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:

\( \frac{2}{4}-\frac{1}{4}=\text{?} \)

Examples with solutions for Subtraction of Fractions

Step-by-step solutions included
Exercise #1

Solve the following exercise:

56βˆ’26=? \frac{5}{6}-\frac{2}{6}=\text{?}

Step-by-Step Solution

In this problem, 56βˆ’26 \frac{5}{6} - \frac{2}{6} , we are tasked with subtracting two fractions with the same denominator.

Steps to solve the fraction problem:

  • Step 1: Confirm that the denominators are the same. Here, both are 6.
  • Step 2: Subtract the numerators. Take the numerator of the first fraction 5 5 and subtract the numerator of the second fraction 2 2 . The calculation is 5βˆ’2=3 5 - 2 = 3 .
  • Step 3: Place the result over the common denominator. This gives us 36 \frac{3}{6} .
  • Step 4: Simplify the fraction if possible. Here, 36 \frac{3}{6} can be simplified to 12 \frac{1}{2} , but since the problem does not require simplification and a matching choice exists, we can leave it as is.

Therefore, the solution to the problem is 36 \frac{3}{6} .

Answer:

36 \frac{3}{6}

Video Solution
Exercise #2

Solve the following exercise:

66βˆ’36=? \frac{6}{6}-\frac{3}{6}=\text{?}

Step-by-Step Solution

Let's solve the problem 66βˆ’36 \frac{6}{6} - \frac{3}{6} .

First, it's important to note that we're dealing with fractions that have the same denominator. This allows us to subtract the numerators directly while keeping the denominator unchanged.

Here are the steps we'll follow:

  • Step 1: Identify the fractions involved: 66 \frac{6}{6} and 36 \frac{3}{6} .
  • Step 2: Subtract the numerators of the fractions: 6βˆ’3 6 - 3 .
  • Step 3: Keep the denominator the same: 6 6 .
  • Step 4: Combine the results to form the new fraction.

Now let's proceed with the calculation:

Step 2: Subtract the numerators: 6βˆ’3=3 6 - 3 = 3 .

Step 3: Since the denominators are the same, the new denominator remains 6 6 .

Step 4: Combine the results: This gives us the fraction 36 \frac{3}{6} .

Therefore, the solution to the problem 66βˆ’36 \frac{6}{6} - \frac{3}{6} is 36 \frac{3}{6} .

Answer:

36 \frac{3}{6}

Video Solution
Exercise #3

Solve the following exercise:

35βˆ’25=? \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 3βˆ’2=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 #4

Solve the following exercise:

67βˆ’27=? \frac{6}{7}-\frac{2}{7}=\text{?}

Step-by-Step Solution

The problem requires us to find the result of subtracting two fractions with the same denominator: 67βˆ’27\frac{6}{7} - \frac{2}{7}.

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

  • Step 1: Identify that the fractions have the same denominator, which is 7.
  • Step 2: Subtract the numerators: 6βˆ’26 - 2.
  • Step 3: Place the result of the subtraction over the unchanged denominator.

Let's work through each step:

Step 1: Observe that 67\frac{6}{7} and 27\frac{2}{7} both have a denominator of 7.

Step 2: Subtract the numerators: 6βˆ’2=46 - 2 = 4.

Step 3: Place the result over the original denominator: 47\frac{4}{7}.

Therefore, the solution to the problem is 47\frac{4}{7}.

Answer:

47 \frac{4}{7}

Video Solution
Exercise #5

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

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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