There are 78
7
8
cups of sugar in a canister in the kitchen. Ms. Johnson used 12
1
2
of the sugar when she was preparing dessert for her daughter's birthday cake. How much sugar did she use?
Ms. Johnson used 12 and 1/2 cups of sugar.
To find out how much sugar Ms. Johnson used, you need to subtract the amount she used from the total amount of sugar in the canister.
Total amount of sugar in the canister: 78 cups
Sugar used by Ms. Johnson: 12 1/2 cups
To convert the mixed number to an improper fraction:
\(12~\frac{1}{2}\) can be written as \(\frac{12\times2}{2} + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2}\)
Now, let's subtract the sugar used from the total amount:
78 cups - \(\frac{25}{2}\) cups
Since we have different units (cups and halves), we need to find a common denominator. The multiple of 2 and 2 is 2. So, we can rewrite 78 cups as \(\frac{78\times2}{2}\) cups.
\(\frac{78\times2}{2}\) cups - \(\frac{25}{2}\) cups
\(\frac{156}{2}\) cups - \(\frac{25}{2}\) cups
Now, subtract the numerators and keep the same denominator:
\(\frac{156 - 25}{2}\) cups
\(\frac{131}{2}\) cups
Therefore, Ms. Johnson used \(\frac{131}{2}\) cups of sugar when she was preparing dessert for her daughter's birthday cake.