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Course: Praxis Core Math > Unit 1
Lesson 2: Number and quantity- Rational number operations | Lesson
- Rational number operations | Worked example
- Ratios and proportions | Lesson
- Ratios and proportions | Worked example
- Percentages | Lesson
- Percentages | Worked example
- Rates | Lesson
- Rates | Worked example
- Naming and ordering numbers | Lesson
- Naming and ordering numbers | Worked example
- Number concepts | Lesson
- Number concepts | Worked example
- Counterexamples | Lesson
- Counterexamples | Worked example
- Pre-algebra word problems | Lesson
- Pre-algebra word problems | Worked example
- Unit reasoning | Lesson
- Unit reasoning | Worked example
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Ratios and proportions | Lesson
What are ratios and proportions?
A ratio is a comparison of two quantities. The ratio of
A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.
What skills are tested?
- Identifying and writing equivalent ratios
- Solving word problems involving ratios
- Solving word problems using proportions
How do we write ratios?
Two common types of ratios we'll see are part to part and part to whole. For example, when we make lemonade:
- The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
- The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
To write a ratio:
- Determine whether the ratio is part to part or part to whole.
- Calculate the parts and the whole if needed.
- Plug values into the ratio.
- Simplify the ratio if needed. Integer-to-integer ratios are preferred.
Equivalent ratios are ratios that have the same value. Given a ratio, we can generate equivalent ratios by multiplying both parts of the ratio by the same value.
How do we use proportions?
If we know a ratio and want to apply it to a different quantity (for example, doubling a cookie recipe), we can use proportional relationships, or equations of equivalent ratios, to calculate any unknown quantities.
To use a proportional relationship to find an unknown quantity:
- Write an equation using equivalent ratios.
- Plug in known values and use a variable to represent the unknown quantity.
- If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
- If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.
Your turn!
Things to remember
A ratio is a comparison of two quantities.
A proportion is an equality of two ratios.
To write a ratio:
- Determine whether the ratio is part to part or part to whole.
- Calculate the parts and the whole if needed.
- Plug values into the ratio.
- Simplify the ratio if needed. Integer-to-integer ratios are preferred.
Equivalent ratios are ratios that have the same value.
To use a proportional relationship to find an unknown quantity:
- Write an equation using equivalent ratios.
- Plug in known values and use a variable to represent the unknown quantity.
- If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
- If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.
Want to join the conversation?
Writing equivalent ratios is mentioned in the "What Skills Are Tested?" section of this article.
What does writing an equivalent ratio of a given ratio mean? Is it the same as converting an a:b ratio to a fraction—a/b—and reducing the fraction to its simplest form, where the denominator and numerator have no common factors?
Conversely, can an equivalent ratio of a given ratio also mean multiplying the numerator and denominator of the fraction with the same number?
In other words, are the following two examples of equivalent ratios correct?
Example A:
24:3 = 24/3 = 8 = 8:1
Example B:
1:2 = 1/2 = 4/8 = 4:8(8 votes)
Both of your examples of equivalent ratios are correct. Good job!(16 votes)
Why does it have to be hard?(11 votes)
Why does it have to be hard?(7 votes)
why is this ratio HA:RD(6 votes)
if you do practice problems it could become EA:SY(5 votes)
Hello! Why does Sal always do easy examples and hard questions?(7 votes)- He's probably trying to see if u understood the topic at a deeper level! :)(1 vote)
- hard i dont understand this(6 votes)
- If I were to take a quiz tomorrow, what would be the best way to study?(5 votes)
- my psychology teacher said taking a mock quiz is psychologically proven to stimulate revision and studying.(3 votes)
- what do the letters a and b represent?(2 votes)
Nothing, they're just showing the positions of numbers(4 votes)
Can you explain how a ratio without fractions works?(3 votes)- Guys I have a percent proportions problem for you please reply if you think you have the answer:
Julie and her crew are picking up the town's litter. The town has (don't ask me how I know, I have my ways) 462 pieces of litter. If they have picked up 91 percent of the litter, how many pieces have they picked up?(1 vote)
462 * 0.91 = 420.42
They have picked up 420.42 pieces of litter.(5 votes)
Greetings. Please give me ten examples of real life use for this equation. Thanks.
(3 votes)