A flour jar contains $123 / 5$ cups of flour. If a recipe to make a cake calls for 2 $1 / 10$ cups of flour, how many cakes can be made with the flour?
Answer (2)
The student has enough flour to make 6 cakes. After converting the mixed fractions to improper fractions, we divide the total flour by the flour needed for one cake. The final result is that 6 cakes can be prepared.
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Convert the mixed fractions to improper fractions: 12 5 3 = 5 63 and 2 10 1 = 10 21 .
Divide the total amount of flour by the amount needed for one cake: 5 63 ÷ 10 21 .
Simplify the division: 5 63 × 21 10 = 6 .
Conclude that 6 cakes can be made: 6 .
Explanation
Understanding the Problem We are given that a flour jar contains 12 5 3 cups of flour and a recipe for a cake requires 2 10 1 cups of flour. We need to find out how many cakes can be made with the available flour.
Converting to Improper Fractions First, convert the mixed fractions to improper fractions. 12 5 3 = 5 12 × 5 + 3 = 5 60 + 3 = 5 63 2 10 1 = 10 2 × 10 + 1 = 10 20 + 1 = 10 21
Dividing the Fractions Now, divide the total amount of flour by the amount of flour required for each cake. 5 63 ÷ 10 21 = 5 63 × 21 10 Simplify the fraction by canceling common factors. 5 63 × 21 10 = 5 3 × 21 × 21 2 × 5 = 5 × 21 3 × 2 × 21 × 5 = 3 × 2 = 6
Finding the Number of Cakes Therefore, 6 cakes can be made with the given amount of flour.
Examples
Understanding how to divide quantities is essential in many real-life situations. For example, if you are planning a party and need to determine how many pizzas to order, you would divide the total number of guests by the number of slices each person is likely to eat. Similarly, if you are a construction worker and need to determine how many bags of cement to buy for a project, you would divide the total volume of cement needed by the volume of cement in each bag. These types of calculations are fundamental to efficient planning and resource management.
