Question

Pleasee helppp meee .

Answer 1

Answer:

Ratio of homework papers to exit tickets

Mr. Rowley: 8/7

Ms. Rivera: 16/15

These ratios are not equal

8/7 > 16/15

Step-by-step explanation:

Ratio of homework papers to exit tickets

Mr. Rowley: 16:14

Expressed as a fraction this is
$\dfrac{16}{14}$

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.

$\dfrac{16 \div 2}{14 \div 2} = \dfrac{8}{7}$

Ms. Rivera: 64:60
Expressed as fraction this is
$\dfrac{64}{60}$

Let's simplify the fraction by dividing numerator and denominator by 2
$\dfrac{64 \div 2}{60 \div 2} = \dfrac{32}{30}$

This can be simplified further by dividing again by 2:
$\dfrac{32 \div 2}{30 \div 2} = \dfrac{16}{15}$

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

$\dfrac{8}{7}$ $\mathrm {\;is\;\bold{not\; equal\;} to\; }$ $\dfrac{16}{15}$

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

$\dfrac{8}{7} \times 105 = 8 \times 15 = 120 \rm \;\;\;\;{ (since 105 \div 7 = 15)}\\\\\dfrac{16}{15} \times 105 = 16 \times 7 = 112 \rm \;\;\;\;{ (since 105 \div 15 = 7)}$

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)