How do you multiply \frac { 3} { 4} \times \frac { 4} { 9} \times \frac { 1} { 8}?

2 Answers
Mar 13, 2017

1/24

Explanation:

a/b\timesc/d\timese/f=(a\timesc\timese)/(b\timesd\timesf)


\therefore 3/4\times4/9\times1/8\rArr(3\times4\times1)/(4\times9\times8)
simplifying...
\rarr(12\times1)/(36\times8)=12/288
288\div12=24
\rarr(12\div12)/(288\div12)=1/24

Mar 13, 2017

1/24" " with a lot of explanation

Explanation:

color(darkorchid)("Preamble")

Demonstrating a principle by example

2xx6 give the same answer as 6xx2=12

So you can swap them around

Also

1/2xx1/3 = (1xx1)/(2xx3)=(1xx1)/(3xx2)=1/3xx1/2

So you can swap those around as well.
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color(darkorchid)("Answering the question")

Given:" "color(green)(3/4)xx color(blue)(4/9)xxcolor(red)(1/8)

What follows is the process that is behind the principle of cancelling out.

Write as:" "(color(blue)(4))/(color(green)(4)) xx(color(green)(3))/(color(blue)(9))xxcolor(red)(1/8)

But 4/4=1 giving:

1xx3/9xx1/8" "larr" in cancelling form this is " 3/(cancel(4))xx(cancel(4))/9xx1/8

3/9xx1/8

(3-:3)/(9-:3)xx1/8" "larr" in canceling form this is "(cancel(3)^1)/(cancel(9)^3)xx1/8

1/3xx1/8 = (1xx1)/(3xx8)= 1/24