Manda finished her English assignment in $\frac{1}{2}$ hours. Then she completed her history assignment in $\frac{4}{5}$ hours. How much more time did she spend on her history assignment?
Answer (1)
Find the difference between the time spent on the history assignment and the English assignment: 5 4 − 2 1 .
Find a common denominator, which is 10.
Convert the fractions: 5 4 = 10 8 and 2 1 = 10 5 .
Subtract the fractions: 10 8 − 10 5 = 10 3 . The history assignment took 10 3 hours more than the English assignment.
Explanation
Understanding the Problem We are given that Amanda finished her English assignment in 2 1 hours and her history assignment in 5 4 hours. We need to find how much more time she spent on the history assignment compared to the English assignment.
Setting up the Subtraction To find the difference in time, we need to subtract the time spent on the English assignment from the time spent on the history assignment. This can be written as: 5 4 − 2 1
Finding a Common Denominator To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 2 is 10. So, we will convert both fractions to have a denominator of 10.
Converting the Fractions To convert 5 4 to a fraction with a denominator of 10, we multiply both the numerator and the denominator by 2: 5 4 × 2 2 = 10 8 To convert 2 1 to a fraction with a denominator of 10, we multiply both the numerator and the denominator by 5: 2 1 × 5 5 = 10 5
Subtracting the Fractions Now we can subtract the fractions: 10 8 − 10 5 = 10 8 − 5 = 10 3
Final Answer The difference in time spent on the two assignments is 10 3 hours.
Examples
Understanding fractions is crucial in everyday life. For instance, when baking, you often need to measure ingredients using fractions. If a recipe calls for 4 3 cup of flour and you only want to make half the recipe, you need to calculate half of 4 3 , which involves multiplying fractions. This skill ensures your baked goods turn out perfectly!
