A recipe calls for 3/4 cup flour and 2/3 cup butter. Does the recipe require more flour or butter? Is this still true if the recipe is doubled? Explain how you determined your answer.
3/4 = 9/12
2/3 = 8/12
Can you take it from here?
Would it be true if you doubled it?
Sure.
2(9/12) = 18/12
2(8/12) = 16/12
No
To determine whether the recipe requires more flour or butter, we can compare the quantities given for each ingredient.
1. Flour: The recipe calls for 3/4 cup flour.
2. Butter: The recipe calls for 2/3 cup butter.
To compare these two quantities, we need to convert them into a common denominator. The least common denominator for 4 and 3 is 12. Therefore, we can express the quantities as:
1. Flour: 9/12 cup flour (since 3/4 = 9/12)
2. Butter: 8/12 cup butter (since 2/3 = 8/12)
Now we can easily compare the quantities:
9/12 cup flour vs. 8/12 cup butter
Since 9/12 is greater than 8/12, we can conclude that the recipe requires more flour than butter.
Now, let's analyze the situation when the recipe is doubled.
If the recipe is doubled, the new quantities would be:
1. Flour: 2 * (3/4) = 6/4 = 3/2 cups flour
2. Butter: 2 * (2/3) = 4/3 cups butter
Again, we need to convert these quantities into a common denominator:
1. Flour: (3/2) * 6/6 = 18/12 cups flour
2. Butter: (4/3) * 4/4 = 16/12 cups butter
Now we can compare the quantities again:
18/12 cups flour vs. 16/12 cups butter
Since 18/12 is also greater than 16/12, even when the recipe is doubled, it still requires more flour than butter.
So, the recipe requires more flour than butter, and this remains true even if the recipe is doubled.