Question

How do you evaluate `7\frac { 3} { 4} + 1\frac { 7} { 8}`?

Answer 1

See a solution process below:

Explanation:

First, convert the mixed numbers to improper fractions

`7 3/4 + 1 7/8 =>`

`(7 + 3/4) + (1 + 7/8) =>`

`([4/4 xx 7] + 3/4) + ([8/8 xx 1] + 7/8) =>`

`(28/4 + 3/4) + (8/8 + 7/8) =>`

`(28 + 3)/4 + (8 + 7)/8 =>`

`31/4 + 15/8`

Next, put the fractions over a common denominator by multiplying the fraction on the left by the appropriate form of `1`:

`(2/2 xx 31/4) + 15/8 =>`

`(2 xx 31)/(2 xx 4) + 15/8 =>`

`62/8 + 15/8 =>`

`(62 + 15)/8 =>`

`77/8`

Now, if necessary, convert the improper fraction to a mixed number:

`(72 + 5)/8 =>`

`72/8 + 5/8 =>`

`9 + 5/8 =>`

`9 5/8`

Answer 2

=`9\frac {5} { 8}`

Explanation:

`7\frac { 3} { 4} + 1\frac { 7} { 8}`

Write in improper form:

=`\frac { 7\times 4 +3} { 4} + \frac { 1\times 8 + 7} { 8}`

=`\frac { 28 +3} { 4} + \frac { 8+ 7} { 8}`

=`\frac {31} { 4} + \frac { 15} { 8}`

Make the denominators equal:

=`\frac {31} { 4}*(2/2) + \frac { 15} { 8}`

=`\frac {62} {8} + \frac { 15} { 8}`
Add:

=`\frac {77} { 8}`

=`9\frac {5} { 8}`