Question

Divide and Simplify: 4a/7b^2 / 5a^2/8b
a. 32/35ab
b. 2/35ab
c. 5a^3/14b^3
d. 32ab/35

Answer 1

divide and simplify: \[4a/7b^2 \div 5a^2/8b \]

Answer 2

Here's a property:

\( \color{Black}{\Rightarrow \Large {a \over b} \div {x \over y} = {a \over b} \times {y \over x}}\)

Note how y/x is the reciprocal of x/y and how a/b is unchanged.

Answer 3

Hint: \[\Huge \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\]

Answer 4

^ That is not readable to me :P

Answer 5

i have weak 62-year-old eyes okay =_=

Answer 6

i hate fractions i can never solve them.. can u add in the numbers?

Answer 7

add in? what do you mean by that?

Answer 8

the numbers i have for my quetion

Answer 9

would you agree that this problem can be rewritten as \[\frac{4a}{7b^2} \div \frac{5a^2}{8b}??\]

Answer 10

yes thats how it is

Answer 11

You can write it as:

\(\Huge {4a \over 7b^2} \times {8b \over 5a^2}\)

Can't you?

Answer 12

then would you agree that the expression i posted is in the form \[\Huge \frac{w}{x} \div \frac{y}{z}??\]

these letters are just mere representations

Answer 13

You can also cancel something :)

Answer 14

im lost again lol... how do u divide it? is it side to side or diagnol

Answer 15

just tell me if you agree that the expression i wrote looks like \(\frac{w}{x} \div \frac{y}{z}\)??

Answer 16

i guess yea?

Answer 17

then what would be "w" in the expression \(\frac{4a}{7b^2} \div \frac{5a^2}{8b}\)??

Answer 18

4a?

Answer 19

great! you're right...and what is x?

Answer 20

7b^2

Answer 21

y?

Answer 22

i mean what's y?

not "why"

Answer 23

5a^2

Answer 24

and z?

Answer 25

8b

Answer 26

great..so..

w = 4a
x = 7b^2
y = 5a^2
z = 8b

now remember that i said \[\frac{w}{x} \div \frac{y}{z} = \frac{w}{x} \times \frac{z}{y}\]

now..using the letters you assigned...what is \(\large \frac{w}{x} \times \frac{z}{y}\)

Answer 27

?

Answer 28

am i cross multiplying?

Answer 29

no no....let's take it from the top...you agreed that \[\frac{4a}{7b^2} \div \frac{5a^2}{8b} \implies \frac{w}{x} \div \frac{y}{z}\] right? you agreed that they are in the same format?

Answer 30

yes

Answer 31

and i told you that \[\huge \frac{w}{x} \div \frac{y}{z} = \frac{w}{x} \times \frac{z}{y}\] right? i made it bigger so you can see the differences ;) this is actually a rule/formula or whatever you wanna call it lol...

Answer 32

yes then....?

Answer 33

THEN you shall turn \[\large \frac{4a}{7b^2} \div \frac{5a^2}{8b}\] into the form \[\Large \frac{w}{x} \times \frac{z}{y}\]

Answer 34

note that

w = 4a
x = 7b^2
y = 5a^2
z = 8b

as we stated before

Answer 35

you just have to substitute 4a into w; 7b^2 into x; 5a^2 into y and 8b into z

Answer 36

would it be answers a or d?

Answer 37

would it be between those 2?

Answer 38

is it a?

Answer 39

nvm i have the answer now but thanks :)

Answer 40

great!!