Question

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Answer 1

See Explanation

Explanation:

Required

Write three equivalent ratios

To solve these questions, we do the following:

Whatever is being applied to a part of the ratio must be done on the other part

Solving (9):

`Ratio = (2)/(7)`

Multiply through by 2

`Ratio = (2*2)/(7*2) = (4)/(14)`

Multiply through by 3

`Ratio = (2*3)/(7*3) = (6)/(21)`

Multiply through by 5

`Ratio = (2*5)/(7*5) = (10)/(35)`

Hence, the equivalents are:
`(4)/(14), (6)/(21), (10)/(35)`

Solving (10):

Ratio = 1.5 to 3.5

Multiply by 2

`Ratio = 1.5 * 2\ to\ 3.5 * 2`

`Ratio = 3\ to\ 7`

Multiply by 3

`Ratio = 1.5 * 3\ to\ 3.5 * 3`

`Ratio = 4.5\ to\ 10.5`

Multiply by 4

`Ratio = 1.5 * 4\ to\ 3.5 * 4`

`Ratio = 6\ to\ 14`

Hence, the equivalents are: 3 to 7, 4.5 to 10.5 and 6 to 14

Solving (11):

Ratio = 6.25 to 1.25

Divide by 5

`Ratio = 6.25/5\ to\ 1.25/5`

`Ratio = 1.25\ to\ 0.25`

Multiply by 2

`Ratio = 6.25*2\ to\ 1.25*2`

`Ratio = 12.5\ to\ 2.5`

Multiply by 4

`Ratio = 6.25*4\ to\ 1.25*4`

`Ratio = 25\ to\ 5`

Hence, the equivalents are: 1.25 to 0.25, 12.5 to 2.5 and 25 to 5

Solving (12):

`Ratio = 3 : 3(1)/(2)`

Multiply by 2

`Ratio = 3 *2: 3(1)/(2)*2`

`Ratio = 6: 7`

Multiply by 4

`Ratio = 3 *4: 3(1)/(2)*4`

`Ratio = 12: 14`

Multiply by 6

`Ratio = 3 *6: 3(1)/(2)*6`

`Ratio = 18: 21`

Hence, the equivalents are: 6:7, 12:14 and 18:21

Solving (13)

`Ratio = 1(2)/(3) : (5)/(4)`

Convert mixed fraction to improper fraction

`Ratio = (5)/(3) : (5)/(4)`

Multiply by 2

`Ratio = (5)/(3)*2 : (5)/(4)*2`

`Ratio = (10)/(3) : (5)/(2)`

Multiply by 3

`Ratio = (5)/(3)*3 : (5)/(4)*3`

`Ratio = 5 : (15)/(4)`

Multiply by 12

`Ratio = (5)/(3)*12 : (5)/(4)*12`

`Ratio = 20 : 15`

Hence, the equivalents are: 10/3:5/2, 5 : 15/4, and 20:15