Fractions and Operations with Fractions
The Fractions domain on Grade 5 FAST Math extends earlier fraction work in three directions: adding and subtracting fractions and mixed numbers with unlike denominators, multiplying fractions by whole numbers and by other fractions, and dividing with unit fractions. It also connects fractions to division and to area, so a single item may ask you to find the area of a rectangle with fractional side lengths or interpret a fraction as a quotient.
Core rules
- To add or subtract unlike denominators, rename with a common denominator, then combine numerators. Keep the denominator.
- Regroup when subtracting mixed numbers: 5 1/4 − 2 3/4 becomes 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2.
- Multiply fractions by multiplying numerators and denominators: 2/3 × 3/4 = 6/12 = 1/2.
- Multiplying by a fraction less than 1 makes a product smaller than the starting number; multiplying by a whole number greater than 1 can make it larger.
- Dividing a unit fraction by a whole number makes a smaller unit fraction: 1/2 ÷ 3 = 1/6.
- Dividing a whole number by a unit fraction asks how many unit fractions fit: 3 ÷ 1/4 = 12.
- A fraction a/b also means a ÷ b.
Worked example
Find 3/4 ÷ 2. Sharing 3/4 into 2 equal groups means finding half of 3/4. Half of three fourths is three eighths: 3/4 × 1/2 = 3/8. Check by multiplying back: 3/8 × 2 = 6/8 = 3/4.
Traps that cost marks
- Adding denominators, as in 1/2 + 1/3 = 2/5. Denominators name the size of the parts and are not added.
- Multiplying a fraction by a whole number by multiplying both numerator and denominator, which changes the value.
- Confusing 3 ÷ 1/4 with 1/4 ÷ 3. The first is 12; the second is 1/12.
- Forgetting to simplify or to convert an improper fraction to a mixed number when the answer choices are mixed numbers.
- In area problems, multiplying only the whole-number parts of mixed-number side lengths.