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Let's work through the questions in the image step by step.

### 5. Use the expression \( -\frac{1}{3} - \left( -\frac{5}{12} \right) \).

#### Part (a): Which shows an equivalent addition expression?

This question asks us to rewrite the subtraction as addition. To do that, we apply the rule that subtracting a negative is the same as adding a positive:
\[
-\frac{1}{3} - \left( -\frac{5}{12} \right) = -\frac{1}{3} + \frac{5}{12}
\]

So, the equivalent addition expression is \( -\frac{1}{3} + \frac{5}{12} \).

The correct answer is **(B)**.

#### Part (b): Represent and Connect - Draw the point on the number line that represents \( -\frac{1}{3} - \left( -\frac{5}{12} \right) \).

First, we need to calculate the exact value of the expression \( -\frac{1}{3} + \frac{5}{12} \).

- Convert \( \frac{1}{3} \) to a fraction with the same denominator as \( \frac{5}{12} \). We have:
  \[
  -\frac{1}{3} = -\frac{4}{12}
  \]
- Now, add \( -\frac{4}{12} + \frac{5}{12} = \frac{1}{12} \).

So the value of the expression is \( \frac{1}{12} \).

On the number line, \( \frac{1}{12} \) is a small positive value. You can place a point slightly to the right of 0, closer to 0 than to 0.1, as \( 0.083 \) (or \( 1/12 \)) is about 1/12 of the way between 0 and 1.

#### Part (c): Find the value of the expression \( -\frac{1}{3} - \left( -\frac{5}{12} \right) \).

We already calculated this in part (b):
\[
-\frac{1}{3} + \frac{5}{12} = \frac{1}{12}.
\]

So, the value of the expression is \( \frac{1}{12} \) or approximately 0.083.

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Do you want further details on any of the steps? 

Here are 5 related questions you might find useful:

1. How do you add fractions with different denominators?
2. What is the rule for subtracting a negative number?
3. How do you convert decimals to fractions?
4. What are other ways to visualize fractions on a number line?
5. How would you solve similar problems involving subtraction of fractions?

**Tip**: When subtracting negative numbers, remember to "flip" the sign and change it to addition.

Use the expression -1/3 - (-5/12). Which shows an equivalent addition expression? Represent and connect the point on the number line, and find the value of the expression.

Learn how to solve the expression -1/3 - (-5/12) by converting it into an addition problem, and find the point on the number line. This step-by-step solution uses key concepts like subtracting negative numbers and adding fractions with different denominators. Suitable for students in Grades 6-8.

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