Free high school math worksheet from Funmaths.com - Free Printable

Let's solve each of these problems step by step and explain the reasoning.

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23. What is the multiplicative inverse of $ x $?

The multiplicative inverse of a number is what you multiply it by to get 1.
So, for $ x $, we want:
$$
x \cdot ? = 1 \Rightarrow ? = \frac{1}{x}
$$

But none of the options say $ \frac{1}{x} $. Let's check:

(1) 1 → no
(2) $ \frac{2}{x} $ → no
(3) $ -\frac{x}{2} $ → no
(4) $ 2x $ → no

Wait — none of these are $ \frac{1}{x} $, which should be the answer.

But let’s double-check the question: “What is the multiplicative inverse of $ x $?”

It should be $ \frac{1}{x} $. But that’s not listed. However, maybe there's a typo or misreading.

Wait — perhaps the question meant something else? Or maybe it's asking for the inverse in a different context?

But as written, the multiplicative inverse of $ x $ is $ \frac{1}{x} $, which is not among the choices.

But option (2) is $ \frac{2}{x} $. That's not the inverse unless $ x = 2 $, which isn't stated.

Wait — unless the question is asking for the inverse of $ \frac{x}{2} $? But it says "of $ x $".

Alternatively, could this be a typo? Maybe it's supposed to be "what is the multiplicative inverse of $ \frac{x}{2} $"?

Then:
Inverse of $ \frac{x}{2} $ is $ \frac{2}{x} $ → which is choice (2).

But the question says "of $ x $", so unless there's a mistake, none of the answers are correct.

But since this is a multiple-choice test, and (2) is $ \frac{2}{x} $, which is not the inverse of $ x $, but is the inverse of $ \frac{x}{2} $, I suspect a typo.

But based on the given, the correct multiplicative inverse of $ x $ is $ \frac{1}{x} $, which is not listed.

Wait — perhaps the question is asking for the additive inverse? No, it says multiplicative.

So unless the options are wrong, this seems problematic.

But let's look again: maybe it's a trick?

No. So I think either the question is flawed, or perhaps it's a formatting issue.

But if the question is correctly stated, then no option is correct.

However, if we assume the intended question was:
"What is the multiplicative inverse of $ \frac{x}{2} $", then answer is $ \frac{2}{x} $, which is (2).

But as written: "of $ x $", so answer should be $ \frac{1}{x} $, not listed.

But let's move on — maybe we’ll see more context.

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24. Which is a rational number?

Rational numbers are those that can be expressed as $ \frac{p}{q} $, where $ p $ and $ q $ are integers and $ q \ne 0 $. They include terminating or repeating decimals.

Check each:

(1) $ \sqrt{7} $ → irrational (not a perfect square)
(2) $ \sqrt{18} $ → $ \sqrt{9 \cdot 2} = 3\sqrt{2} $ → irrational
(3) $ \sqrt{49} = 7 $ → rational ✔
(4) $ \sqrt{20} = 2\sqrt{5} $ → irrational

✔ Answer: (3) $ \sqrt{49} $

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25. Which sentence illustrates the associative property for multiplication?

Associative property: $ a(bc) = (ab)c $

That is, grouping doesn’t matter when multiplying.

Look at options:

(1) $ ab = ba $ → commutative
(2) $ a(bc) = (ab)c $ → associative ✔
(3) $ a \cdot 1 = a $ → identity
(4) $ a(b + c) = ab + ac $ → distributive

✔ Answer: (2)

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26. Which expression represents an irrational number?

Irrational numbers cannot be written as fractions and have non-repeating, non-terminating decimals.

(1) $ \pi $ → irrational ✔
(2) $ -2 $ → rational
(3) $ 3 $ → rational
(4) $ \sqrt{9} = 3 $ → rational

✔ Answer: (1) $ \pi $

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27. Which expression is undefined when $ y = 4 $?

Undefined usually means division by zero.

