Question

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

a. Show that the ratios 10/20and 30/60 form a proportion by finding a common multiplier.
b.Show that the ratios in part (a) are equal by writing them in simplest form.

Answer 1

`\left[A]` The ratios
`(10)/(20)` form a proportion by common multiplier 3 to get
`(30)/(60)`

`\left[B]` Both ratio are equal to
`(1)/(2)` in simplest form

Explanation:

`\left[A]` We need to show both fraction of same proportion.

Ratio 1:
`(10)/(20)`

If we multiply by 3 at numerator and denominator

`(10*3)/(20*3)`

`(30)/(60)`

Therefore
`(30)/(60)` is equivalent ratio to second one 30/60

Hence, The ratio 10/20 form a proportion by common multiplier 3 to get 30/60

∴-----------------------------------------------------------------------------------------------------∴

`\left[B]` Now we simplify both ration into simplest form

→
`(10/10)/(20/10) =(1)/(2)`

→
`(30/30)/(60/30) =(1)/(2)`

→
`(1)/(2) =(1)/(2)`

Hence, Both ratio are equal to
`(1)/(2)` in simplest form.

Answer 2

a) "common multiplier" is 3

b) both reduce to 1/2

Explanation:

a)

`(30)/(60)=(3\cdot10)/(3\cdot20)=(3)/(3)\cdot(10)/(20)=1\cdot(10)/(20)=(10)/(20)`

Perhaps your "common multiplier" is 3. It multiplies both numerator and denominator in 10/20 to give you 30/60.

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b)

`(10)/(20)=(10)/(10)\cdot(1)/(2)=(1)/(2)\\\\(30)/(60)=(30)/(30)\cdot(1)/(2)=(1)/(2)`

The simplest form of both fractions is 1/2.