Janet made a shirt using $\frac{5}{8}$ yards of blue fabric and $\frac{1}{2}$ yards of yellow fabric. How many more yards of blue fabric did she use? Write your answer as a fraction in simplest form.
Answer (1)
Set up the subtraction problem: 8 5 − 2 1 .
Find a common denominator: 2 1 = 8 4 .
Subtract the fractions: 8 5 − 8 4 = 8 1 .
The difference is 8 1 yards.
Explanation
Understanding the problem We are given that a shirt was made using 8 5 yards of blue fabric and 2 1 yards of yellow fabric. We need to find how many more yards of blue fabric were used than yellow fabric. This involves subtracting the amount of yellow fabric from the amount of blue fabric.
Setting up the subtraction To find the difference, we subtract the amount of yellow fabric from the amount of blue fabric: 8 5 − 2 1
Finding a common denominator To subtract these fractions, we need a common denominator. The least common denominator (LCD) of 8 and 2 is 8. We convert the fraction 2 1 to an equivalent fraction with a denominator of 8: 2 1 = 2 × 4 1 × 4 = 8 4
Subtracting the fractions Now we can subtract the fractions: 8 5 − 8 4 = 8 5 − 4 = 8 1
Final Answer The result is 8 1 . We check if the fraction can be simplified. Since 1 and 8 have no common factors other than 1, the fraction is already in simplest form. Therefore, 8 1 yards more of blue fabric was used.
Examples
Imagine you're baking a cake and the recipe calls for 8 5 cup of sugar and 2 1 cup of flour. This problem helps you determine how much more sugar you need compared to flour. Understanding fraction subtraction is crucial in cooking, construction, and many other fields where precise measurements are essential. By mastering these concepts, you can accurately adjust recipes, measure materials, and ensure your projects are perfectly balanced.
