Subtraction of Fractions Practice Problems & Solutions

Master subtracting fractions with different denominators through step-by-step practice problems. Learn common denominator methods and solve mixed exercises.

πŸ“šMaster Fraction Subtraction with Interactive Practice
  • Find common denominators using simplification and multiplication methods
  • Subtract fractions with same denominators by subtracting numerators only
  • Solve problems where one denominator is a multiple of another
  • Apply the cross-multiplication method for different denominators
  • Subtract three or more fractions using sequential common denominators
  • Simplify final answers to lowest terms and mixed numbers

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:

\( \frac{6}{7}-\frac{2}{7}=\text{?} \)

Examples with solutions for Subtraction of Fractions

Step-by-step solutions included
Exercise #1

Solve the following exercise:

85βˆ’45=? \frac{8}{5}-\frac{4}{5}=\text{?}

Step-by-Step Solution

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

  • Step 1: Confirm the fractions have the same denominator. Here, both denominators are 5.
  • Step 2: Subtract the numerators of the fractions: 8βˆ’4 8 - 4 .
  • Step 3: Write the result over the common denominator: 45 \frac{4}{5} .

Now, let's calculate:
Step 1: Both fractions 85 \frac{8}{5} and 45 \frac{4}{5} have a common denominator of 5.
Step 2: Subtract the numerators: 8βˆ’4=4 8 - 4 = 4 .
Step 3: Place the result over the common denominator: 45 \frac{4}{5} .

Therefore, the solution to the problem is 45\mathbf{\frac{4}{5}}.

Answer:

45 \frac{4}{5}

Video Solution
Exercise #2

Solve the following exercise:

75βˆ’45=? \frac{7}{5}-\frac{4}{5}=\text{?}

Step-by-Step Solution

To solve this problem, we'll execute the following steps:

  • Step 1: Identify like denominators.
  • Step 2: Subtract numerators, keeping the common denominator.
  • Step 3: Simplify if necessary.

Let's work through the solution:

Step 1: Both fractions, 75\frac{7}{5} and 45\frac{4}{5}, have the same denominator of 5.

Step 2: Subtract the numerators: 7βˆ’4=37 - 4 = 3.

Step 3: The result is 35\frac{3}{5}, with no further simplification necessary.

The correct solution to the given subtraction problem is 35\frac{3}{5}.

Answer:

35 \frac{3}{5}

Video Solution
Exercise #3

Solve the following exercise:

33βˆ’13=? \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:

33βˆ’13 \frac{3}{3} - \frac{1}{3}

Step 3: Subtract the numerators:

3βˆ’1=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:

46βˆ’36=? \frac{4}{6}-\frac{3}{6}=\text{?}

Step-by-Step Solution

The task is to perform a simple subtraction of fractions with like denominators. Here's how we solve it:

Initially, we have the fractions 46\frac{4}{6} and 36\frac{3}{6}. Both fractions have the same denominator, which is 6.

  • Step 1: Since the denominators are the same, we subtract only the numerators. This means we subtract 3 from 4, as follows:

46βˆ’36=4βˆ’36=16 \frac{4}{6} - \frac{3}{6} = \frac{4 - 3}{6} = \frac{1}{6}

The fraction 16\frac{1}{6} is already in its simplest form. Therefore, the result of subtracting 36\frac{3}{6} from 46\frac{4}{6} is 16\frac{1}{6}.

The correct answer among the given choices is 16\frac{1}{6}. This corresponds to choice number 2 in the list of options provided.

Therefore, the solution to the problem is 16\frac{1}{6}.

Answer:

16 \frac{1}{6}

Video Solution
Exercise #5

Solve the following exercise:

39βˆ’19=? \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 3βˆ’1=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

Frequently Asked Questions

How do you subtract fractions with different denominators?

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To subtract fractions with different denominators, first find a common denominator by either expanding one fraction or multiplying both denominators together. Then subtract only the numerators while keeping the common denominator unchanged.

What is the easiest way to find common denominators when subtracting fractions?

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The easiest method is to multiply the first fraction by the second fraction's denominator and the second fraction by the first fraction's denominator. This creates a common denominator equal to the product of both original denominators.

Do you subtract denominators when subtracting fractions?

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No, you never subtract denominators when subtracting fractions. Once you have a common denominator, you only subtract the numerators and keep the denominator the same.

How do you subtract three fractions with different denominators?

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When subtracting three fractions, first find the common denominator for the two easiest fractions, then find the common denominator between your result and the third fraction. Work step by step rather than trying to find a common denominator for all three at once.

What should you do after subtracting fractions?

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After subtracting fractions, always check if your answer can be simplified to lowest terms. Look for common factors in the numerator and denominator that can be divided out to create the simplest form.

Why do you multiply both numerator and denominator when finding common denominators?

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You must multiply both the numerator and denominator by the same number to maintain the fraction's original value. This is called equivalent fractions - the value stays the same even though the numbers change.

When is one denominator already the common denominator in fraction subtraction?

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One denominator is already the common denominator when it's a multiple of the other denominator. For example, in 5/6 - 1/3, since 6 is a multiple of 3, you only need to convert 1/3 to 2/6.

What are common mistakes students make when subtracting fractions?

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Common mistakes include: subtracting denominators instead of keeping them the same, forgetting to multiply both numerator and denominator when finding common denominators, and not simplifying the final answer to lowest terms.

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