Equivalent Ratios Practice Problems & Worksheets

Master equivalent ratios with step-by-step practice problems. Learn to identify, simplify, and solve ratio problems using multiplication and division methods.

๐Ÿ“šPractice Equivalent Ratios Skills
  • Identify whether two ratios are equivalent using cross multiplication
  • Simplify ratios to their lowest terms by finding common factors
  • Find missing values in equivalent ratio problems
  • Convert between fraction and ratio notation confidently
  • Apply equivalent ratios to solve real-world word problems
  • Use multiplication and division to create equivalent ratios

Understanding Equivalent Ratios

Complete explanation with examples

To easily solve ratio problems and to gain a better understanding of the topic in general, it is convenient to know about equivalent ratios.

Equivalent ratios are, in fact, ratios that seem different, are not expressed in the same way but, by simplifying or expanding them, you arrive at exactly the same relationship.

Think of it this way,

Equivalent ratios

Detailed explanation

Practice Equivalent Ratios

Test your knowledge with 28 quizzes

In the clothing factory there are two t-shirt machines

Machine A produces 30 t-shirts in 3 minutes,
Machine B produces 16 t-shirts in 2 minutes.

Which machine will produce more t-shirts in 10 minutes?

Examples with solutions for Equivalent Ratios

Step-by-step solutions included
Exercise #1

In a basket, there are 15 apples and 10 oranges. What is the ratio of apples to oranges?

Step-by-Step Solution

To find the ratio of apples to oranges, divide the number of apples by the number of oranges.
Therefore, apples:oranges=1510=3:2 \text{apples:oranges} = \frac{15}{10} = 3:2 .
Thus, the ratio of apples to oranges is 3:2 3:2 .

Answer:

3:2 3:2

Exercise #2

A recipe calls for 400g of flour and 200g of sugar. What is the ratio of flour to sugar in the recipe?

Step-by-Step Solution

To find the ratio of flour to sugar, divide the amount of flour by the amount of sugar.
Thus, we have flour:sugar=400200=2:1 \text{flour:sugar} = \frac{400}{200} = 2:1 .
Therefore, the ratio of flour to sugar is 2:1 2:1 .

Answer:

3:2 3:2

Exercise #3

What is the ratio between the number of fingers and the number of toes?

Step-by-Step Solution

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

  • Step 1: Identify the number of fingers, which is typically 10.
  • Step 2: Identify the number of toes, which is also typically 10.
  • Step 3: Write the ratio of fingers to toes.
  • Step 4: Simplify the ratio.

Now, let's work through each step:
Step 1: The typical number of fingers on a human is 10 10 .
Step 2: The typical number of toes on a human is 10 10 .
Step 3: The ratio of fingers to toes is 10:10 10:10 .
Step 4: Simplifying this ratio 10:10 10:10 gives us 1:1 1:1 .

Therefore, the solution to the problem is 1:1 1:1 , which corresponds to answer choice 4.

Answer:

1:1 1:1

Exercise #4

A tank fills with water at a rate of 20 liters every 5 minutes.
What is the flow rate of the water in liters per minute?

Step-by-Step Solution

The total volume of water that fills the tank is 20 20 liters over 5 5 minutes. The flow rate is given by the volume divided by time:
Flowย Rate=Totalย VolumeTime=205=4 \text{Flow Rate} = \frac{\text{Total Volume}}{\text{Time}} = \frac{20}{5} = 4
Thus, the water flows at a rate of 4 4 liters per minute.

Answer:

4 4 liters/minute

Exercise #5

According to a recipe, one cup of flour is needed for 3 cookies. How many cups of flour are needed for six cookies?

Step-by-Step Solution

To solve this problem, let's determine how many cups of flour are needed to make six cookies using proportions.

Initially, we know that 1 cup of flour produces 3 cookies. Our task is to determine how many cups (x x ) will be necessary for 6 cookies.

We can set up a proportion based on the information given:

13=x6\frac{1}{3} = \frac{x}{6}

To solve for x x (the unknown number of cups), we cross-multiply:

(1ร—6)=(3ร—x)(1 \times 6) = (3 \times x)

This simplifies to:

6=3x6 = 3x

Next, divide both sides of the equation by 3 to isolate x x :

x=63=2x = \frac{6}{3} = 2

Therefore, 2 cups of flour are needed for six cookies.

The solution to the problem is 2 cups.

Answer:

2 cups

Frequently Asked Questions

How do you know if two ratios are equivalent?

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Two ratios are equivalent if they simplify to the same reduced form or if you can multiply or divide both terms by the same number to get from one ratio to the other. For example, 2:4 and 6:12 are equivalent because both simplify to 1:2.

What is the easiest way to find equivalent ratios?

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The easiest method is to multiply or divide both terms of the ratio by the same number. To create equivalent ratios for 3:5, you can multiply both by 2 to get 6:10, or by 4 to get 12:20.

How do you simplify ratios to lowest terms?

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Find the greatest common factor (GCF) of both terms and divide each term by it. For the ratio 12:18, the GCF is 6, so dividing both terms gives you the simplified ratio 2:3.

Can equivalent ratios be written as fractions?

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Yes, ratios can be expressed as fractions and follow the same rules. The ratio 4:8 can be written as 4/8, which simplifies to 1/2, just like the equivalent ratio 1:2.

What are some real-world examples of equivalent ratios?

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Common examples include: recipe scaling (2 cups flour to 4 cups water = 1 cup flour to 2 cups water), map scales, and mixing paint colors. If a recipe serves 4 people with 2 cups of rice, then 4 cups of rice serves 8 people.

How do you solve missing value problems with equivalent ratios?

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Set up a proportion and cross multiply, or find the scale factor between known terms. If 3:x = 6:10, you can see that 3ร—2=6, so xร—2=10, meaning x=5.

What's the difference between a ratio and a fraction?

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While ratios and fractions look similar, ratios compare two quantities (like 3 boys to 5 girls), while fractions represent parts of a whole (like 3/8 of a pizza). However, equivalent ratio rules work the same as equivalent fraction rules.

Why is it important to learn equivalent ratios?

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Equivalent ratios help solve proportion problems, scale recipes, understand maps, compare rates, and work with percentages. They're essential for algebra, geometry, and many real-world applications like cooking and construction.

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