Math Problem Statement

Johan's cookie recipe calls for 1 1 3 1 3 1 ​ cups of sugar. Today he wants to make a half batch of cookies.

How much sugar will Johan need to use?

Solution

Johan's cookie recipe calls for 1131 \frac{1}{3} cups of sugar. To make a half batch, we need to calculate half of 1131 \frac{1}{3} cups.

First, convert the mixed number 1131 \frac{1}{3} into an improper fraction:

113=431 \frac{1}{3} = \frac{4}{3}

Now, calculate half of 43\frac{4}{3}:

12×43=46=23\frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}

So, Johan will need 23\frac{2}{3} cups of sugar for a half batch of cookies.

Would you like further details or have any questions?

Here are 5 related questions for practice:

  1. If Johan wanted to make a double batch, how much sugar would he need?
  2. How would you calculate a quarter batch of the recipe?
  3. If the recipe calls for 2 cups of flour, how much would be needed for a half batch?
  4. What if the recipe called for 1121 \frac{1}{2} cups of butter—how much for a half batch?
  5. How can you convert mixed numbers to improper fractions?

Tip: To divide mixed numbers or fractions, always convert them into improper fractions first for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Multiplication of Fractions

Formulas

Converting Mixed Numbers to Improper Fractions
Multiplying Fractions

Theorems

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Suitable Grade Level

Grades 5-7