A recipe calls for 1/2 cup of sugar, 3/4 cup of flour, and 1/3 cup of butter. Put them in order from least to greatest amount used.
Understand the Problem
The question asks us to order the amounts of sugar, flour, and butter in a recipe from least to greatest. The amounts given are 1/2 cup of sugar, 3/4 cup of flour, and 1/3 cup of butter. We need to compare these fractions and arrange them in ascending order.
Answer
Butter, Sugar, Flour
Answer for screen readers
Butter, Sugar, Flour
Steps to Solve
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Identify the fractions The recipe calls for $1/2$ cup of sugar, $3/4$ cup of flour, and $1/3$ cup of butter.
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Find a common denominator To compare the fractions, we need to find a common denominator. The least common multiple of 2, 3, and 4 is 12.
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Convert the fractions to equivalent fractions with the common denominator Convert each fraction: $1/2 = (1 \times 6) / (2 \times 6) = 6/12$ $3/4 = (3 \times 3) / (4 \times 3) = 9/12$ $1/3 = (1 \times 4) / (3 \times 4) = 4/12$
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Compare the fractions Now we can easily compare the fractions: $4/12 < 6/12 < 9/12$.
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Order the ingredients from least to greatest This means $1/3 < 1/2 < 3/4$. So, butter < sugar < flour.
Butter, Sugar, Flour
More Information
This problem emphasizes the importance of finding a common unit (in this case, a common denominator) to compare quantities. Fractions are easier to compare when they have the same denominator.
Tips
A common mistake is to try and directly compare the fractions without converting them to a common denominator. This can lead to incorrect ordering. For example, someone might incorrectly assume that $1/3$ is greater than $1/2$ because 3 is greater than 2, without considering that these are denominators.
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