QuestionDetermine if the following statements are True or False about unit rates: a. The ratio to has a unit rate of . b. The ratio has a unit rate of 54. c. The ratio has a unit rate of . d. The ratio has a unit rate of .
Studdy Solution
STEP 1
Assumptions1. The unit rate is the ratio of the two quantities in simplest form. . The ratio is calculated by dividing the first quantity by the second quantity.
STEP 2
Let's start with statement a. The ratio is to . We need to find the unit rate of this ratio.
STEP 3
Plug in the values for the first and second quantities to calculate the unit rate.
STEP 4
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
STEP 5
Calculate the unit rate.
The unit rate of the ratio to is , not . So, statement a is False.
STEP 6
Now, let's move on to statement b. The ratio is . We need to find the unit rate of this ratio.
STEP 7
Plug in the values for the first and second quantities to calculate the unit rate.
STEP 8
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
STEP 9
Calculate the unit rate.
The unit rate of the ratio is54. So, statement b is True.
STEP 10
Next, let's check statement c. The ratio is . We need to find the unit rate of this ratio.
STEP 11
Plug in the values for the first and second quantities to calculate the unit rate.
STEP 12
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
STEP 13
Calculate the unit rate.
The unit rate of the ratio is . So, statement c is True.
STEP 14
Finally, let's check statement d. The ratio is . We need to find the unit rate of this ratio.
STEP 15
Convert the mixed numbers to improper fractions.
STEP 16
Plug in the values for the first and second quantities to calculate the unit rate.
STEP 17
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
STEP 18
Calculate the unit rate.
The unit rate of the ratio is . So, statement d is True.
So, the correct answers area. Falseb. Truec. Trued. True
Was this helpful?