Question

Pleasee helppp meee .

Answer 1

Ratio of homework papers to exit tickets

Mr. Rowley: 8/7

Ms. Rivera: 16/15

These ratios are not equal

8/7 > 16/15

Explanation:

Ratio of homework papers to exit tickets

Mr. Rowley: 16:14

Expressed as a fraction this is

`(16)/(14)`

Let's simplify the fraction by dividing numerator and denominator by 2. This is essentially dividing by 1 since 2/2 =1 so the fractional value itself is unchanged.

`(16 / 2)/(14 / 2) = (8)/(7)`

Ms. Rivera: 64:60
Expressed as fraction this is

`(64)/(60)`

Let's simplify the fraction by dividing numerator and denominator by 2

`(64 / 2)/(60 / 2) = (32)/(30)`

This can be simplified further by dividing again by 2:

`(32 / 2)/(30 / 2) = (16)/(15)`

(We could have divided by 4 the first time also)

`(8)/(7)`
`\mathrm {\;is\;\bold{not\; equal\;} to\; }`
`(16)/(15)`

We can see that if we multiply both fractions by 105 which is the product of the denominators

`(8)/(7) * 105 = 8 * 15 = 120 \rm \;\;\;\;{ (since 105 / 7 = 15)}\\\\(16)/(15) * 105 = 16 * 7 = 112 \rm \;\;\;\;{ (since 105 / 15 = 7)}\\\\\\`

Since we are multiplying both fractions by the same amount to get rid of the denominator it is easy to see which one is bigger

Obviously 8/7 is bigger than 16/15

We could have converted to decimal also and checked
8/7 = 1.14 rounded to 2 decimal places
16/15 = 1.07 rounded to 2 decimal places

1.14 > 1.07 so 8/7 > 16/15

(You can choose which of the above methods you like)