To evaluate the expression 2/3 + 4/5 + 1/3 + 2/5, we first need to find a common denominator. The denominators here are 3 and 5.
The least common multiple of 3 and 5 is 15.
Now we convert each fraction to have this common denominator:
- For 2/3: Multiply both the numerator and denominator by 5:
2/3 = (2 × 5)/(3 × 5) = 10/15 - For 4/5: Multiply both the numerator and denominator by 3:
4/5 = (4 × 3)/(5 × 3) = 12/15 - For 1/3: Multiply both the numerator and denominator by 5:
1/3 = (1 × 5)/(3 × 5) = 5/15 - For 2/5: Multiply both the numerator and denominator by 3:
2/5 = (2 × 3)/(5 × 3) = 6/15
Now we have transformed the expression into:
10/15 + 12/15 + 5/15 + 6/15
Next, we can add the fractions together:
(10 + 12 + 5 + 6) / 15 = 33/15
Now, let’s simplify 33/15. Both numbers can be divided by 3:
33 ÷ 3 = 11 and 15 ÷ 3 = 5
So, we simplify it to:
11/5 or 2.2
In conclusion, the value of 2/3 + 4/5 + 1/3 + 2/5 is 11/5 or 2.2.