Flvs.net one year ago Medal and Fan Sara left a bin outside in her garden to collect rainwater. She notices that 1/8 gallon of water fills 2/3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.

1. anonymous

So, One-eighth gallon of water will fill two-thirds of the bin. We want the sentence: "x gallons of water will fill three-thirds of the bin." What we do is multiply two-thirds by its reciprocal (three-halves) and make sure we do it on both sides. \frac{1}{8} = \frac{2}{3} x \frac{3}{2} * \frac{1}{8} = x \frac{3}{16}\ gal. = x So your equation would look like this: \frac{1}{8} * \frac{3}{2}\ gal._{water} = x

2. Flvs.net

$\frac{1}{8} * \frac{3}{2}\ gal._{water} = x$

3. Flvs.net

This?

4. anonymous

yup

5. Flvs.net

What is X?

6. Flvs.net

What does it equal?

7. anonymous

just use the equation and solve yourself

8. Flvs.net

9. DanJS

$\frac{ 1~bin }{ 1 } * \frac{ 1/ 8 ~gal }{ 2/3~bin } = ~~~gal$

10. Flvs.net

I meant

11. Flvs.net

How do I solve that @DanJS

12. DanJS

you wanted gallons in 1 bin, so start with 1 bin, multiply that by the given ratio of 1/8 gallon to 2/3 bin... notice it is set up so that the units for bin will cancel... just take care of the numbers

13. Flvs.net

so I do 1/8 * 2/3?

14. DanJS

when dividing a fraction by a fraction, you can flip the bottom one over and multiply it to the top

15. Flvs.net

Isn't it "keep Change Flip?"

16. DanJS

$\frac{ 1 }{ 8 }*\frac{ 3 }{ 2 }$

17. Flvs.net

$\frac{ 1 }{ 8 } * \frac{ 3 }{ 2 } = \frac{ 3 }{ 16 }$ Is that correct?

18. DanJS

yep, 3/16 gal per full bin

19. Flvs.net

Thank you!