Math worksheet with exercises on multiplicative and additive inverses of numbers.

Let's solve each of the problems step by step.

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1. Write multiplicative inverse of numbers: 10, 5, −20, −40, 100, 7

Multiplicative inverse of a number $ a $ is $ \frac{1}{a} $, such that $ a \times \frac{1}{a} = 1 $.

So:
- Multiplicative inverse of $ 10 $ is $ \frac{1}{10} $
- Multiplicative inverse of $ 5 $ is $ \frac{1}{5} $
- Multiplicative inverse of $ -20 $ is $ -\frac{1}{20} $
- Multiplicative inverse of $ -40 $ is $ -\frac{1}{40} $
- Multiplicative inverse of $ 100 $ is $ \frac{1}{100} $
- Multiplicative inverse of $ 7 $ is $ \frac{1}{7} $

✔ Answer:
$ \frac{1}{10},\ \frac{1}{5},\ -\frac{1}{20},\ -\frac{1}{40},\ \frac{1}{100},\ \frac{1}{7} $

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2. Write multiplicative inverse of numbers: $ \frac{1}{2},\ \frac{7}{3},\ 1\frac{2}{3},\ -3\frac{7}{10},\ -1\frac{2}{9} $

Convert mixed numbers to improper fractions:

- $ 1\frac{2}{3} = \frac{5}{3} $
- $ -3\frac{7}{10} = -\frac{37}{10} $
- $ -1\frac{2}{9} = -\frac{11}{9} $

Now find inverses:
- $ \frac{1}{2} \Rightarrow 2 $
- $ \frac{7}{3} \Rightarrow \frac{3}{7} $
- $ \frac{5}{3} \Rightarrow \frac{3}{5} $
- $ -\frac{37}{10} \Rightarrow -\frac{10}{37} $
- $ -\frac{11}{9} \Rightarrow -\frac{9}{11} $

✔ Answer:
$ 2,\ \frac{3}{7},\ \frac{3}{5},\ -\frac{10}{37},\ -\frac{9}{11} $

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3. Write multiplicative inverse of numbers: 0.5, 0.2, −1.2, 2.45, −3.05, 0.008

Convert decimals to fractions or directly compute reciprocal:

- $ 0.5 = \frac{1}{2} \Rightarrow \text{inverse} = 2 $
- $ 0.2 = \frac{1}{5} \Rightarrow \text{inverse} = 5 $
- $ -1.2 = -\frac{6}{5} \Rightarrow \text{inverse} = -\frac{5}{6} $
- $ 2.45 = \frac{245}{100} = \frac{49}{20} \Rightarrow \text{inverse} = \frac{20}{49} $
- $ -3.05 = -\frac{305}{100} = -\frac{61}{20} \Rightarrow \text{inverse} = -\frac{20}{61} $
- $ 0.008 = \frac{8}{1000} = \frac{1}{125} \Rightarrow \text{inverse} = 125 $

✔ Answer:
$ 2,\ 5,\ -\frac{5}{6},\ \frac{20}{49},\ -\frac{20}{61},\ 125 $

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4. Is there multiplicative inverse of zero?

No. Because division by zero is undefined. There is no number that you can multiply by 0 to get 1.

✔ Answer: No, there is no multiplicative inverse of zero.

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5. Write additive inverse of numbers: 4, 3, 1023, −2, −1, −100

Additive inverse of a number $ a $ is $ -a $, such that $ a + (-a) = 0 $.

- Additive inverse of $ 4 $ is $ -4 $
- Additive inverse of $ 3 $ is $ -3 $
- Additive inverse of $ 1023 $ is $ -1023 $
- Additive inverse of $ -2 $ is $ 2 $
- Additive inverse of $ -1 $ is $ 1 $
- Additive inverse of $ -100 $ is $ 100 $

✔ Answer:
$ -4,\ -3,\ -1023,\ 2,\ 1,\ 100 $

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6. Write additive inverse of numbers: $ \frac{1}{2},\ 1\frac{3}{7},\ -2\frac{5}{6},\ -\frac{4}{9} $

Convert mixed numbers:
- $ 1\frac{3}{7} = \frac{10}{7} $
- $ -2\frac{5}{6} = -\frac{17}{6} $

Now find additive inverses:
- $ \frac{1}{2} \Rightarrow -\frac{1}{2} $
- $ \frac{10}{7} \Rightarrow -\frac{10}{7} $
- $ -\frac{17}{6} \Rightarrow \frac{17}{6} $
- $ -\frac{4}{9} \Rightarrow \frac{4}{9} $

✔ Answer:
$ -\frac{1}{2},\ -\frac{10}{7},\ \frac{17}{6},\ \frac{4}{9} $

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7. Write additive inverse of numbers: 0.3, 1.7, −1.3, −7.02, −0.143

Additive inverse is just the negative of the number:
- $ 0.3 \Rightarrow -0.3 $
- $ 1.7 \Rightarrow -1.7 $
- $ -1.3 \Rightarrow 1.3 $
- $ -7.02 \Rightarrow 7.02 $
- $ -0.143 \Rightarrow 0.143 $

✔ Answer:
$ -0.3,\ -1.7,\ 1.3,\ 7.02,\ 0.143 $

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8. Is there additive inverse of zero?

Yes! The additive inverse of zero is zero itself, because $ 0 + 0 = 0 $.

✔ Answer: Yes, the additive inverse of zero is zero.

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✔ Final Summary Answers:

1. Multiplicative inverses:
$ \frac{1}{10},\ \frac{1}{5},\ -\frac{1}{20},\ -\frac{1}{40},\ \frac{1}{100},\ \frac{1}{7} $

2. Multiplicative inverses:
$ 2,\ \frac{3}{7},\ \frac{3}{5},\ -\frac{10}{37},\ -\frac{9}{11} $

3. Multiplicative inverses:
$ 2,\ 5,\ -\frac{5}{6},\ \frac{20}{49},\ -\frac{20}{61},\ 125 $

4. Multiplicative inverse of zero? → No

5. Additive inverses:
$ -4,\ -3,\ -1023,\ 2,\ 1,\ 100 $

6. Additive inverses:
$ -\frac{1}{2},\ -\frac{10}{7},\ \frac{17}{6},\ \frac{4}{9} $

7. Additive inverses:
$ -0.3,\ -1.7,\ 1.3,\ 7.02,\ 0.143 $

8. Additive inverse of zero? → Yes, it is 0

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