Question

Complete the equation. Whte the sum as a mixed number. 2(2)/(3)+(1)/(5)=(40)/(15)+(12)/(15)

Answer 1

To solve
`\(2 \cdot (2)/(3) + (1)/(5)\)`:

Convert
`\(2 (2)/(3)\)` to an improper fraction:
`\(2 \cdot (2)/(3) = (8)/(3)\).`

Add
`\((8)/(3) + (1)/(5) = (43)/(15)\), or as a mixed number, \(2 (13)/(15)\).`

let's solve
`\(2 \cdot (2)/(3) + (1)/(5)\)` step by step.

First, convert the mixed number to improper fractions:

`\(2 \cdot (2)/(3) + (1)/(5)\)`

To convert
`\(2 (2)/(3)\)` to an improper fraction, multiply the whole number (2) by the denominator (3) and add the numerator (2), then place it over the denominator:

`\(2 \cdot (2)/(3) = (6)/(3) + (2)/(3) = (8)/(3)\)`

Now the equation becomes:
`\((8)/(3) + (1)/(5)\)`

To add these fractions, find a common denominator, which is 15 in this case:

`\((8)/(3) + (1)/(5)\)`

Multiply the first fraction by
`\((5)/(5)\)` to make the denominators the same:

`\((8)/(3) + (1)/(5) = (40)/(15) + (3)/(15)\)`

Now add the fractions:

`\((40)/(15) + (3)/(15) = (43)/(15)\)`

Therefore,
`\(2 \cdot (2)/(3) + (1)/(5) = (43)/(15)\)`n, which as a mixed number is
`\(2 (13)/(15)\).`