Question

Use estimation to determine the values, then solve 6 2 /5+ 3 9/12.

Option 1: 7 7/6
Option 2: 9 7/10
Option 3: 8 1/3
Option 4: 10 1/4

Answer 1

The solution for 6 2 /5+ 3 9/12 is
`\(8 (1)/(3)\)`. So, The correct option is Option 3:
`\(8 (1)/(3)\)`.

Step-by-step explanation:

To solve the expression 6 2/5 + 3 9/12, we need to find the common denominator for the fractions. The common denominator for 5 and 12 is 60.

Now, we convert the fractions to have the common denominator:

`\[ (6 * 12)/(5 * 12) + (3 * 5)/(9 * 5) = (72)/(60) + (15)/(60) \]`

Adding these fractions gives:

`\[ (72 + 15)/(60) = (87)/(60) \]`

Now, we convert the improper fraction
`\((87)/(60)\)` to a mixed number:

`\[ 1 (27)/(60) \]`

Next, we add this result to the whole numbers in the original expression:

`\[ 6 + 3 + 1 (27)/(60) \]`

Combine the whole numbers:

10

Now, simplify the fraction
`\((27)/(60)\)` by dividing both the numerator and denominator by their greatest common factor, which is 3:

`\[ 1 (9)/(20) \]`

Combine this fraction with the whole number:

`\[ 10 (9)/(20) \]`

So, the final answer is
`\(10 (9)/(20)\)`, which is equivalent to the mixed number
`\(8 (1)/(3)\)`. Therefore, the correct option is Option 3:
`\(8 (1)/(3)\)`.