Number and Operations-Fractions: Unlike Denominators, Multiplication, and Division
Number and Operations-Fractions in Grade 5 extends to unlike denominators, multiplication and division involving fractions, and multiplication as scaling.
Fractions as division and equivalent fractions
A fraction a/b means a ÷ b, so 3 ÷ 4 = 3/4 and 7/4 = 1 3/4. To add or subtract unlike denominators, build equivalent fractions with a common denominator, combine numerators, and keep the denominator: 2/3 + 1/4 = 8/12 + 3/12 = 11/12. For mixed numbers, regroup when needed: 5 1/4 − 2 3/4 = 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2.
Multiplying fractions
Multiply numerator by numerator and denominator by denominator; a whole number n can be written as n/1. An area model shows why: 3/4 × 2/3 is the overlap of 3 of 4 columns and 2 of 3 rows, or 6 of 12 equal parts = 1/2.
Multiplication as scaling
Multiplying by a fraction less than 1 makes the product smaller than the starting number; multiplying by a fraction greater than 1 makes it larger; multiplying by 1 leaves it unchanged. Therefore 3/4 × 8 < 8, while 5/4 × 8 > 8.
Dividing with unit fractions
Interpret 4 ÷ 1/3 as “how many one-thirds are in 4?” - 12. Interpret 1/3 ÷ 4 as sharing one-third among 4 equal groups - 1/12. Use a model or a story rather than a memorized “flip” rule, which belongs to Grade 6.
Worked example
Multiply 2/3 × 3/4 with an area model. Draw a rectangle split into 3 rows and 4 columns, making 12 equal parts. Shade 2 rows for 2/3 and 3 columns for 3/4. The overlap is 6 parts, so the product is 6/12 = 1/2.
Traps that cost marks
- Adding denominators: 2/3 + 1/4 is not 3/7.
- Forgetting to regroup in mixed-number subtraction.
- Confusing 1/3 ÷ 4 with 4 ÷ 1/3.
- Assuming multiplication always makes a number larger.