Procedure: Multiplying a Whole Number by a Fraction
Multiplying a Whole Number by a Fraction is a Grade 5 math procedure from Illustrative Mathematics Chapter 2 (Fractions as Quotients and Fraction Multiplication) that states: (a/b) × c = (a × c)/b. Students multiply the numerator by the whole number and keep the denominator unchanged. This builds on finding a unit fraction of a number and extends to any non-unit fraction, producing results that may 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
How do you multiply a whole number by a fraction?
Multiply the numerator of the fraction by the whole number and keep the denominator the same. The formula is (a/b) × c = (a × c)/b. For example, (2/3) × 9 = (2 × 9)/3 = 18/3 = 6.
What is the procedure for fraction times whole number in Grade 5?
Multiply the numerator by the whole number: (a/b) × c = (a × c)/b. Then simplify if possible. For example, (3/5) × 4 = (3 × 4)/5 = 12/5, which remains as an improper fraction or can be written as 2 2/5.
What chapter covers fraction multiplication in Illustrative Mathematics Grade 5?
Multiplying a whole number by a fraction is covered in Chapter 2 of Illustrative Mathematics Grade 5, titled Fractions as Quotients and Fraction Multiplication.
Why does the denominator stay the same when multiplying a fraction by a whole number?
The denominator represents the size of each equal part. Multiplying by a whole number increases how many parts you have (numerator), but does not change the size of each part (denominator).
How does multiplying a fraction by a whole number relate to unit fractions?
Finding (2/3) × 9 is the same as finding (1/3) of 9 and taking 2 of those parts. (1/3) of 9 = 3, so 2 × 3 = 6. Multiplying the numerator by the whole number directly shortcodes this two-step process.