Leanne is making a recipe that calls for $\frac{2}{3}$ teaspoon of salt, but she uses only $\frac{1}{2}$ that amount. How much salt does she use?
A. $\frac{1}{6}$ teaspoon
B. $\frac{1}{3}$ teaspoon
C. $\frac{3}{4}$ teaspoon
D. $\frac{7}{6}$ teaspoon
Answer (1)
Multiply the fractions: 2 1 × 3 2 = 6 2 .
Simplify the resulting fraction: 6 2 = 3 1 .
Leanne uses 3 1 teaspoon of salt.
The final answer is 3 1 teaspoon .
Explanation
Understanding the Problem Let's break down this problem. Leanne is using a fraction of a fraction of salt. The recipe calls for 3 2 teaspoon of salt, but she only uses 2 1 of that amount. This means we need to find what 2 1 of 3 2 is.
Setting up the Calculation To find a fraction of a fraction, we multiply the two fractions together. So, we need to calculate 2 1 × 3 2 .
Multiplying the Fractions When multiplying fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers). So, we have: 2 1 × 3 2 = 2 × 3 1 × 2 = 6 2
Simplifying the Fraction Now, we simplify the fraction 6 2 . Both the numerator and the denominator are divisible by 2. Dividing both by 2, we get: 6 2 = 6 ÷ 2 2 ÷ 2 = 3 1
Finding the Answer So, Leanne uses 3 1 teaspoon of salt. Looking at the answer choices, we see that B 3 1 teaspoon is the correct answer.
Examples
Fractions are used in cooking all the time! Imagine you're baking a cake, and the recipe calls for 4 3 cup of flour. But you only want to make half a cake. To figure out how much flour you need, you would multiply 2 1 × 4 3 to get 8 3 cup of flour. This is just one example of how understanding fractions can help you in the kitchen.
