Multiplying by a Fraction
Multiplying by a fraction means finding a fractional part of a number in Grade 8 math (Yoshiwara Core Math). The word 'of' signals multiplication — '3/4 of 20' means 3/4 × 20 = 15. To multiply a whole number by a fraction, multiply by the numerator then divide by the denominator. For fractions times fractions, multiply numerators together and denominators together. This skill connects directly to percent calculations, scaling, and proportional reasoning throughout Grade 8 mathematics.
Key Concepts
Property Taking $\frac{2}{3}$ of something means to divide the quantity into 3 equal parts, and then take 2 of them. This is the same as multiplying by $\frac{2}{3}$.
To multiply two fractions: 1. Multiply the numerators together. 2. Multiply the denominators together. $$ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} $$.
Examples What is $\frac{3}{4}$ of 24? We can calculate this by multiplying: $\frac{3}{4} \times \frac{24}{1} = \frac{3 \times 24}{4 \times 1} = \frac{72}{4} = 18$.
Common Questions
How do you multiply a whole number by a fraction?
Multiply by the numerator, then divide by the denominator. For example, 3/4 × 20 = 60/4 = 15.
What does 'of' mean in a fraction problem?
In math, 'of' means multiply. '2/3 of 18' = 2/3 × 18 = 12.
How do you multiply two fractions together?
Multiply numerators together and denominators together. (2/3) × (3/4) = 6/12 = 1/2.
How does multiplying by a fraction relate to percents?
Percents are fractions of 100. Finding 25% of a number equals multiplying by 1/4.
Does multiplying by a proper fraction give a smaller result?
Yes. Multiplying by a fraction less than 1 always gives a result smaller than the original number.