Answer:
13 5/24
Step-by-step explanation:
The sum of the given mixed numbers can be calculated as the sum of the integers plus the sum of the fractions:
(4 1/8) +(5 5/12) +(3 2/3) = (4 +5 +3) +(1/8 +5/12 +2/3)
= 12 +(3/24 +10/24 +16/24)
= 12 + 29/24
= 12 + (24/24) + (5/24)
= 13 5/24 . . . . . distance units
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In general, you add fractions using a common denominator. That denominator is the least common multiple (LCM) of the given denominators. Here, that is the least common multiple of 8, 12, 3, which is 24.
There are several ways to find the LCM. One way is to look at the prime factors, and form the product of the unique factor to their highest powers.
8 = 2³
12 = 2²·3
3 = 3
The unique factors are 2 and 3. The highest power of 2 is 3, and the highest power of 3 is 1. Then the LCM is ...
LCM = 2³·3 = 8·3 = 24
You will note that we expressed each of the fractions above using the denominator 24. This is done by multiplying numerator and denominator by the same value so that the denominator ends up as 24.
- 1/8 = (1/8)·(3/3) = 3/24
- 5/12 = (5/12)·(2/2) = 10/24
- 2/3 = (2/3)·(8/8) = 16/24
