Let's go through each question one by one and solve them step-by-step, explaining the reasoning.
---
1. Which expression must be added to $3x - 7$ to equal 0?
We want:
$$
(3x - 7) + ? = 0
$$
So, we need the
additive inverse of $3x - 7$, which is:
$$
-(3x - 7) = -3x + 7
$$
✔ Answer: (4) $-3x + 7$
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2. What is the multiplicative inverse of $\frac{3}{4}$?
The multiplicative inverse (reciprocal) of a number is what you multiply it by to get 1.
$$
\frac{3}{4} \times ? = 1 \Rightarrow ? = \frac{4}{3}
$$
✔ Answer: (2) $\frac{4}{3}$
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3. The multiplicative inverse of $-\frac{1}{3}$ is
We want:
$$
-\frac{1}{3} \times ? = 1 \Rightarrow ? = -3
$$
Because:
$$
-\frac{1}{3} \times (-3) = 1
$$
✔ Answer: (3) $-3$
---
4. The additive inverse of $\frac{1}{a}$ is
Additive inverse means the number that adds to zero:
$$
\frac{1}{a} + ? = 0 \Rightarrow ? = -\frac{1}{a}
$$
✔ Answer: (2) $-\frac{1}{a}$
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5. The reciprocal of 5 is
Reciprocal means multiplicative inverse:
$$
\frac{1}{5}
$$
✔ Answer: (2) $\frac{1}{5}$
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6. What is the additive inverse of $\frac{2}{3}$?
Additive inverse of $\frac{2}{3}$ is:
$$
-\frac{2}{3}
$$
✔ Answer: (3) $-\frac{2}{3}$
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7. What is the additive inverse of the expression $a - b$?
Additive inverse of $a - b$ is:
$$
-(a - b) = -a + b = b - a
$$
But among the options, we look for equivalent form.
Option (4): $-a + b$ → same as $b - a$
✔ Answer: (4) $-a + b$
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8. If $a \ne 0$ and the sum of $x$ and $\frac{1}{a}$ is 0, then...
We are told:
$$
x + \frac{1}{a} = 0 \Rightarrow x = -\frac{1}{a}
$$
✔ Answer: (3) $x = -\frac{1}{a}$
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9. The reciprocal of the expression $2 + \frac{3}{x}$ is
First simplify the expression:
$$
2 + \frac{3}{x} = \frac{2x}{x} + \frac{3}{x} = \frac{2x + 3}{x}
$$
Now, take the reciprocal:
$$
\frac{x}{2x + 3}
$$
✔ Answer: (2) $\frac{x}{2x + 3}$
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10. Which equation illustrates the multiplicative inverse property?
The
multiplicative inverse property states:
$$
a \cdot \frac{1}{a} = 1 \quad \text{(for } a \ne 0\text{)}
$$
Let’s check each option:
1) $1 \cdot x = x$ → This is the
identity property, not inverse
2) $\frac{1}{x} \cdot x = 1$ → Yes! This shows multiplicative inverse
3) $1 \cdot 0 = 0$ → Identity with zero
4) $-1 \cdot x = -x$ → Not inverse property
✔ Answer: (2) $\frac{1}{x} \cdot x = 1$
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✔ Final Answers Summary:
| Question | Answer |
|--------|--------|
| 1 | (4) $-3x + 7$ |
| 2 | (2) $\frac{4}{3}$ |
| 3 | (3) $-3$ |
| 4 | (2) $-\frac{1}{a}$ |
| 5 | (2) $\frac{1}{5}$ |
| 6 | (3) $-\frac{2}{3}$ |
| 7 | (4) $-a + b$ |
| 8 | (3) $x = -\frac{1}{a}$ |
| 9 | (2) $\frac{x}{2x + 3}$ |
| 10 | (2) $\frac{1}{x} \cdot x = 1$ |
Let me know if you'd like these explained in more detail or formatted for printing!
Parent Tip: Review the logic above to help your child master the concept of property of numbers worksheet.
