Question

What is `1\frac { 3 } { 4 } \div 7 \frac { 7 } { 8 }`?

Answer 1

`1 3/4-:7 7/8=2/9`

Explanation:

To divide by a fraction `a/b` is equivalent to multiplying by its reciprocal, which is `b/a`, obtained by just reversing numerator and denominator. If the divisor is a mixed fraction (as given in the question), we need to first convert it to improper fraction.

Hence `1 3/4-:7 7/8`

`hArr7/4-:63/8`

= `7/4xx8/63`

= `7/4xx(4xx2)/(7xx9)`

= `cancel7/cancel4xx(cancel4xx2)/(cancel7xx9)`

= `2/9`

Answer 2

Just an alternative way of solving this problem type

`2/9`

Explanation:

Write `1 3/4" as "7/4`

Write `7 7/8" as "63/8`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`7/4-:63/8`

Multiply by 1 and you do not change the value but 1 comes in many forms.

`[7/4color(magenta)(xx1)]-:63/8" "->" "[7/4color(magenta)(xx2/2)]-:63/8`

`14/8-:63/8" "=14-:63 =14/63`

`(14-:7)/(63-:7) = 2/9`