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102 LearnersLast updated on September 9, 2025
Subtraction of Fractions with Like Denominators
The mathematical operation of finding the difference between two fractions with the same denominator is known as subtraction of fractions with like denominators. It helps simplify expressions and solve problems that involve fractions efficiently.
What is Subtraction of Fractions with Like Denominators?
Subtracting fractions with like denominators involves finding the difference between the numerators while keeping the denominator the same. This simplifies the subtraction process as it does not require finding a common denominator. There are three components of a fraction:
Numerator: The top part representing how many parts are being considered.
Denominator: The bottom part representing the total number of equal parts.
Fraction Bar: The line separating the numerator and denominator.
How to do Subtraction of Fractions with Like Denominators?
When subtracting fractions with like denominators, students should follow these steps:
Subtract the numerators: The denominators stay the same, so simply subtract the numerators.
Simplify the result: After subtracting, check if the fraction can be simplified further by finding the greatest common divisor of the numerator and denominator.
Methods to do Subtraction of Fractions with Like Denominators
The following are methods for subtracting fractions with like denominators:
Method 1: Horizontal Method
To apply the horizontal method for subtraction of fractions, follow these steps.
Step 1: Write both fractions in a single line with a subtraction sign between them.
Step 2: Subtract the numerators while keeping the denominator the same.
Step 3: Simplify the fraction if possible.
Example: Subtract 5/7 from 3/7.
Step 1: Write both fractions in the same line: 5/7 - 3/7.
Step 2: Subtract the numerators: 5-3/7 = 2/7.
Step 3: The fraction 2/7 is already in its simplest form.
Method 2: Column Method
When using the column method, write the fractions one below the other. Then subtract the numerators directly.
Example: Subtract 4/9 from 7/9.
Solution: Arrange the fractions vertically: 7/9 - 4/9 --------- 3/9
Simplify 3/9 to 1/3.
Properties of Subtraction of Fractions with Like Denominators
In subtraction of fractions with like denominators, certain properties hold: Subtraction is not commutative In subtraction, changing the order of the terms changes the result, i.e., a/b - c \neq c/b - a/b.
Subtraction is not associative Unlike addition, we cannot regroup in subtraction. When three or more fractions are involved, changing the grouping changes the result. a/b − c/b − d/b \neq a/b − c/b− d/b.
Subtraction is the addition of the opposite Subtracting a fraction is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the sign of the numerator of the second fraction.a/b − c/b = a/b + (−c/b).
Subtracting zero from a fraction leaves the fraction unchanged Subtracting zero from any fraction results in the same fraction: a/b - 0 = a/b.
Tips and Tricks for Subtraction of Fractions with Like Denominators
Tips and tricks are useful for students to efficiently deal with the subtraction of fractions with like denominators. Some helpful tips are listed below:
Tip 1: Always ensure that the denominators are the same before subtracting the numerators.
Tip 2: Simplify fractions whenever possible to make calculations easier and results clearer.
Tip 3: Visual aids like fraction bars can help beginners understand the subtraction process better.
Forgetting to keep the denominator the same
Students sometimes change the denominator during subtraction. Always remember to keep the denominator constant and only subtract the numerators.
Mistake 1
Combining fractions with different denominators
Fractions must have the same denominator for direct subtraction; otherwise, a common denominator must be found.
Mistake 2
Misalignment in vertical subtraction
When using the column method, ensure that the fractions are aligned correctly to avoid errors in subtraction.
Mistake 3
Leaving fractions unsimplified
Always check if the resulting fraction can be simplified by finding the greatest common divisor of the numerator and denominator.
Mistake 4
Ignoring negative results
When subtracting a larger fraction from a smaller one, the result will be negative. Be careful not to overlook this.
Mistake 5
Examples of Subtraction of Fractions with Like Denominators
Subtract \( \frac{3}{5} \) from \( \frac{4}{5} \).
\( \frac{1}{5} \)
Problem 1
Using the horizontal method: \( \frac{4}{5} - \frac{3}{5} = \frac{4-3}{5} = \frac{1}{5} \).
Subtract 5/8 from 7/8.
Explanation
1/4
Problem 2
Using the horizontal method: \( \frac{7}{8} - \frac{5}{8} = \frac{7-5}{8} = \frac{2}{8} \). Simplify \( \frac{2}{8} \) to \( \frac{1}{4} \).
Subtract 2/6 from 5/6.
Explanation
1/2
Problem 3
Using the horizontal method: \( \frac{5}{6} - \frac{2}{6} = \frac{5-2}{6} = \frac{3}{6} \). Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \).
Subtract 1/4 from 3/4.
Explanation
1/2
Problem 4
Using the horizontal method: \( \frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4} \). Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \).
Subtract 3/7 from 6/7.
Explanation
3/7
No, fractions must have the same denominator for direct subtraction. If they do not, you must first find a common denominator.
1.Is subtraction commutative for fractions?
2.What are like fractions?
3.What is the first step in subtracting fractions with like denominators?
4.What method is used for subtraction of fractions with like denominators?
Common Mistakes and How to Avoid Them in Subtraction of Fractions with Like Denominators
Subtraction of fractions can be challenging, often leading to common mistakes. However, being aware of these errors can help students avoid them.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
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: She loves to read number jokes and games.
