Question

1. $1.4 + (- 3.1) + (- 4.5) =$
2. $-\frac{1}{7} + (-\frac{4}{7}) =$
3. $-\frac{3}{8} + \frac{1}{2} =$

Explanation:

Problem 4: \( 1.4 + (-3.1) + (-4.5) \)

Step 1: Add the first two terms

\( 1.4 + (-3.1) = 1.4 - 3.1 = -1.7 \)

Step 2: Add the result to the third term

\( -1.7 + (-4.5) = -1.7 - 4.5 = -6.2 \)

Step 1: Combine the fractions (same denominator)

When adding two negative fractions with the same denominator, we add the numerators and keep the denominator. So, \( -\frac{1}{7} - \frac{4}{7} = \frac{-1 - 4}{7} \)

Step 2: Simplify the numerator

\( -1 - 4 = -5 \), so the result is \( \frac{-5}{7} = -\frac{5}{7} \)

Step 1: Find a common denominator

The common denominator of 8 and 2 is 8. Convert \( \frac{1}{2} \) to eighths: \( \frac{1}{2} = \frac{4}{8} \)

Step 2: Add the fractions

\( -\frac{3}{8} + \frac{4}{8} = \frac{-3 + 4}{8} = \frac{1}{8} \)

Answer:

\( -6.2 \)

Problem 2: \( -\frac{1}{7} + (-\frac{4}{7}) \)