Adding and Subtracting Fractions

Q: What is the difference between like fractions and unlike fractions?

Like fractions share the same denominator, so you can add or subtract their numerators directly. Unlike fractions have different denominators. Before you add or subtract unlike fractions, you must find a common denominator by using the lowest common multiple of the two denominators.

Q: Why do you need a common denominator to add or subtract fractions?

Fractions with different denominators represent parts of different sizes. You cannot add or subtract parts of different sizes directly. A common denominator converts both fractions into equal-sized parts so the numerators can be added or subtracted meaningfully.

Q: When should you use division to convert an improper fraction to a mixed number?

Division is particularly useful for larger numbers where you cannot easily spot the largest whole number by inspection. For smaller numbers, you can split the fraction by finding the nearest multiple of the denominator. Both methods give the same result.

Q: Is 7/7 a proper or improper fraction?

7/7 is an improper fraction because the numerator is equal to the denominator. A proper fraction requires the numerator to be smaller than the denominator. Since 7 equals 7, the fraction represents exactly one whole. Improper fractions have a numerator that is greater than or equal to the denominator.

Key concept

Adding and subtracting fractions is easy when the denominators are the same. Just add or subtract the numerators and keep the denominator. If the fractions are unlike, first find a common denominator.

Adding and Subtracting Fractions - introduction visual

Video Lesson

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$Adding and Subtracting Fractions poster$

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Flashcards

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$Explanation of the addition of fractions with the same denominator using pizza slices to illustrate.$ $Adding and subtracting fractions with different denominators. Showing the steps to make the denominators the same and subtract fractions 5/6 and 1/4.$ $Different types of fractions in a diagram showing proper fractions, improper fractions, and mixed fractions with examples.$ $Converting between improper fractions and mixed numbers with step-by-step calculations.$

Adding and Subtracting Like Fractions

Like fractions have the same denominator.
Add or subtract the numerators only, keep the denominator the same, then simplify if possible.

Practice Questions

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Q1Easy

Which of the following is a proper fraction?

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Interactive Activity

Practice adding and subtracting fractions algebraically

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Instructions

Step 1 / 4

Start with the expression. The denominators are different (3 and 5).

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Students Also Ask

The questions students bump into most on this topic

What is the difference between like fractions and unlike fractions?

Like fractions share the same denominator, so you can add or subtract their numerators directly. Unlike fractions have different denominators. Before you add or subtract unlike fractions, you must find a common denominator by using the lowest common multiple of the two denominators.

What is the difference between proper and improper fractions?

A proper fraction has a numerator smaller than its denominator, so its value is less than 1. An improper fraction has a numerator greater than or equal to its denominator, so its value is 1 or more. Improper fractions are often converted to mixed numbers for clarity.

How do you find the lowest common multiple of two denominators?

List the multiples of each denominator separately. Then identify the smallest number that appears in both lists. This shared multiple becomes the new denominator. For example, the multiples of 6 are 6, 12, 18 and the multiples of 4 are 4, 8, 12, so the LCM is 12.

Why do you need a common denominator to add or subtract fractions?

Fractions with different denominators represent parts of different sizes. You cannot add or subtract parts of different sizes directly. A common denominator converts both fractions into equal-sized parts so the numerators can be added or subtracted meaningfully.

When should you use division to convert an improper fraction to a mixed number?

Division is particularly useful for larger numbers where you cannot easily spot the largest whole number by inspection. For smaller numbers, you can split the fraction by finding the nearest multiple of the denominator. Both methods give the same result.

Is 7/7 a proper or improper fraction?

7/7 is an improper fraction because the numerator is equal to the denominator. A proper fraction requires the numerator to be smaller than the denominator. Since 7 equals 7, the fraction represents exactly one whole. Improper fractions have a numerator that is greater than or equal to the denominator.

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