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Equivalent Ratios: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Equivalent RatiosEquivalent Ratios: Definition and ExampleTable of ContentsDefinition of Equivalent Ratios

Equivalent ratios are two or more ratios that represent the same relationship between quantities when reduced to their simplest form. A ratio itself is defined as a comparison between two quantities of the same kind and same unit, expressed in the form a:ba:ba:b or as a fraction ab\frac{a}{b}ba​. When writing a ratio, the first quantity (aaa) is called the antecedent, and the second quantity (bbb) is called the consequent. For example, in the ratio 1:21:21:2, 111 is the antecedent and 222 is the consequent.

There are multiple methods to identify equivalent ratios. The cross multiplication method is useful for smaller numbers, where you cross multiply the terms and check if the products are equal. The Highest Common Factor (HCF) method involves finding the simplest form of each ratio by dividing both terms by their HCF and checking if the resulting ratios are equal. To create equivalent ratios from an existing ratio, you can multiply or divide both the antecedent and consequent by the same non-zero number. For instance, multiplying both terms of 2:32:32:3 by 222 gives 4:64:64:6, which is an equivalent ratio.

Examples of Equivalent Ratios Example 1: Finding an Equivalent Ratio Problem:

Find one equivalent ratio of 3:223:223:22.

Step-by-step solution:

Step 1, let's understand what we're looking for. We need to find another ratio that has the same value as 3:223:223:22 when reduced to simplest form.

Step 2, we can create an equivalent ratio by multiplying both terms by the same number. Let's choose 222 as our multiplier:

3:22=3223:22 = \frac{3}{22}3:22=223​

Step 3, multiply both the numerator and denominator by 222:

3×222×2=644=6:44\frac{3 \times 2}{22 \times 2} = \frac{6}{44} = 6:4422×23×2​=446​=6:44

Step 4, therefore, 6:446:446:44 is an equivalent ratio of 3:223:223:22. You can verify this by reducing both ratios to their simplest form and confirming they're the same.

Example 2: Finding Multiple Equivalent Ratios Problem:

Find any two equivalent ratios of 14:2114:2114:21.

Step-by-step solution:

Step 1, we need to understand that we can multiply both terms of the ratio by any number to create equivalent ratios.

Let's start by writing the given ratio as a fraction:

14:21=142114:21 = \frac{14}{21}14:21=2114​

Step 2, for the first equivalent ratio, let's multiply both numerator and denominator by 333:

14×321×3=4263=42:63\frac{14 \times 3}{21 \times 3} = \frac{42}{63} = 42:6321×314×3​=6342​=42:63

For the second equivalent ratio, let's multiply by 555:

14×521×5=70105=70:105\frac{14 \times 5}{21 \times 5} = \frac{70}{105} = 70:10521×514×5​=10570​=70:105

Step 3, therefore, two equivalent ratios of 14:2114:2114:21 are 42:6342:6342:63 and 70:10570:10570:105.

Example 3: Checking if Two Ratios are Equivalent Problem:

Are the ratios 18:1018:1018:10 and 63:3563:3563:35 equivalent?

Step-by-step solution: Step 1, we'll apply the HCF method to check if these ratios are equivalent. This means reducing both ratios to their simplest form. Step 2, for the first ratio, let's find the HCF of 181818 and 101010: The HCF of 181818 and 101010 is 222. Now, divide both terms by their HCF: 18÷210÷2=95=9:5\frac{18 \div 2}{10 \div 2} = \frac{9}{5} = 9:510÷218÷2​=59​=9:5 Step 3, for the second ratio, let's find the HCF of 636363 and 353535: The HCF of 636363 and 353535 is 777. Then, divide both terms by their HCF: 63÷735÷7=95=9:5\frac{63 \div 7}{35 \div 7} = \frac{9}{5} = 9:535÷763÷7​=59​=9:5 Step 4, since both ratios reduce to the same value (9:59:59:5), we can conclude that 18:1018:1018:10 and 63:3563:3563:35 are equivalent ratios. Step 5, alternatively, we could have used the cross multiplication method: 18×35=63018 \times 35 = 63018×35=630 and 10×63=63010 \times 63 = 63010×63=630 Since the products are equal, the ratios are equivalent. Comments(9)SSportsTutorLanaNovember 6, 2025This glossary page on equivalent ratios is a lifesaver! It helped my students grasp the concept easily with its clear def and examples.

TTravelBugFinnNovember 5, 2025I've used this equivalent ratios definition with my students. It's clear and the examples helped them grasp the concept quickly. Great resource!

NNurseBethNovember 4, 2025I've used this glossary page to teach equivalent ratios. The clear def and examples really helped my students grasp the concept. Great resource!

NNatureLover85September 17, 2025This explanation of equivalent ratios was super clear! I used the examples to help my kids with their homework, and the step-by-step method made it so much easier for them to understand. Thanks!

MCMs. CarterSeptember 10, 2025I’ve used the Equivalent Ratios definition and examples from this page to help my kids with their homework. The step-by-step methods made it so easy to explain! Highly recommend checking it out.

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