I am a mom that can't figure out how to help my daughter with this problem.
Alicia is making pies. She uses 1 1/2 cups of sugar for every 2 pies. She has 5 1/4 cups left. How many more pies can she make?
I think the answer is 7 pies but not sure how to teach her how do figure this out. Do I take the 1 1/2 and convert to 3/2 and the 5 1/4 to 21/4 and add together to get 27/4?
help please
Thanks
To solve this problem, you have essentially divided it into two steps: converting the mixed numbers to fractions and then adding them together. However, you made a mistake in your calculation.
Let's break it down step by step and explain how to solve this problem correctly.
Step 1: Convert the mixed numbers to fractions
- The mixed number 1 1/2 can be written as the improper fraction (3/2) because there are 1 whole pie and 1/2 of another pie.
- The mixed number 5 1/4 can be written as the improper fraction (21/4) because there are 5 whole pies and 1/4 of another pie.
Step 2: Add the fractions
To find out how many pies can be made, we need to subtract the amount of sugar used from the amount of sugar left.
- The amount of sugar used for each set of 2 pies is 3/2 cups.
- The amount of sugar left is 21/4 cups.
To find out how many more sets of 2 pies can be made, we need to divide the amount of sugar left by the amount of sugar used for each set of 2 pies.
Step 3: Divide the fractions
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(21/4) ÷ (3/2) can be rewritten as (21/4) × (2/3).
Multiplying the numerators gives 42, and multiplying the denominators gives 12.
So, (21/4) ÷ (3/2) = 42/12.
Step 4: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator (42 and 12 respectively), which is 6.
Divide both the numerator and denominator by 6:
42 ÷ 6 = 7
12 ÷ 6 = 2
So, 42/12 simplifies to 7/2.
Step 5: Interpret the fraction
The simplified fraction 7/2 means that Alicia can make an additional 7/2 sets of 2 pies. Since we cannot have half of a set, we need to convert this fraction to a mixed number.
7 divided by 2 equals 3 with a remainder of 1. So, the mixed number is 3 1/2.
Therefore, Alicia can make an additional 3 1/2 sets of 2 pies, which is equivalent to 7 more pies.
To summarize, based on the given amount of sugar left, Alicia can make 7 more pies.
1 1 / 2 = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2
If She uses 1 1/2 cups of sugar for every 2 pies she use
( 1 1 / 2 ) / 2 = ( 3 / 2 ) / 2 = 3 / 4 cup for one pie.
5 1 / 4 = 5 + 1 / 4 = 20 / 4 + 1 / 4 = 21 / 4
5 1 / 4 / ( 3 / 4 ) = 21 / 4 / ( 3 / 4 ) = 21 / 3 = 7 pies