Question
Add and Subtract Rational Numbers
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.
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.
Answers
GPT-4o mini
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:
\[
-\frac{7}{20}
\]
\[
−0.5 + (−0.25) + 0.4
\]
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:
\[
-\frac{7}{20}
\]