Question

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find the three rational numbers equivalent to each of the following rational numbers
-2/5
3/7

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Answer 1

SOLUTION

To Find:

Three rational numbers equivalent to each of the following rational numbers.

1. - 2/5
2. 3/7

Concept:

For finding the equivalent rational numbers we have to multiply and divide the given rational number by the same number.

Finding the three rational numbers equivalent to - 2/5:

Multiply and divide by 2.

⟶ (- 2 × 2)/(5 × 2) = - 4/10

Multiply and divide by 3.

⟶ (- 2 × 3)/(5 × 3) = - 6/15

Multiply and divide by 4.

⟶ (- 2 × 4)/(5 × 4) = - 8/20

Hence,

Three rational numbers equivalent to - 2/5 are - 4/10, - 6/15 and - 8/20.

Finding the three rational numbers equivalent to 3/7:

Multiply and divide by 2.

⟶ (3 × 2)/(7 × 2) = 6/14

Multiply and divide by 3.

⟶ (3 × 3)/(7 × 3) = 9/21

Multiply and divide by 4.

⟶ (3 × 4)/(7 × 4) = 12/28

Hence,

Three rational numbers equivalent to 3/7 are 6/14, 9/21 and 12/28.

Answer 2

Question:-

• Find the three rational numbers equivalent to each of the following rational numbers -2/5 , 3/7.

To Find:-

• Find three rational numbers.

Solution:-

First ,

We have to find rational numbers equivalent to -2/5:-

$\sf\dashrightarrow \: - \dfrac { 2 } { 5 } \times \dfrac { 2 } { 2 } = - \dfrac { 4 } { 10 }$

$\sf\dashrightarrow \: - \dfrac { 2 } { 5 } \times \dfrac { 10 } { 10 } = - \dfrac { 20 } { 50 }$

$\sf\dashrightarrow \: - \dfrac { 2 } { 5 } \times \dfrac { 12 } { 12 } = - \dfrac { 24 } { 60 }$

Now ,

We have to find rational numbers equivalent to 3/7:-

$\sf\dashrightarrow \: \dfrac { 3 } { 7 } \times \dfrac { 3 } { 3 } = \dfrac { 9 } { 21 }$

$\sf\dashrightarrow \: \dfrac { 3 } { 7 } \times \dfrac { 6 } { 6 } = \dfrac { 18 } { 42 }$

$\sf\dashrightarrow \: \dfrac { 3 } { 7 } \times \dfrac { 9 } { 9 } = \dfrac { 27 } { 63 }$

Hence ,

• Equivalent rational numbers of $\sf \dfrac { 9 } { 21 } , \dfrac { 18 } { 42 } , \dfrac { 27 } { 63 }$