Add and Subtract Rational Numbers

Question

Consider this expression:

















− 0.5 +
















− 0.25 +
















+ 0.4
Question 1
You 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
Question 2
Find the sum.

Answer 1

To solve the expression:

\[ −0.5 + (−0.25) + 0.4 \]

we first convert the decimals into fractions.

1. Convert the decimals:
   • \( -0.5 = -\frac{1}{2} \)
   • \( -0.25 = -\frac{1}{4} \)
   • \( 0.4 = \frac{2}{5} \)

Now we rewrite the expression using fractions:

\[ -\frac{1}{2} + \left(-\frac{1}{4}\right) + \frac{2}{5} \]

Next, we look for a common denominator to add these fractions. The denominators are 2, 4, and 5. The least common multiple (LCM) of these numbers is 20.

2. Convert each fraction to have a common denominator of 20:
   • \( -\frac{1}{2} = -\frac{10}{20} \)
   • \( -\frac{1}{4} = -\frac{5}{20} \)
   • \( \frac{2}{5} = \frac{8}{20} \)

Now the expression becomes:

\[ -\frac{10}{20} - \frac{5}{20} + \frac{8}{20} \]

3. Combine the fractions:

   • First, add the negative fractions:

   \[ -\frac{10}{20} - \frac{5}{20} = -\frac{15}{20} \]

   • Then, add the resulting fraction with \( \frac{8}{20} \):

   \[ -\frac{15}{20} + \frac{8}{20} = -\frac{15 - 8}{20} = -\frac{7}{20} \]

The sum of the expression \( -0.5 + (-0.25) + 0.4 \) is:

\[ -\frac{7}{20} \]

Answers to Questions:

Question 1: Which expression could you use?

• The correct response would be A: \[ -\frac{1}{4} - \frac{1}{2} + \frac{1}{2} - \frac{1}{4} + \frac{3}{5} + \frac{2}{5} \]

Question 2: Find the sum.

• The sum is: \[ -\frac{7}{20} \]