How to reduce a ratio to lowest terms

It is usual to represent ratios in their simplest form so that we are not operating with large numbers. Reducing ratios to their simplest form is directly linked to equivalent fractions.

For example: On a farm there are 4 Bulls and 200 Cows. Write this as a ratio in its simplest form.

Bulls : Cows

4 : 200

If we halve the number of bulls then we must halve the number of cows so that the relationship between the bulls and cows stays constant. This gives us:

Bulls : Cows

2 : 100

Halving again gives us

1 : 50

So the ratio of Bulls to Cows equals 1 : 50. The ratio is now represented in its simplest form.

An example where we have 3 quantities.

On the farm there are 24 ducks, 36 geese and 48 hens.

Ratio of ducks : geese : hens

24 : 36 : 48

Dividing each quantity by 12 gives us

2 : 3 : 4

So the ratio of ducks to geese to hens equals 2 : 3 : 4 which is the simplest form since we can find no further common factor.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

the answer to your question a or b but i am pretty sure it is b. i hope this : )

step-by-step explanation: