How do you know if a ratio is proportional?

How Do You Determine if Two Ratios are Proportional Using Cross Products?

Note:

Trying to figure out if two ratios are proportional? If they're in fraction form, set them equal to each other to test if they are proportional. Cross multiply and simplify. If you get a true statement, then the ratios are proportional! This tutorial gives you a great example!

Keywords:

• problem
• ratios
• form proportion
• proportion
• equivalent
• same
• cross multiply
• multiply
• means extremes of proportions
• ratio
• proportions

Background Tutorials

• Ratio Definitions

  • • 
      

    What's a Ratio?

    Ratios are everywhere! The scale on a map or blueprint is a ratio. Ingredients sometimes need to be mixed using ratios such as the ratio of water to cement mix when making cement. Watch this tutorial to learn about ratios. Then think of some ratios you've encountered before!

• Determining Proportionality

  • • 
      

    What's a Proportion?

    The idea of proportions is that a ratio can be written in many ways and still be equal to the same value. That's why proportions are actually equations with equal ratios. This is a bit of a tricky definition, so make sure to watch the tutorial!

• Solving Proportions

  • • 
      

Further Exploration

• Solving Proportions

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What's a Numerator and What's A Denominator?

Numerators and denominators are the key ingredients that make fractions, so if you want to work with fractions, you have to know what numerators and denominators are. Lucky for you, this tutorial will teach you some great tricks for remembering what numerators and denominators are all about.

A ratio is a way of expressing the relative sizes of parts of a group.[1] Ratios are used often in baking, science, and any time you want to compare or exchange amounts of something. When two ratios are equivalent, they are in proportion.[2] Sometimes you will be presented with two ratios, and you will need to determine whether or not they are in proportion. To solve you need to treat the ratios as equivalent fractions, and see if you can make true statements about their values. Using simple algebra, you can also find the missing value of a ratio that will make it proportional to another ratio.

1. 

   1

2. 

   2

   Find the least common multiple for the two denominators. To find the least common multiple, look for the smallest multiple each denominator has in common.[4] If there is no least common multiple, then the ratios cannot be in proportion and no further steps are required.

   • For example, the denominators 4 and 26 are both multiples of 52.

3. 

   3

   Write the equivalent fraction for the first ratio. To find the equivalent fraction, divide the least common multiple by the denominator. Multiply the numerator by this quotient. This will give you the new numerator of your equivalent fraction.

4. 

   4

   Write the equivalent fraction for the second ratio. Follow the same steps you did to find the equivalent fraction for the first ratio.

5. 

   5

   Compare the two equivalent fractions. If the two fractions are equal, then the two original ratios are in proportion.[5]

1. 

   1

2. 

   2

   Multiply the numerator of the first fraction and the denominator of the second fraction. Place this product to the right of the equation.

3. 

   3

   Multiply the denominator of the first fraction and the numerator of the second fraction. Place this product to the left of the equation.

4. 

   4

   Compare the two products. If they are the same, then the ratios are in proportion.[7]

1. 

   1

2. 

   2

   Multiply the numerator of the first fraction and the denominator of the second fraction. Place this product to the right of the equation.

3. 

   3

   Multiply the denominator of the first fraction and the numerator of the second fraction. Place this product to the left of the equation.

4. 

   4

   Solve for . This will give you the missing number in your second ratio. The two ratios are now in proportion.[9]

Add New Question

• Question

  In the ratio as a fraction in lowest terms 6' to 74", do I change the feet to 72 inches?

  

  Yes. 6 feet is 72 inches. The ratio is 72 : 74, or 36 : 37 in lowest terms.

• Question

  I cant really understand how you got the number 30 in the example above. Can you show me the solution?

  

  In Method 3 above, the fraction 6/4 is set equal to the fraction x/20, and we're supposed to find the value of x that will make that equation true. After cross-multiplying, 4x = 120. After dividing both sides of this equation by 4, x = 30.

• Question

  How can I find the value of x here: 45:12:x:9?

  

  Since they are in proportion, 45/12 = x/9. Hence 9X45 = xX12. This gives x as 33.75.

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