Bongie,Khanyisa and Mfanelo are participating in a baking challenge to create the most delicious cupcakes. Each baker is responsible for a different part of the recipe Bongie decides to make the cupcakes batter. She uses 3/4 cup of sugar, 1/2 cup of flour, and 1/3 cup of butter. How much flour did Bongie use compared to the total amount of sugar and butter combined?

Mathematics

ScanSolve AI Answer

Answer

613\frac{6}{13}

Step-by-step solution

3 steps

  1. Identify the amount of flour used.

    Bongie used 12\frac{1}{2} cup of flour.

  2. Calculate the total amount of sugar and butter combined.

    Amount of sugar = 34\frac{3}{4} cup
    Amount of butter = 13\frac{1}{3} cup
    Total amount of sugar and butter = 34+13\frac{3}{4} + \frac{1}{3}

    To add these fractions, find a common denominator, which is 12.

    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} 13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}

    Now, add the fractions:

    912+412=9+412=1312 cups\frac{9}{12} + \frac{4}{12} = \frac{9+4}{12} = \frac{13}{12} \text{ cups}

  3. Compare the amount of flour to the total amount of sugar and butter combined.

    This comparison is expressed as a ratio: Amount of flourTotal amount of sugar and butter\frac{\text{Amount of flour}}{\text{Total amount of sugar and butter}}.

    121312\frac{\frac{1}{2}}{\frac{13}{12}}

    To simplify this complex fraction, multiply the numerator by the reciprocal of the denominator:

    12×1213=1×122×13=1226\frac{1}{2} \times \frac{12}{13} = \frac{1 \times 12}{2 \times 13} = \frac{12}{26}

    Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

    12÷226÷2=613\frac{12 \div 2}{26 \div 2} = \frac{6}{13}

    Bongie used 613\frac{6}{13} as much flour compared to the total amount of sugar and butter combined.

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