Mathematics
Grade 7
15 min
Find what percent one number is of another
Find what percent one number is of another
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1
Introduction & Learning Objectives
Learning Objectives
Define and understand the concept of a percent.
Identify the 'part' and the 'whole' in a given problem.
Set up and solve a proportion to find an unknown percent.
Use division to convert a fraction or ratio into a decimal and then into a percent.
Solve real-world problems that require finding what percent one number is of another, including those with decimals.
Accurately convert between decimal and percent forms.
Ever wonder how stores calculate discounts or how much of your phone battery is left? 🔋 These are all examples of percentages in action!
In this lesson, you'll learn a fundamental skill: how to express one number as a percentage of another. This skill is super useful for understanding data, making comparisons, and solvi...
2
Key Concepts & Vocabulary
TermDefinitionExample
PercentA way to express a number as a fraction of 100. The word 'percent' means 'per hundred' or 'out of one hundred'. It is denoted by the symbol '%'.If you score 85% on a test, it means you got 85 out of every 100 points possible.
RatioA comparison of two numbers by division. It can be written as a fraction, with a colon, or with the word 'to'.The ratio of 3 red apples to 5 green apples can be written as 3/5, 3:5, or 3 to 5.
ProportionAn equation that states that two ratios are equal. Proportions are often used to solve for an unknown value when one ratio is known.1/2 = 50/100 is a proportion, showing that one-half is equal to fifty hundredths.
PartThe specific portion or amount being compared to the total or whole....
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Core Formulas
Percent Proportion Formula
$\frac{\text{Part}}{\text{Whole}} = \frac{\text{Percent}}{100}$
This formula sets up a proportion where the ratio of the part to the whole is equal to the ratio of the percent to 100. You can use this to find an unknown percent when the part and whole are known.
Direct Division Method
$\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\%$
To find what percent one number is of another, divide the part by the whole. This will give you a decimal. Then, multiply the decimal by 100% to convert it into a percentage.
5 more steps in this tutorial
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Challenging
If 'x' is a positive number, what percent of 5x is 2x?
A.2.5%
B.25%
C.40%
D.It cannot be determined without knowing the value of x.
Challenging
A student is asked to find what percent 15.3 is of 25.5. They incorrectly set up the proportion as $\frac{25.5}{15.3} = \frac{x}{100}$. What will their incorrect answer be (approximately), and why is the setup wrong?
A.60%; the setup is correct.
B.167%; the setup is wrong because they inverted the Part and Whole.
C.0.6%; the setup is wrong because they forgot to multiply by 100.
D.10.2%; the setup is wrong because they should have subtracted.
Challenging
A box contains 150 marbles. 20% are red, 40% are blue, and the rest are green. Of the green marbles, 18 are large and the rest are small. What percent of ALL the marbles in the box are green?
A.60%
B.40%
C.12%
D.30%
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