Select the best answer for the question.
The sum of [tex]$1 / 6, 2 / 3$[/tex], and [tex]$1 / 4$[/tex] is
A. [tex]$4 / 12$[/tex], or [tex]$1 / 3$[/tex].
B. [tex]$2 / 72$[/tex], or [tex]$1 / 36$[/tex].
C. [tex]$11 / 12$[/tex].
D. [tex]$13 / 12$[/tex], or [tex]$1 \frac{1}{12}$[/tex].
Answer (2)
Find a common denominator for the fractions: The least common denominator for 6, 3, and 4 is 12.
Convert each fraction to an equivalent fraction with the common denominator: 6 1 = 12 2 , 3 2 = 12 8 , 4 1 = 12 3 .
Add the equivalent fractions: 12 2 + 12 8 + 12 3 = 12 13 .
The sum of the fractions is 12 13 .
Explanation
Finding a Common Denominator We need to find the sum of the fractions 6 1 , 3 2 , and 4 1 . To do this, we first need to find a common denominator for these fractions.
Converting to Equivalent Fractions The least common multiple (LCM) of 6, 3, and 4 is 12. So, we will use 12 as our common denominator. Now, we convert each fraction to an equivalent fraction with a denominator of 12:
6 1 = 6 × 2 1 × 2 = 12 2
3 2 = 3 × 4 2 × 4 = 12 8
4 1 = 4 × 3 1 × 3 = 12 3
Adding the Fractions Now that we have the fractions with a common denominator, we can add them:
12 2 + 12 8 + 12 3 = 12 2 + 8 + 3 = 12 13
Simplifying the Result The sum of the fractions is 12 13 . This is an improper fraction, which means the numerator is greater than the denominator. We can convert it to a mixed number:
12 13 = 1 12 1
Selecting the Correct Answer Now, we compare our result, 12 13 , with the given options:
A. 12 4 , or 3 1
B. 72 2 , or 36 1
C. 12 11
D. 12 13 , or 1 12 1
The correct answer is D, since 12 13 is the sum of the given fractions.
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 6 1 cup of flour, 3 2 cup of sugar, and 4 1 cup of butter, you need to add these fractions to determine the total amount of ingredients needed. Understanding how to add fractions is essential for accurately following recipes and achieving the desired results in cooking and baking.
The sum of the fractions 6 1 , 3 2 , and 4 1 is 12 13 or 1 12 1 . Therefore, the correct answer is option D. This is found by converting each fraction to a common denominator and then adding them together.
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