denominators.
  • Step 3: Calculate the result by subtracting the numerators and keeping the denominator constant.

Let's proceed with these steps:
Step 1: We are given the fractions 24\frac{2}{4} and 14\frac{1}{4}. Both fractions have a denominator of 4.
Step 2: Since the denominators are the same, we apply the formula for subtracting fractions: abcb=acb\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}.
Step 3: Subtract the numerators: 21=12 - 1 = 1. Keep the denominator 4 unchanged. Therefore, 2414=14\frac{2}{4} - \frac{1}{4} = \frac{1}{4}.

Thus, the solution to the problem is 14\frac{1}{4}.

Answer:

14 \frac{1}{4}

Video Solution

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