Question

There were 48 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 3/4 of the remaining runners dropped out. How many runners finished the race?

Answer 1

what is one third of 48?

Answer 2

16

Answer 3

ok and what is 48-16?

Answer 4

32
but i thought you had to make the fractions equal?

Answer 5

no we can do it step by step
one third of the runners dropped out
16 of the runners dropped out
that leaves 32

now what is three fourths of 32? i.e. what is \(32\times \frac{3}{4}\) ?

Answer 6

3/8?

Answer 7

no it should be a whole number
4 goes in to 32 8 times, and 8 times 3 is 24

Answer 8

i.e.
\[32\times \frac{3}{4}=8\times 3=24\] so 24 more runners drop out, leaving
\[32-24=8\]

Answer 9

we could do it another way if you like and get the same answer
if one third drop out, then two thirds stay
two thirds of 48 is 32 and then if three fourths drop out, one fourth remains
one fourth of 32 is 8

Answer 10

oh cool

Answer 11

i have another question \[w ^{3}u ^{7}/wu ^{5}\]

Answer 12

subtract the exponents
\[\frac{w^3u^7}{wu^5}=w^{3-1}u^{7-5}=w^2u^2\]

Answer 13

thank you

Answer 14

yw

Answer 15

x\[x ^{3}y ^{4}/xy ^{7} \]

Answer 16

so what would i do if the y for example on the bottom was larger that the top?