Consider this expression:
1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4
ou are asked to find the sum by using fractions. Which expression could you use?
Responses
A
1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
B
1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5
C
1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5
D
1/4 - 1/2 - 1/2 - 1/4 + 3/5 + 2/5
B
1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5
To find the sum of the expression using fractions, we need to combine like terms. Looking at the expression, we can see that the fractions have the same denominators. So, we can add the numerators together and keep the denominator the same.
Let's go through each option one by one to see which one matches the given expression:
A) 1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
B) 1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5
C) 1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5
D) 1/4 - 1/2 - 1/2 - 1/4 + 3/5 + 2/5
By simplifying each option, we find that option B matches the given expression:
1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5
Therefore, the correct expression to use is option B.
To find the sum using fractions, you need to simplify the expression by combining like terms. In this case, the like terms are fractions with the same denominator. The denominator in this expression is 5.
Let's evaluate each expression to determine which one can be simplified:
A: 1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5 = (1/4 - 1/4) + (1/2 + 1/2) + (3/5 + 2/5) = 0 + 1 + 5/5 = 1 + 1 = 2
B: 1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5 = (1/4 - 1/4) + (1/2 + 1/2) + (3/5 + 2/5) = 0 + 1 + 5/5 = 1 + 1 = 2
C: 1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5 = (1/4 - 1/4) + (1/2 + 1/2) + (4/5 + 2/5) = 0 + 1 + 6/5 = 1 + 6/5 = 11/5
D: 1/4 - 1/2 - 1/2 - 1/4 + 3/5 + 2/5 = (1/4 - 1/4) + (-1/2 - 1/2) + (3/5 + 2/5) = 0 - 1 - 1 + 5/5 = -2 + 1 = -1
Only option C: 1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5 results in a sum of 11/5.