Brent divided 3/1/8 by a number and got 4/1/2 what number did he divide by?

So (3 and 1/8) / x=4 and 1/2

convert all to inmroper fractions

3=24/8

3 and 1/8=25/8

4 and 1/2

4=8/2

4 and 1/2=9/2

(25/8) / x=9/2

multiply both sides by x

25/8 = (9/2) x

multiply both sides by 2/9 to clear fraction on right side

50/72=x

25/36=x

the number is 25/36

3 1/8 : x = 4 1/2

for easier computation, convert the mixed fractions into fractions

3 1/8 = 8 * 3 = 24 + 1 = 25 ⇒ 25/8

4 1/2 = 2 * 4 = 8 + 1 = 9 ⇒ 9/2

In dividing fractions, we have to get the reciprocal of the 2nd fraction and multiply it to the first fraction.

25/8 * 1/x = 25/8x

25/8x = 9/2

to get the value of x, we must cross multiply the fractions

25 (2) = 9 (8x)

50 = 72x

x = 50/72

x = 25/36

simplified to

25/36 * both divided by 2

to check:

25/8 : x = 9/2

25/8 : 25/36 = 9/2

25/8 * 36/25 = 9/2

25 * 36 / 25 * 8 = 9/2 * cancel out 25

36/8 = 9/2 * divide 36 and 8 by 4 to simplify the fraction

9/2 = 9/2