Add and Subtract Rational Numbers
Consider this expression:
14 − 0.5 + 12 − 0.25 + 35 + 0.4
Question 1
You are asked to find the sum by using fractions. Which expression could you use?
Responses
A 14 − 12 + 12 − 14+ 35 + 251 4 − 1 2 + 1 2 − 1 4 + 3 5 + 2 5
B 14 − 14 + 12 − 14+ 35 + 251 4 − 1 4 + 1 2 − 1 4 + 3 5 + 2 5
C 14 − 12 + 12 − 14+ 45 + 251 4 − 1 2 + 1 2 − 1 4 + 4 5 + 2 5
D 14 − 12 − 12 − 14+ 35 + 25
The correct expression to find the sum by using fractions would be:
A) 14 − 12 + 12 − 14+ 35 + 25/14 − 1/2 + 1/2 − 1/4 + 35 + 2/5
To find the sum of the given expression using fractions, you need to rewrite the decimal numbers as fractions first.
14 − 0.5 can be written as 14 − 1/2
12 − 0.25 can be written as 12 − 1/4
35 + 0.4 can be written as 35 + 2/5
Now, let's look at the answer choices:
A) 14 − 12 + 12 − 14 + 35 + 2/5
B) 14 − 14 + 12 − 14 + 35 + 2/5
C) 14 − 12 + 12 − 14 + 45 + 2/5
D) 14 − 12 − 12 − 14 + 35 + 25
Among the answer choices, option A correctly represents the given expression with the decimal numbers replaced by their corresponding fractions. So, the answer is A.
To find the sum using fractions, we need to convert the decimal numbers to fractions.
Converting the decimal numbers to fractions:
0.5 = 1/2
0.25 = 1/4
0.4 = 2/5
Now, we can rewrite the expression:
14 - 1/2 + 12 - 1/4 + 35 + 2/5
To add and subtract rational numbers, we need to find a common denominator. In this case, the common denominator is 20. Let's rewrite the expression with the common denominator:
(14 * 20) / 20 - (1/2 * 20) / 20 + (12 * 20) / 20 - (1/4 * 20) / 20 + (35 * 20) / 20 + (2/5 * 20) / 20
Simplifying:
(280/20) - (10/20) + (240/20) - (5/20) + (700/20) + (8/20)
Next, we can add and subtract the fractions:
280/20 - 10/20 + 240/20 - 5/20 + 700/20 + 8/20
= (280 - 10 + 240 - 5 + 700 + 8) / 20
= 1253/20
So, the correct expression out of the given options is:
A) 14 - 1/2 + 12 - 1/4 + 35 + 2/5 = 1253/20