Question

2 2/3(2 1/3+2 5/12)-4 4/5=

Answer 1

2 2/3*(2 1/3+2 5/12)-4 4/5=8/3*(7/3+29/12)-24/5=8/3*(28+29/12)-24/5=8/3*57/12-24/5=38/3-24/5=190-72/15=118/15=7 13/15

Answer 2

To solve the expression, let's break it down step by step:

First, let's simplify the expression within the parentheses:

2 1/3 + 2 5/12

To add these mixed numbers, we need to convert them to improper fractions:

2 1/3 = (3 * 2 + 1)/3 = 7/3

2 5/12 = (12 * 2 + 5)/12 = 29/12

Now we can add them:

7/3 + 29/12

To add fractions, we need a common denominator. The least common multiple (LCM) of 3 and 12 is 12.

Now we can rewrite the fractions with a common denominator:

7/3 = (7/3) * (4/4) = 28/12

29/12 remains the same.

Adding them together:

28/12 + 29/12 = (28 + 29)/12 = 57/12

Next, let's substitute the result back into the original expression:

2 2/3 * (57/12) - 4 4/5

To multiply mixed numbers, we need to convert them to improper fractions:

2 2/3 = (3 * 2 + 2)/3 = 8/3

4 4/5 = (5 * 4 + 4)/5 = 24/5

Now we can multiply:

(8/3) * (57/12) = (8 * 57)/(3 * 12) = 456/36

To subtract mixed numbers, we need to convert them to improper fractions:

4 4/5 = (5 * 4 + 4)/5 = 24/5

Now we can subtract:

456/36 - 24/5

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 36 and 5 is 180.

Now we can rewrite the fractions with a common denominator:

456/36 = (456/36) * (5/5) = 2280/180

24/5 remains the same.

Subtracting them:

2280/180 - 24/5 = (2280 - 432)/180 = 1848/180

Finally, let's simplify the fraction:

1848/180 = (4 * 462)/(4 * 45) = 462/45

Therefore, the value of the expression 2 2/3(2 1/3 + 2 5/12) - 4 4/5 is equal to 462/45.