Check:

(1) $ 4y $ → $ 4 \times 4 = 16 $ → defined
(2) $ \frac{1}{y} $ → $ \frac{1}{4} $ → defined
(3) $ \frac{4}{y - 4} $ → $ \frac{4}{4 - 4} = \frac{4}{0} $ → undefined ✔
(4) $ y^4 = 4^4 = 256 $ → defined

✔ Answer: (3)

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28. If $ a = -3 $, $ b = 4 $, find value of $ -5a^2b $

First, compute $ a^2 = (-3)^2 = 9 $

Now:
$ -5 \times 9 \times 4 = -5 \times 36 = -180 $

✔ Answer: (4) -180

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29. Express $ 0.003146 $ in scientific notation

Move decimal point to right of first non-zero digit:
$ 3.146 \times 10^{-3} $

Because we moved decimal 3 places left.

Now check options:

(1) $ 31.46 \times 10^4 $ → too big
(2) $ 3.146 \times 10^3 $ → 3146 → too big
(3) $ 3.146 \times 10^{-3} $ → yes ✔
(4) $ 3.146 \times 10^{-2} $ → 0.03146 → no

✔ Answer: (3)

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30. What is the additive inverse of $ 3t $?

Additive inverse is what you add to get zero:
$ 3t + ? = 0 \Rightarrow ? = -3t $

✔ Answer: (2) $ -3t $

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31. If $ 0.00063 $ is expressed as $ 6.3 \times 10^n $, what is $ n $?

Move decimal:
0.00063 → move 4 places right to get 6.3 → so $ 10^{-4} $

Thus, $ n = -4 $

✔ Answer: (3) -4

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32. If $ a = 2 $, $ b = -1 $, evaluate $ 3ab^2 $

Note: exponent applies only to $ b $, not $ a $, unless parentheses.

So:
$ b^2 = (-1)^2 = 1 $
$ ab^2 = 2 \times 1 = 2 $
$ 3ab^2 = 3 \times 2 = 6 $

✔ Answer: (1) 6

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33. Distance from Sun to Neptune: 2,790,000,000 miles

Write in scientific notation.

Move decimal: 2.79 × 10⁹

Because:
2,790,000,000 = 2.79 × 10⁹

Check options:

(1) $ 2.79 \times 10^9 $ → ✔
(2) $ 2.79 \times 10^{-9} $ → tiny
(3) $ 27.9 \times 10^7 $ → same as $ 2.79 \times 10^8 $ → too small
(4) $ 27.9 \times 10^{-7} $ → very small

✔ Answer: (1)

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34. Which property is illustrated by $ -8 + 0 = -8 $?

Adding zero leaves the number unchanged → additive identity

(1) additive inverse → would be $ -8 + 8 = 0 $
(2) additive identity → ✔
(3) commutative → order changes
(4) distributive → involves multiplication over addition

✔ Answer: (2) additive identity

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Final Answers:

| Q | Answer |
|---|--------|
| 23 | Not listed (should be $ \frac{1}{x} $, but closest possible typo might be (2) if question was $ \frac{x}{2} $) |
| 24 | (3) $ \sqrt{49} $ |
| 25 | (2) $ a(bc) = (ab)c $ |
| 26 | (1) $ \pi $ |
| 27 | (3) $ \frac{4}{y - 4} $ |
| 28 | (4) $ -180 $ |
| 29 | (3) $ 3.146 \times 10^{-3} $ |
| 30 | (2) $ -3t $ |
| 31 | (3) $ -4 $ |
| 32 | (1) $ 6 $ |
| 33 | (1) $ 2.79 \times 10^9 $ |
| 34 | (2) additive identity |

> ⚠️ Note: Question 23 has no correct answer among the choices if interpreted literally. The multiplicative inverse of $ x $ is $ \frac{1}{x} $, which is not listed. Option (2) $ \frac{2}{x} $ is the inverse of $ \frac{x}{2} $, not $ x $. So likely a typo in the question or options.

If the question was: *"What is the multiplicative inverse of $ \frac{x}{2} $"*, then (2) would be correct.

But as written, none of the options are correct.

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Let me know if you'd like a corrected version of the question!