Question

How do you evaluate `14 1/ 2- 7\frac { 11} { 18}`?

Answer 1

Method 1 of 2

`6 8/9`

Explanation:

Multiply by 1 and you do not change the value. However, 1 comes in many forms. So you can change the way a number looks without changing its intrinsic value.

The bottom number in a fraction has the name denominator. In reality it is a sort of unit of measurement. Consequently you can not DIRECTLY add or subtract the top numbers unless the units of measurement (denominators) are the same.

`color(blue)("Making the denominators the same")`

`color(brown)("Consider the "14 1/2" write as "14+1/2)`

`color(green)([14color(red)(xx1)]+1/2 )`

`color(green)([14color(red)(xx2/2)]+1/2 )`

`color(green)([28/2]+1/2 =29/2 )`

but this denominator (unit of measurement) does not match that of`7 11/18`

`color(green)(29/2color(red)(xx1)=29/2color(red)(xx9/9)=261/18 )`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Consider the "7 11/18)`

`color(green)("Using the above method we have "7 11/18 = 137/18)`

`"===================================="`
`color(blue)("Putting it all together")`

`261/18-137/18color(white)("d")=color(white)("d")(261-137)/18color(white)("d")= color(white)("d")124/18color(white)("d")=color(white)("d")6 8/9`

color(white)("d")

Answer 2

Method 2 of 2

It take longer to explain that actually doing the maths.

`6 8/9`

Explanation:

`color(blue)("Method")`

Directly subtract whole number from whole number and fraction from fraction.
~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Preperation")`

Starting point: `(14-7)+(1/2-11/18)`

Note that `1/2` is the same as `9/18` so we have:

`(14-7)+(9/18-11/18)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Doing the maths")`

But `9/18` is less than `11/18` so lets move a 1 from the 14 giving

`(13-7)+(1+9/18-11/18)`

`(13-7)+(18/18+9/18-11/18)`

`(6)+(7/18+9/18)`

`6+(16/18)`

`6+((16-:2)/(18-:2))`

`6 8/9`