Procedure: Multiplying a Whole Number by a Fraction
Multiplying a Whole Number by a Fraction (second entry) is a Grade 5 math procedure from Illustrative Mathematics Chapter 2 (Fractions as Quotients and Fraction Multiplication) teaching students that (a/b) × c = (a × c)/b — multiply the numerator by the whole number and keep the denominator unchanged. This procedure builds directly on unit fraction multiplication and produces results that can be proper fractions, improper fractions, or whole numbers.
Key Concepts
To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same. $$\frac{a}{b} \times c = \frac{a \times c}{b}$$.
Common Questions
What is the rule for multiplying a fraction by a whole number?
Multiply the numerator by the whole number and keep the denominator the same: (a/b) × c = (a × c)/b. For example, (2/3) × 9 = (2 × 9)/3 = 18/3 = 6.
What does the fraction multiplication procedure look like step by step?
Step 1: Write (a/b) × c. Step 2: Multiply numerator: a × c. Step 3: Keep denominator b unchanged. Step 4: Simplify if possible. Example: (3/5) × 4 = 12/5.
What chapter in Illustrative Mathematics Grade 5 covers this fraction multiplication procedure?
This procedure is covered in Chapter 2 of Illustrative Mathematics Grade 5, titled Fractions as Quotients and Fraction Multiplication.
How does multiplying (2/3) × 9 relate to unit fractions?
Finding (2/3) × 9 equals finding (1/3) of 9 twice: (1/3) × 9 = 3, and 2 × 3 = 6. Multiplying the numerator by the whole number is a direct shortcut for this two-step process.
When does multiplying a fraction by a whole number give a whole number result?
When the whole number is divisible by the denominator. For example, (2/3) × 9: 9 is divisible by 3, so 18/3 = 6, a whole number. When there's no exact divisibility, the result is an improper fraction.