Question

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Answer 1

Answer:

3/20

distributive property

0

0

4/-3

-3/2

1

1 and -1

Step-by-step explanation:

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Answer 2

1.

$\frac{3}{20}\times\frac{2}{3}+\frac{3}{20}\times\frac{1}{3}$

$\frac{3}{20}(\frac{2}{3}+\frac{1}{3})$

$\frac{3}{20}(\frac{3}{3} )$

$\frac{3}{20}\times 1$

$\frac{3}{20}$

2. $\frac{4}{7}(\frac{2}{3} +\frac{3}{4})=\frac{4}{7}\times\frac{2}{3}+\frac{4}{7}\times \frac{3}{4}$

$\frac{4}{7}(\frac{2\times4}{3\times4 } +\frac{3\times3}{4\times3})=\frac{8}{21}+\frac{3}{7}$

$\frac{4}{7}(\frac{8}{12 } +\frac{9}{12})=\frac{8}{21}+\frac{3\times 3 }{7\times3 }$

$\frac{4}{7}(\frac{17}{12 } )=\frac{8}{21}+\frac{9 }{21}$

$\frac{4}{7}\times \frac{17}{12 } =\frac{8}{21}+\frac{9 }{21}$

$\frac{17}{21 } =\frac{17}{21}$

3.

a. Zero is the additive identity for rational numbers.

b. Zero has no reciprocal.

c. Multiplicative inverse of $\frac{-3}{4}$ is $\frac{-4}{3}$.

d. Additive inverse of $\frac{3}{2}$ is $\frac{2}{3}$.

e. One is the multiplicative identity for rational numbers.

f. 1 and -1 are the only two rational numbers which are having their own reciprocals.

Additional Information :)

What is distributive property?

A property which is used for multiplying a single value and two or more values inside a set of brackets is known as distributive property.

What are the types of distributive properties?

There are two types of distributive property. They are -

Distributive Property over Addition ⇒ $a(b+c)=a\times b+a\times c$

Distributive Property over Subtraction ⇒ $a(b-c)=a\times b-a\times c$

What is the additive identity?

The Additive Identity is 0.

Why is zero known as the additive identity?

This is because adding 0 to a number does not change it.

What is the multiplicative identity?

The Multiplicative Identity is 1.

Why is one known as the multiplicative identity?

This is because multiplying 1 to a number does not change it.