SOLUTION: One recipe calls for 1/4 teaspoon vanilla. A second recipe requires for 1/8 teaspoon vanilla flour, and a third recipe calls for 1/2 teaspoon vanilla. How much vanilla is requir

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: One recipe calls for 1/4 teaspoon vanilla. A second recipe requires for 1/8 teaspoon vanilla flour, and a third recipe calls for 1/2 teaspoon vanilla. How much vanilla is requir      Log On


   

Question 104029: One recipe calls for 1/4 teaspoon vanilla. A second recipe requires for 1/8 teaspoon vanilla flour, and a third recipe calls for 1/2 teaspoon vanilla. How much vanilla is required to make all three recipes? Help.
Found 2 solutions by jim_thompson5910, TP:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find out how many teaspoons are needed, simply add all of the fractions together


1%2F4%2B1%2F8%2B1%2F2 Start with the given expression

We need to get every denominator to the same number. So let's get every denominator to the LCM. So the LCM of 4, 8, and 12 is 24 (note: if you need help with finding the LCM, check out this solver)

%281%2F4%29%286%2F6%29%2B1%2F8%2B1%2F2 Multiply 1%2F4 by 6%2F6 this will get the denominator equal to 24



6%2F24%2B1%2F8%2B1%2F2 Multiply


6%2F24%2B%283%2F3%29%281%2F8%29%2B1%2F2 Multiply 1%2F8 by 3%2F3 this will get the denominator equal to 24


6%2F24%2B3%2F24%2B1%2F2 Multiply


6%2F24%2B3%2F24%2B%2812%2F12%29%281%2F2%29 Multiply 1%2F2 by 12%2F12 this will get the denominator equal to 24


6%2F24%2B3%2F24%2B12%2F24 Multiply



Now that every denominator is equal to twelve, we can add the fractions


%286%2B3%2B12%29%2F24 Combine the fractions



21%2F24 Combine the numerators


So 1%2F4%2B1%2F8%2B1%2F2=21%2F24


So all three recipes need 21%2F24 teaspoon of vanilla

Answer by TP(29) About Me  (Show Source):
You can put this solution on YOUR website!
You need to work out 1/4+1/8+1/2.
The bottom numbers of the fractions (the DENOMINATORS) are 2,4 and 8 and they have an LCM (Lowest Common Multiple or the smallest number that is in EACH of the times tables of 2,4 and 8) of 8.
Since the LCM is 8 change your fractions to eighths and then you can add them together.
1/4 = 2/8 ( 1/4= 1/4*(2/2)= (1*2)/4*2)=2/8 ).
1/8=1/8 (no change needed )
and 1/2 =4/8 ( 1/2=1/2*(4/4)= (1*4)/(2*4)=4/8 ).
So 1/4+1/8+1/2 = (2/8)+(1/8)+(4/8) = 7/8.
And so 7/8ths of a teaspoon are needed.ANS