Final answer:
The correct answer is achieved by multiplying (2/3) and (12/22), which simplifies to approximately 0.182, then adding this result to (24/60), which simplifies to 0.4, giving a final result of approximately 0.582, which doesn't match any of the provided options.
Step-by-step explanation:
To find the value of the expression (2/3) * (12/22) + (24/60), we should first simplify and calculate each term separately. We start by multiplying the first two fractions:
(2/3) * (12/22) = (2 * 12) / (3 * 22) = 24 / 66
Now we simplify 24/66, which can be reduced to 4/11 by dividing both numerator and denominator by 6.
Next, we simplify the second fraction (24/60) which reduces to 2/5 when both numerator and denominator are divided by 12.
To add these two fractions, we must first find a common denominator. The least common denominator (LCD) for 11 and 5 is 55. We convert both fractions to have the LCD:
4/11 = (4*5) / (11*5) = 20/55
2/5 = (2*11) / (5*11) = 22/55
Now we can add the two fractions:
20/55 + 22/55 = 42/55
Converting this fraction to a decimal, 42/55 is approximately 0.7636, which is not one of the options provided, so we need to double-check our calculations.
We notice that the original provided options likely expected simplification of fractions to decimals directly:
(2/3) * (12/22) converts to approximately 0.182
as (24/60) converts to 0.4.
Add these two decimals together:
0.182 + 0.4 = 0.582
Therefore, the correct answer is none of the options: a) 0.6 b) 0.4 c) 0.7 d) 0.5