Finding the Whole Number
Finding the whole number in a percent problem means determining the original total when you know a percentage and the part it represents. Use the formula Percent x Whole = Part, then solve for the whole by dividing the part by the percent. For example, if 20% of a number is 50, then the whole number is 50 / 0.20 = 250. This skill is covered in Chapter 8 of Saxon Math Course 2 and is a key 7th grade math concept for solving real-world percent problems involving discounts, taxes, and data analysis.
Key Concepts
Property To find the original number when you know the percent and the part, use the equation: $$ \text{Percent} \times W N = \text{is} $$, where $$W N$$ represents 'What Number'.
Examples Twenty percent of what number is 50? $$ 0.20 \times W N = 50 \rightarrow W N = \frac{50}{0.20} = 250 $$ Seventy five percent of what number is 300? $$ \frac{3}{4} \times W N = 300 \rightarrow W N = 300 \times \frac{4}{3} = 400 $$ Ninety is 150 percent of what number? $$ 1.5 \times W N = 90 \rightarrow W N = \frac{90}{1.5} = 60 $$.
Explanation Here, the total amount is the mystery you need to solve. Start by converting the given percentage into a decimal or a fraction. Set up your equation, then use inverse operations to isolate the unknown number ($$W N$$). If you used a fraction, multiply by its reciprocal; if a decimal, divide. It's that simple to find the whole enchilada!
Common Questions
How do you find the whole number in a percent problem?
Divide the part by the percent expressed as a decimal. If 75% of a number is 300, divide 300 by 0.75 to get 400.
What formula do you use to find the whole from a percent?
Use Percent x Whole = Part. Rearrange to Whole = Part / Percent. Make sure to convert the percent to a decimal or fraction before dividing.
What does it mean to find the whole number?
It means finding the original total amount when you only know what fraction or percentage of it a given value represents. For example, knowing that 50 is 20% of some number, the whole is 250.
Can you use fractions instead of decimals?
Yes. If 3/4 of a number is 300, multiply both sides by the reciprocal: 300 x 4/3 = 400. Using fractions can sometimes be easier than using decimals.
What are common mistakes when finding the whole number?
Students often multiply instead of dividing, or they forget to convert the percent to a decimal. For example, dividing by 20 instead of 0.20 gives a very wrong answer.
Is this skill part of 7th grade math?
Yes. Saxon Math Course 2 teaches finding the whole number in percent equations in Chapter 8, building on earlier work with fractions and proportional reasoning.