Consider this expression:
1/4 − 0.5 + 1/2− 0.25 + 3/5+ 0.4You are asked to find the sum by using fractions. Which expression could you use?
Responses
A 14
− 1/2
+ 1/2
− 1/4
+ 3/5
+ 2/5
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
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
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
1 /4 − 1/ 2 − 1 /2 − 1 /4 + 3/ 5 + 2/ 5
The correct expression that can be used to find the sum of the given expression is:
C) 1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5
This expression correctly represents the given expression and sums up all the fractions.
To find the sum of the given expression using fractions, we need to evaluate each term separately and then add them up.
The given expression is: 1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4
To organize the expression using fractions, we can write it as:
1/4 - 1/2 + 1/2 - 1/4 + 3/5 + 2/5
Now we can simplify each term:
1/4 - 1/2 = -1/4 (the fractions have a common denominator of 4, so we can subtract the numerators)
1/2 - 1/4 = 1/4 (the fractions have a common denominator of 4, so we can subtract the numerators)
3/5 + 2/5 = 5/5 = 1 (the fractions have a common denominator of 5, so we can add the numerators)
Now we can substitute the simplified terms back into the expression:
-1/4 + 1/4 - 1/4 + 1 + 1/4
Combine the like terms:
-1/4 - 1/4 + 1/4 + 1 + 1/4 = -1/4 + 1/4 + 1/4 + 1 + 1/4 = 1 + 1/4
Therefore, the expression that represents the given expression when simplified using fractions is:
A) 1/4 - 1/2 + 1/2 - 1/4 + 3/5 + 2/5 = 1 + 1/4
To find the sum using fractions, you need to add or subtract the fractions in the given expression. Let's break down the expression and compare it with the options given to find the correct one.
The given expression is:
1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4
To perform addition or subtraction with fractions, we need to make sure they have common denominators. Let's convert the decimals to fractions with common denominators in order to compare the expression with the options.
0.5 is equivalent to 1/2 since 0.5 divided by 1 is the same as 1 divided by 2.
0.25 is equivalent to 1/4 since 0.25 divided by 1 is the same as 1 divided by 4.
0.4 is equivalent to 2/5 since 0.4 divided by 1 is the same as 2 divided by 5.
Now let's compare the options with the converted expression.
Option A: 1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5
In this option, all the fractions have the same denominators as the converted expression. So this option is a valid expression to represent the given sum.
Option B: 1/4 − 1/4 + 1/2 − 1/4 + 3/5 + 2/5
In this option, the first term 1/4 is correct, but the expression starts with subtracting 1/4 instead of adding 1/4 as in the given expression. So this option is incorrect.
Option C: 1/4 − 1/2 + 1/2 − 1/4 + 4/5 + 2/5
In this option, the last term is different from the converted expression. The converted expression has 3/5 for the last term, but option C has 4/5. So this option is incorrect.
Option D: 1/4 − 1/2 − 1/2 − 1/4 + 3/5 + 2/5
In this option, the expression has an extra term of -1/2 in the middle, which is not present in the given expression. So this option is incorrect.
Therefore, the expression that represents the given sum using fractions is Option A:
1/4 − 1/2 + 1/2 − 1/4 + 3/5 + 2/5