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.

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.