https://file.aiquickdraw.com/mathbot/file/1727843212548lunm8lak.jpg

Let's go through the math problems step by step from the image.

### 1. What is the additive inverse of −4.3? Explain how you know.

The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. For \(-4.3\), the additive inverse is \(4.3\), because:
\[
-4.3 + 4.3 = 0
\]
This is how we know \(4.3\) is the additive inverse.

### 2. What numbers could be added to −4.3 that would result in a sum less than 0?

Any negative number added to \(-4.3\) will give a sum less than 0. For example:
\[
-4.3 + (-1) = -5.3 \quad \text{(which is less than 0)}
\]
Similarly, adding numbers like \(-2\), \(-0.5\), or \(-3\) will result in a negative sum.

### 3. What numbers could be added to −4.3 that would result in a sum greater than 0?

To get a sum greater than 0, we would need to add a number greater than \(4.3\). For instance:
\[
-4.3 + 5 = 0.7 \quad \text{(which is greater than 0)}
\]
Any number larger than \(4.3\) (e.g., \(4.4\), \(6\), \(10\)) will result in a positive sum.

### Problems 4-11: Find the Sum

**4.**
\[
-\frac{1}{4} + \left( -\frac{2}{4} \right) = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}
\]

**5.**
\[
-3.5 + 2.2 = -1.3
\]

**6.**
\[
-4.6 + (-2.7) = -7.3
\]

**7.**
\[
-\frac{5}{6} + \frac{1}{6} = -\frac{5}{6} + \frac{1}{6} = -\frac{4}{6} = -\frac{2}{3}
\]

**9.**
\[
\frac{7}{5} + \left( -\frac{3}{5} \right) = \frac{7}{5} - \frac{3}{5} = \frac{4}{5}
\]

**11.**
\[
-1.2 + 2.1 = 0.9
\]

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Do you want more details on any specific part or have any questions about the calculations?

Here are some related questions for practice:
1. What is the additive inverse of \(-7\)?
2. What number added to \(-5.6\) would result in a sum of 0?
3. If you add \(-8\) to a number and the result is greater than 0, what might the number be?
4. Simplify \(\frac{4}{9} + \left(-\frac{7}{9}\right)\).
5. Calculate \(7.4 + (-2.8)\).

**Tip:** The additive inverse of a number always changes its sign (positive to negative or vice versa).

The math worksheet includes questions on additive inverses, sums involving negative and positive numbers, and fractions.

Solve problems on finding additive inverses, adding fractions, and working with sums of negative and positive numbers. This worksheet helps Grade 7 students practice key math concepts.

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