2 5/8+ 1/3 Simplify the expression above. Which of the following is correct?
A. 7 7/8
B. 1 1/7
C. 7/8
D. 8/63
5 / 8 = 5 * 3 / ( 8 * 3 ) =
15 / 24
1 / 3 = 8 * 1 / ( 8 * 3 ) = 8 / 24
2 5 / 8 + 1 / 3 = 2 + 5 / 8 + 1 / 3 =
2 + 15 / 24 + 8 / 24 = 2 + 23 / 24 =
2 * 24 / 24 + 23 / 24 =
48 / 24 + 23 / 24 =
71 / 24
To simplify the expression 2 5/8 + 1/3, we need to find a common denominator for the fractions.
The denominators are 8 and 3. The least common multiple (LCM) of 8 and 3 is 24.
Next, we need to convert the fractions to have a denominator of 24.
For 2 5/8, the whole number part is 2, and the fraction part needs to be multiplied by (24/8) to get a denominator of 24:
2 5/8 = 2 + (5/8) = 2 + (5/8) x (24/8) = 2 + (30/24) = 2 + 1 6/24
For 1/3, we multiply the fraction by (24/3) to get a denominator of 24:
1/3 = (1/3) x (24/3) = 8/24
Now, we can add the fractions together:
2 5/8 + 1/3 = 2 + 1 6/24 + 8/24 = 2 + 14/24 = 2 14/24
To simplify this mixed number further, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 2:
2 14/24 = 2 + (14/2)/(24/2) = 2 + 7/12
So, the simplified expression is 2 7/12.
None of the provided options (A, B, C, D) is correct.