Solve Word Problems Involving Fraction Multiplication
Solving Word Problems Involving Fraction Multiplication is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) that teaches students to recognize when a situation calls for finding a fractional part of a quantity and set up the expression part = fraction × whole. Common contexts include scaling recipes, calculating distances, and finding portions of measured amounts.
Key Concepts
Property To find a fractional part of a quantity, you multiply the fraction by the quantity. This applies to situations involving scaling recipes, calculating distances, or finding a portion of a given amount. The operation is represented as: $$ \text{part} = \text{fraction} \times \text{whole} $$.
Examples A recipe calls for $\frac{3}{4}$ cup of sugar. If you are making $\frac{1}{2}$ of the recipe, how much sugar do you need? $$ \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \text{ cup of sugar} $$ A runner wants to complete $\frac{2}{3}$ of a race that is $\frac{9}{10}$ of a mile long. What distance did the runner cover? $$ \frac{2}{3} \times \frac{9}{10} = \frac{18}{30} = \frac{3}{5} \text{ of a mile} $$.
Explanation This skill involves translating real world scenarios into fraction multiplication problems. Key phrases like "fraction of a quantity" or "part of a total" often indicate that multiplication is needed. To solve, you multiply the numerators together and the denominators together to find the resulting fraction. This skill extends the concept of "fraction of a fraction" to a wider variety of practical applications.
Common Questions
How do you set up a word problem involving fraction multiplication?
Identify the fraction and the whole quantity in the problem. The key phrases are often "fraction of a quantity" or "part of a total." Set up the equation: part = fraction × whole. Multiply the numerators and denominators separately to find the result.
What are examples of fraction multiplication word problems?
A recipe uses 3/4 cup of sugar and you make 1/2 the recipe: (1/2) × (3/4) = 3/8 cup. A runner completes 2/3 of a 9/10-mile race: (2/3) × (9/10) = 18/30 = 3/5 mile.
What chapter covers fraction multiplication word problems in Illustrative Mathematics Grade 5?
Solving word problems involving fraction multiplication is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
What keyword signals that you need to multiply fractions in a word problem?
The word "of" when connecting a fraction to a quantity usually signals multiplication. Phrases like "a fraction of the total," "half of the remaining," or "2/3 of a distance" all indicate fraction multiplication.
How do you multiply two fractions in a word problem?
Multiply the numerators together and multiply the denominators together. Then simplify the result if possible. For (1/2) × (3/4): numerators 1 × 3 = 3, denominators 2 × 4 = 8, result = 3/8.