Comparing Fractions

Q: What is the simplest way to compare fractions?

The simplest case is two fractions with the same denominator. When the denominators match, you only compare the numerators, and the fraction with the larger numerator is greater. For example, with five eighths and three eighths, five is greater than three, so five eighths is greater.

Q: How do you compare two fractions with different denominators?

To compare two fractions with different denominators, find the lowest common multiple of the denominators, convert each fraction so both share that common denominator, and then compare the new numerators. The fraction whose equivalent has the larger numerator is greater than the other.

Q: Why is a fraction with a smaller denominator greater when numerators are equal?

When two fractions share the same numerator, the fraction with the smaller denominator is greater because the whole is divided into fewer, larger parts. Picture taking four slices from a pizza cut into 5 portions versus one cut into 9: each slice from the smaller cut is bigger.

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

List the multiples of each denominator and pick the smallest value that appears in both lists. If one denominator is already a multiple of the other, the larger denominator is the lowest common multiple. If the denominators share no common factors, multiply them together.

Q: Do you always need to convert both fractions to a common denominator?

Not always. If one denominator is already a multiple of the other, only the fraction with the smaller denominator needs converting. For example, with one quarter and three sixteenths, 16 is already a multiple of 4, so convert one quarter to four sixteenths and then compare.

Key concept

Comparing fractions means finding which one is larger or smaller. If the denominators match, the larger numerator wins, so 5/8 > 3/8. If they differ, convert both to a common denominator, then compare.

Comparing Fractions - introduction visual

Video Lesson

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$Comparing Fractions poster$

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Flashcards

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$Comparing fractions, showing 5/8 is greater than 3/8 with chocolate bars, and 4/5 is greater than 4/9 with pizza slices.$ $Steps to compare fractions by finding the lowest common multiple (LCM) of denominators and converting fractions to have the same denominator.$ $Comparing fractions by finding the lowest common multiple (LCM) of denominators, converting fractions, and identifying the larger numerator.$ $Step-by-step method comparing 4/11 and 5/12 by finding LCM 132, converting fractions to 48/132 and 55/132, showing 4/11 < 5/12.$

Quick Comparison Rules

If the denominators are the same, the fraction with the larger numerator is greater.
If the numerators are the same, the fraction with the smaller denominator is greater.

Practice Questions

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Q1Easy

Which is greater, $\frac{3}{7}$ or $\frac{5}{7}$ ?

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Interactive Activity

Adjust the denominators to compare the fractions

Match the denominators below

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Students Also Ask

The questions students bump into most on this topic

What is the simplest way to compare fractions?

The simplest case is two fractions with the same denominator. When the denominators match, you only compare the numerators, and the fraction with the larger numerator is greater. For example, with five eighths and three eighths, five is greater than three, so five eighths is greater.

How do you compare two fractions with different denominators?

To compare two fractions with different denominators, find the lowest common multiple of the denominators, convert each fraction so both share that common denominator, and then compare the new numerators. The fraction whose equivalent has the larger numerator is greater than the other.

Why is a fraction with a smaller denominator greater when numerators are equal?

When two fractions share the same numerator, the fraction with the smaller denominator is greater because the whole is divided into fewer, larger parts. Picture taking four slices from a pizza cut into 5 portions versus one cut into 9: each slice from the smaller cut is bigger.

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

List the multiples of each denominator and pick the smallest value that appears in both lists. If one denominator is already a multiple of the other, the larger denominator is the lowest common multiple. If the denominators share no common factors, multiply them together.

Do you always need to convert both fractions to a common denominator?

Not always. If one denominator is already a multiple of the other, only the fraction with the smaller denominator needs converting. For example, with one quarter and three sixteenths, 16 is already a multiple of 4, so convert one quarter to four sixteenths and then compare.

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Comparing Fractions

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Quick Comparison Rules