Question

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

Answer 1

`-17/18`

Explanation:

In a calculation which involves different operations, identify the number of terms first. (Terms are separated by `+ and -` signs)

`color(blue)(1/4 xx2/3)color(red)( -2/3 div 3/5)" "larr` there are 2 terms.

Simplify each term to a single answer and then subtract them in the final step.

To divide is the same as multiplying by the reciprocal

`=color(blue)(1/cancel4^2 xxcancel2/3)color(red)( -2/3 xx5/3)" "(" cancel where possible" /"then multiply straight across")`

`=" "color(blue)(1/6)" "-" "color(red)(10/9)`

`=color(blue)(1/6)xx3/3 color(red)(-10/9)xx2/2" "larr` convert to a common denominator

`=(3-20)/18`

`=-17/18`

Answer 2

See the explanation

Explanation:

`1/4**2/3-2/3-:3/5`

`a/b**c/d=>(ac)/(bd)`
`a/b-:c/d=>a/b*d/c=>(ad)/(bc)`

From this,

`=>1/4**2/3-2/3-:3/5`

`=>(1*2)/(4*3)-2/3*5/3`

`=>2/12-(2*5)/(3*3)`

`=>2/12-10/9`

`a/b-c/d=>((a*d)-(b*c))/(b*d)`

From this,

`=>2/12-10/9`

`=>((2*9)-(12*10))/(12*9)`

`=>(18-120)/108`

`=>(-102)/108`

`=>-102/108`

`=>-(6*17)/(6*18)`

`=>-(cancelcolor(red)6*17)/(cancelcolor(red)6*18)`

`=>-17/18`