Number and Operations-Fractions
What this domain covers
Number and Operations-Fractions tests equivalent fractions, comparing fractions with unlike denominators, adding and subtracting fractions with like denominators, multiplying a fraction by a whole number, and writing fractions with denominators 10 or 100 as decimals.
Core rules to know
- Equivalent fractions: multiply or divide numerator and denominator by the same nonzero number. 3/4 = 6/8 = 9/12.
- Comparing: rewrite with a common denominator, or compare to a benchmark such as 1/2. For 2/3 and 3/5, use fifteenths: 10/15 > 9/15.
- Like denominators: add or subtract numerators and keep the denominator. 3/8 + 2/8 = 5/8.
- Fraction times whole number: use repeated addition. 4 × 2/3 = 8/3 = 2 2/3.
- Decimals: 7/10 = 0.7; 43/100 = 0.43. Tenths and hundredths are place-value positions.
Worked example
A recipe uses 3/8 cup of oil. Making four batches uses 4 × 3/8 cup. 4 × 3/8 = (4 × 3)/8 = 12/8 = 1 4/8 = 1 1/2 cups. The denominator names the size of the pieces; multiplying by 4 gives 12 eighths, then regroup to a mixed number.
Traps that cost marks
- Adding denominators: 1/4 + 2/4 is 3/4, not 3/8.
- Comparing numerators alone when denominators differ.
- Forgetting to convert an improper fraction to a mixed number when the answer calls for it.
- Writing 0.4 for 4/100 (that is 0.04).
- Treating a whole number as a fraction without putting it over 1.