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Fractions of an Amount
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Foundational skills
Identify numerator and denominator
\[ \frac{3}{4} \text{ of } 20 \text{ — which number?} \]
Identify parts of a fraction in context.
Link unit fractions to division
\[ \frac{1}{5} \text{ of } 30 = 30 \div \square \]
Unit fractions mean divide by denominator.
Two-step calculation method
\[ \frac{3}{4} \text{ of } 20 \text{: find } \frac{1}{4} \text{ then } \times 3 \]
Non-unit fractions use two steps.
Unit fractions of 2-digit amounts
Find half of 2-digit amounts
\[ \frac{1}{2} \text{ of } 48 = \square \]
Divide by 2 to find half.
Find quarter of 2-digit amounts
\[ \frac{1}{4} \text{ of } 36 = \square \]
Divide by 4 to find a quarter.
Find tenth of 2-digit amounts
\[ \frac{1}{10} \text{ of } 70 = \square \]
Divide by 10 to find a tenth.
Find third of 2-digit amounts
\[ \frac{1}{3} \text{ of } 27 = \square \]
Divide by 3 to find a third.
Find fifth of 2-digit amounts
\[ \frac{1}{5} \text{ of } 45 = \square \]
Divide by 5 to find a fifth.
Find 1/6, 1/7, 1/8, 1/9 of 2-digit
\[ \frac{1}{6} \text{ of } 42 = \square \]
Unit fractions with larger denominators.
Unit fractions of 3-digit amounts
Find half of 3-digit amounts
\[ \frac{1}{2} \text{ of } 246 = \square \]
Divide 3-digit numbers by 2.
Find quarter of 3-digit amounts
\[ \frac{1}{4} \text{ of } 348 = \square \]
Divide 3-digit numbers by 4.
Find tenth of 3-digit amounts
\[ \frac{1}{10} \text{ of } 350 = \square \]
Divide 3-digit numbers by 10.
Find third of 3-digit amounts
\[ \frac{1}{3} \text{ of } 369 = \square \]
Divide 3-digit numbers by 3.
Find fifth of 3-digit amounts
\[ \frac{1}{5} \text{ of } 425 = \square \]
Divide 3-digit numbers by 5.
Find 1/6 to 1/12 of 3-digit
\[ \frac{1}{8} \text{ of } 256 = \square \]
Larger denominators with 3-digit amounts.
Non-unit fractions of 2-digit amounts
Find three-quarters of 2-digit
\[ \frac{3}{4} \text{ of } 48 = \square \]
Divide by 4, multiply by 3.
Find two-thirds of amounts
\[ \frac{2}{3} \text{ of } 36 = \square \]
Divide by 3, multiply by 2.
Find non-unit fifths of 2-digit
\[ \frac{3}{5} \text{ of } 45 = \square \]
Find 2/5, 3/5, or 4/5.
Find non-unit tenths of amounts
\[ \frac{7}{10} \text{ of } 80 = \square \]
Find 3/10, 7/10, or 9/10.
Find other non-unit fractions
\[ \frac{5}{6} \text{ of } 42 = \square \]
Fractions like 5/6, 3/8, 7/8.
Non-unit fractions of 3-digit amounts
Find three-quarters of 3-digit
\[ \frac{3}{4} \text{ of } 240 = \square \]
Three-quarters of larger amounts.
Find non-unit fifths of 3-digit
\[ \frac{4}{5} \text{ of } 350 = \square \]
2/5, 3/5, 4/5 of 3-digit numbers.
Find other non-unit of 3-digit
\[ \frac{5}{8} \text{ of } 240 = \square \]
Various fractions of 3-digit amounts.
Finding the whole from unit fractions
Half known → 2-digit answer
\[ \frac{1}{2} \text{ of } \square = 24 \]
Find the whole when half is given.
Half known → 3-digit answer
\[ \frac{1}{2} \text{ of } \square = 86 \]
Larger answers from known half.
Quarter known → find whole
\[ \frac{1}{4} \text{ of } \square = 15 \]
Multiply by 4 to find the whole.
Tenth known → find whole
\[ \frac{1}{10} \text{ of } \square = 7 \]
Multiply by 10 to find the whole.
Third or fifth known → whole
\[ \frac{1}{3} \text{ of } \square = 12 \]
Find whole from 1/3 or 1/5.
Other unit fraction → whole
\[ \frac{1}{8} \text{ of } \square = 6 \]
Find whole from 1/6, 1/7, 1/8, 1/9.
Finding the whole from non-unit fractions
Three-quarters known → whole
\[ \frac{3}{4} \text{ of } \square = 18 \]
Divide by 3, multiply by 4.
Two-thirds known → whole
\[ \frac{2}{3} \text{ of } \square = 24 \]
Divide by 2, multiply by 3.
Non-unit fifth known → whole
\[ \frac{2}{5} \text{ of } \square = 16 \]
Find whole from 2/5, 3/5, or 4/5.
Non-unit tenth known → whole
\[ \frac{3}{10} \text{ of } \square = 21 \]
Find whole from 3/10, 7/10, 9/10.
Other non-unit fraction → whole
\[ \frac{5}{8} \text{ of } \square = 25 \]
Find whole from 5/8, 5/6, etc.
Finding one fraction from another
Unit → non-unit (same denom)
\[ \frac{1}{4} = 7, \text{ so } \frac{3}{4} = \square \]
Use unit fraction to find non-unit.
Non-unit → unit (same denom)
\[ \frac{3}{4} = 21, \text{ so } \frac{1}{4} = \square \]
Find unit fraction from non-unit.
Non-unit → different non-unit
\[ \frac{2}{5} = 14, \text{ so } \frac{3}{5} = \square \]
Convert between non-unit fractions.
Convert halves and quarters
\[ \frac{1}{4} = 9, \text{ so } \frac{1}{2} = \square \]
Relationship between 1/2 and 1/4.
Related different denominators
\[ \frac{1}{3} = 12, \text{ so } \frac{1}{6} = \square \]
Find fraction with related denominator.
Special cases
Find multiple related fractions
\[ \frac{1}{4} \text{ of } 40 = \square, \; \frac{3}{4} = \square \]
Find two or more related fractions.
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