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QuestionCalculate the sum of 1015+412\frac{10}{15} + \frac{4}{12} and find the LCD. Options: a. 180 b. 1 c. 180180\frac{180}{180} d. 60

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions. . We need to find the least common denominator (LCD) to add these fractions.

STEP 2

The LCD of two fractions is the least common multiple (LCM) of their denominators. In this case, the denominators are15 and12.

STEP 3

To find the LCM of15 and12, we first list the prime factors of each number.
For15, the prime factors are3 and5. For12, the prime factors are2,2, and3.

STEP 4

The LCM is the product of the highest powers of all the factors that appear in either number.In this case, the LCM is 22×3×2^2 \times3 \times.

STEP 5

Calculate the LCM.
LCM=22×3×5=4×3×5=60LCM =2^2 \times3 \times5 =4 \times3 \times5 =60

STEP 6

Now that we have the LCD, we can rewrite each fraction with this new denominator.The first fraction becomes 1015×44=4060\frac{10}{15} \times \frac{4}{4} = \frac{40}{60}.
The second fraction becomes 412×55=2060\frac{4}{12} \times \frac{5}{5} = \frac{20}{60}.

STEP 7

Now, add the two fractions.
4060+2060=6060\frac{40}{60} + \frac{20}{60} = \frac{60}{60}

STEP 8

implify the fraction.
6060=1\frac{60}{60} =1So, the answer is1.

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