To find the total amount of sugar required for the cupcakes, you need to add the sugar needed for the batter and the sugar needed for the icing.
The batter requires \( \frac{3}{4} \) cup of sugar, and the icing requires \( \frac{2}{3} \) cup of sugar.
First, let's find a common denominator to add these two fractions. The denominators are 4 and 3. The least common multiple of 4 and 3 is 12.
Now, convert each fraction to have a denominator of 12:
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For \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
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For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
Now, add the two fractions: \[ \frac{9}{12} + \frac{8}{12} = \frac{9 + 8}{12} = \frac{17}{12} \]
Thus, the total sugar required is \( \frac{17}{12} \) cups.
To convert this to a more understandable form, \( \frac{17}{12} \) can also be expressed as: \[ 1 \frac{5}{12} \text{ cups} \]
Therefore, the total amount of sugar required to make the cupcakes is \( \frac{17}{12} \) cups or \( 1 \frac{5}{12} \) cups.
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