Question

How do you evaluate `\frac { 1} { 2} \div \frac { 1} { 4} \times \frac { 2} { 5} \div \frac { 1} { 3}`?

Answer 1

`12/5`

Explanation:

In the order of operation multiply and divide have equal ranking. So as we only have multiply and divide we should work left to right.

Given: `color(magenta)(1/2-:1/4xx2/5-:1/3)`

Step 1
`color(magenta)(1/2-:1/4) ->1/cancel(2)^1xxcancel(4)^2/1 = 2/1=color(blue)( 2)`

What's left: `color(blue)(2)xxcolor(magenta)(2/5-:1/3)`
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Step 2
`color(blue)(2)color(magenta)(xx2/5) = 2/1xx2/5 = (2xx2)/(1xx5)=color(blue)(4/5)`

What's left : `color(blue)(4/5)color(magenta)(-:1/3)`
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Step 3

`color(blue)(4/5)color(magenta)(-:1/3) = 4/5xx3/1 =(4xx3)/(5xx1)=color(blue)(12/5)`