Stephanie has a recipe that calls for StartFraction 2 over 3 EndFraction tablespoons of vanilla to make 3 and StartFraction 1 over 2 EndFraction dozen cookies.
How many tablespoons of vanilla are needed per dozen cookies?
Option D is the correct answer.
To convert 0.9 to a fraction, we can write it as 9/10. Then, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:
- 9/10 ÷ 1/1 = 9/10
- Therefore, 0.9 as a fraction is StartFraction 9 over 10 EndFraction, which is equivalent to StartFraction 3 over 3 EndFraction x StartFraction 3 over 10 EndFraction, or StartFraction 3 over 7 EndFraction.
First, we need to find out how many tablespoons of vanilla are needed for one cookie.
To do this, we can divide the amount of vanilla needed to make 3 and 1/2 dozen cookies by the total number of cookies:
- 3 and 1/2 dozen cookies is the same as 3 x 12 + 1/2 x 12 = 42 cookies
- 2/3 tablespoons of vanilla is needed to make 3 and 1/2 dozen cookies
- Therefore, 2/3 ÷ 42 = 0.01587 tablespoons of vanilla is needed per cookie
To find out how many tablespoons of vanilla are needed per dozen cookies, we simply multiply the above amount by 12:
- 0.01587 x 12 = 0.19044, which we can round to 0.19 tablespoons of vanilla per dozen cookies
Therefore, Stephanie needs approximately 0.19 tablespoons of vanilla to make one dozen cookies.
So then what is 0.9 as a fraction? My options are: A.
StartFraction 1 over 21 EndFraction
B.
StartFraction 1 over 7 EndFraction
C.
StartFraction 4 over 21 EndFraction
D.
StartFraction 3 over 7 EndFraction
To find out how many tablespoons of vanilla are needed per dozen cookies, we need to divide the total amount of vanilla by the number of dozens.
The recipe calls for StartFraction 2 over 3 EndFraction tablespoons of vanilla to make 3 and StartFraction 1 over 2 EndFraction dozen cookies.
First, we need to convert the mixed number of dozens, which is 3 and StartFraction 1 over 2 EndFraction, into an improper fraction to make the calculation easier.
3 and StartFraction 1 over 2 EndFraction can be written as a mixed number: 3 + StartFraction 1 over 2 EndFraction = 3 StartFraction 1 over 2 EndFraction.
To convert the mixed number into an improper fraction, we multiply the whole number (3) by the denominator of the fractional part (2), and then add the numerator of the fractional part (1). So, 3 * 2 + 1 = 7.
Therefore, StartFraction 3 and 1 over 2 EndFraction dozen cookies can be written as an improper fraction: StartFraction 7 over 2 EndFraction dozen cookies.
Now we can calculate the number of tablespoons of vanilla per dozen cookies by dividing the total amount of vanilla (2/3 tablespoons) by the number of dozens (7/2).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
2/3 tablespoons ÷ 7/2 dozen cookies = 2/3 tablespoons * 2/7 dozen cookies.
Multiplying the numerators (2 * 2) gives us 4, and multiplying the denominators (3 * 7) gives us 21.
Therefore, 2/3 tablespoons ÷ 7/2 dozen cookies = 4/21 tablespoons.
So, approximately 4/21 tablespoons of vanilla are needed per dozen cookies.