Finding the unknown fraction
Finding the unknown fraction means determining what fractional or decimal part one number is of another using the equation: unknown fraction x total = part. For example, to find what fraction of 80 is 20, set up W x 80 = 20, giving W = 20/80 = 1/4. This skill is covered in Chapter 8 of Saxon Math Course 2 for 7th grade math and connects fraction, decimal, and percent concepts. It is essential for solving word problems involving ratios, proportions, and percent-of-a-number calculations.
Key Concepts
Property To find what fraction or decimal part one number is of another, set up the equation: $W F \times \operatorname{Total} = \operatorname{Part}$.
Examples What fraction of 80 is 20? $\rightarrow W F \times 80 = 20 \rightarrow W F = \frac{20}{80} = \frac{1}{4}$. What decimal part of 200 is 50? $\rightarrow W D \times 200 = 50 \rightarrow W D = \frac{50}{200} = 0.25$. Fifteen is what fraction of 75? $\rightarrow 15 = W F \times 75 \rightarrow W F = \frac{15}{75} = \frac{1}{5}$.
Explanation Once you have your equation, the unknown fraction is stuck in a multiplication problem. To get it by itself, just do the opposite! Divide both sides of the equation by the total number. This isolates your variable, leaving you with a simple fraction to reduce or convert to a decimal.
Common Questions
How do you find what fraction one number is of another?
Divide the part by the total. To find what fraction of 80 is 20, calculate 20/80 = 1/4. You can also set up the equation W x 80 = 20 and solve for W by dividing both sides by 80.
What is the formula for finding the unknown fraction?
The formula is: Unknown Fraction x Total = Part, or equivalently, Unknown Fraction = Part / Total. This works for both fractions and decimals. For example, what decimal part of 200 is 50? Answer: 50/200 = 0.25.
How do you convert the answer to a percent?
Once you find the fraction, multiply by 100 to convert to a percent. If 20 is 1/4 of 80, then 1/4 = 0.25 = 25%. This three-way conversion between fractions, decimals, and percents is a core 7th grade skill.
What is an example of finding an unknown fraction in a word problem?
If a class has 30 students and 12 are wearing glasses, the fraction wearing glasses is 12/30 = 2/5. This means two-fifths, or 40%, of the class wears glasses.
What are common mistakes when finding unknown fractions?
Students often divide the total by the part instead of the part by the total. Remember, the part goes on top (numerator) and the total goes on the bottom (denominator). Another mistake is forgetting to simplify the resulting fraction.
Which textbook covers finding the unknown fraction?
Saxon Math Course 2 teaches this in Chapter 8, building on earlier fraction and percent skills. Students practice setting up and solving equations to find what fraction, decimal, or percent one number is of another.