Lesson 74: Fractional Part of a Number, Part 2

New Concept

Translate word problems into equations to find an unknown fraction or total. Replace 'of' with multiplication and 'is' with an equals sign.

To find an unknown part or total, translate the problem into an equation:

What fraction of 80 is 60?
What fraction ($W_F$) of ($\times$) 80 is ($=$) 60

$$W_F \times 80 = 60$$

Two thirds of what number is 50?
Two thirds ($\frac{2}{3}$) of ($\times$) what number ($W_N$) is ($=$) 50

$$\frac{2}{3} \times W_N = 50$$

What’s next

This is the foundation for algebraic thinking. Next, you'll tackle worked examples and practice problems to master finding the missing part or the whole.

Property

Translate problems into equations by replacing the word 'of' with a multiplication sign and the word 'is' with an equal sign. Use a variable for the unknown value.

Examples

• 'What fraction of 100 is 25?' translates to $W_F \times 100 = 25$.
• 'Three fifths of what number is 30?' translates to $\frac{3}{5} \times W_N = 30$.
• 'Seventy is 0.7 of what number?' translates to $70 = 0.7 \times W_N$.

Explanation

Think of it like being a word detective! 'Of' is your secret code for 'multiply,' and 'is' is the code for 'equals.' Swapping words for these symbols turns a tricky word problem into a straightforward algebra puzzle that you already know how to solve with ease.

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.

Property

When the total number is the unknown, set up the equation using a variable for the total: $\operatorname{Fraction} \times W_N = \operatorname{Part}$.

Examples

• Two thirds of what number is 50? $\rightarrow \frac{2}{3} \times W_N = 50 \rightarrow W_N = 50 \times \frac{3}{2} = 75$.
• Sixty is 0.4 of what number? $\rightarrow 60 = 0.4 \times W_N \rightarrow W_N = \frac{60}{0.4} = 150$.
• Five fourths of what number is 25? $\rightarrow \frac{5}{4} \times W_N = 25 \rightarrow W_N = 25 \times \frac{4}{5} = 20$.

Explanation

To find the unknown total, you must free it from the fraction! You can do this by multiplying both sides by the fraction's reciprocal, which cancels it out and reveals the answer. If you are working with a decimal instead of a fraction, simply divide both sides by it.