Finding a Fraction of a Whole
Finding a fraction of a whole number means dividing the total by the denominator to find one equal part, then multiplying by the numerator to count the desired number of parts. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students apply the two-step rule: divide total by denominator, then multiply by numerator. For 3/5 of 40: 40 ÷ 5 = 8 (one part), then 8 × 3 = 24. This is identical to multiplying the fraction by the whole number (3/5 × 40 = 120/5 = 24). Real-world applications include finding discounts, splitting groups, and determining recipe amounts.
Key Concepts
Property To find a fraction of a whole number, first divide the total by the denominator to find the size of one fractional part. Then, multiply that result by the numerator to find the value of the desired number of parts.
Examples To find $\frac{2}{3}$ of 12 musicians: first $12 \div 3 = 4$, then $2 \times 4 = 8$ musicians. To find $\frac{3}{4}$ of 28 problems: first $28 \div 4 = 7$, then $3 \times 7 = 21$ problems. To find $\frac{5}{6}$ of 24 pizzas: first $24 \div 6 = 4$, then $5 \times 4 = 20$ pizzas.
Explanation Imagine a bag of 12 cookies! To find $\frac{2}{3}$ of them, the '3' tells you to split the cookies into 3 equal groups, meaning each group has 4 cookies. The '2' then tells you to take 2 of those groups. So, you get $2 \times 4 = 8$ cookies. It's the secret to fairly sharing any treasure!
Common Questions
What is the two-step method for finding a fraction of a whole number?
Step 1: divide the whole number by the denominator to find one fractional part. Step 2: multiply that result by the numerator.
Find 3/5 of 40.
40 ÷ 5 = 8 (one fifth). Then 8 × 3 = 24. So 3/5 of 40 is 24.
Find 2/3 of 27.
27 ÷ 3 = 9 (one third). Then 9 × 2 = 18.
How is finding a fraction of a whole related to multiplication?
It is identical: 2/3 × 27 = 54/3 = 18. The division-then-multiplication method and direct fraction multiplication give the same result.
A school has 360 students and 5/8 participate in sports. How many participate?
360 ÷ 8 = 45, then 45 × 5 = 225 students participate in sports.