Question

Easy Fractions help? I dont know why im confused :P

Answer 1

@Hero

Answer 2

you can first add (the fractions inside the parens) then multiply by ⅔
or
multiply each fraction inside the parens by ⅔ and then add the two fractions

which way do you want to do it?

Answer 3

the 1st one

Answer 4

ok, so we add
⅓ + 3 ¼

the first step is change 3 ¼ to an improper fraction.
can you do that ?

Answer 5

13/4?

Answer 6

yes
now you have
\[ \frac{1}{3} + \frac{13}{4} \]

next, you need a common denominator. one way is to multiply the two denominators (this sometimes gives a bigger number than we would get if we were smarter, but it always works).
in other words, let the common denominator be 3*4= 12

Answer 7

next step. multiply the first fraction by 4/4 (which means multiply top and bottom by 4.

Answer 8

can you multiply the first fraction by 4/4 ?

Answer 9

13/12? sorry im confused

Answer 10

we are working on
\[ \frac{1}{3} + \frac{13}{4} \]

we know a common denominator is 12.
to get a 12 in the bottom of the first fraction we multiply by 4 (because 3*4 is 12)
but to keep things "fair" we also multiply the top by 4. Like this
\[ \frac{1}{3}\cdot \frac{4}{4} + \frac{13}{4} \]

to multiply fractions, multiply top times top and bottom times bottom.
can you do that for
\[ \frac{1}{3}\cdot \frac{4}{4} \]

Answer 11

3 and 8? sorry once again sorry

Answer 12

to multiply
\[ \frac{1}{3}\cdot \frac{4}{4} \]
you multiply the top numbers. what is 1*4 ?
and then multiply the bottom numbers. what is 3*4 ?

Answer 13

4/12?

Answer 14

yes

Answer 15

sweet thx

Answer 16

so far you have
\[ \frac{4}{12} + \frac{13}{4} \]

now we need a 12 in the denominator (bottom) of the second fraction (the 13/4)

Answer 17

to get a 12 we multiply by 3. but we must multiply top and bottom by 3
can you do this one:
\[ \frac{13}{4}\cdot \frac{3}{3} \]

Answer 18

13/4?

Answer 19

yes, that is the simplest way to write
\[ \frac{13}{4}\cdot \frac{3}{3} \]
but we want to write it so its denominator is 12

multiply top times top
multiply bottom times bottom

can you do that?

Answer 20

52/9? i m soo sorry if its worng im quite tired

Answer 21

you want to do 13*3
and
4*3

Answer 22

39 and 12?

Answer 23

yes. you get 39/12

now you have
\[ \frac{4}{12} + \frac{39}{12} \]
to add fractions with the same denominator, add the tops.
the denominator stays 12

what is 4+39 ?

Answer 24

43

Answer 25

and the denominator stays 12
the sum of 4/12 + 39/12 is 43/12

Answer 26

so simplify?

Answer 27

now we go back to the original problem. we have to multiply by ⅔
\[ \frac{2}{3} \cdot \frac{43}{12} \]

Answer 28

43/18

Answer 29

I would first simplify by dividing the top by 2, and the bottom by 2
\[ \frac{1}{3} \cdot \frac{43}{6} \]
now multiply top times top
and multiply bottom times bottom
what do you get ?

Answer 30

Okay so i simplify 43/18?

Answer 31

yes, 43/18

we could change that to a proper fraction
it depends on what the answer choices are.

Answer 32

divide 18 into 43 to get 2 remainder 7
that means the answer can also be written as
2 \(\frac{7}{18}\)

Answer 33

2 and 7 over 18