1. ## ratio questions

hi im really confused about these questions i can do whole numbers but not decimals:

Josiah is making rectangular tiles.

The ratio of length:width must always be 5:3

q1. He makes a tile 4.5cm wide how long must the tile be?

1b.He makes a miniature tile in the same ratio with a length of 2.5cm. how wide must the tile be?

Thank you if you can help me asap please.

2. If this is "due in tomorrow", then it's likely homework for a grade. It's forum policy not knowingly to help with such problems.

3. would you be able to tell me how to do these kind of questions that are similar to these?

4. Yeah, I don't have any problem doing that. Why don't you post a new problem that isn't for homework, but uses the same concepts?

5. hmm ok heres one

George is making bricks for a house, each brick must always be in the ratio of width to length 7:5

He makes the tile 5.5 cm wide how long must the brick be?

6. So what ideas do you have?

7. hmm do you maybe have to divide 7 by 5.5 or divide 5 by 5.5 or maybe make 5.5 into a fraction i really have no clue or you could maybe multiply

8. Well, one way to think of this problem is in terms of unit conversion: units of width to units of length or vice versa. So, the ratio statement itself is saying that

$\displaystyle \displaystyle\frac{\text{units of width}}{\text{units of length}}=\frac{7}{5}.$

You can also just as easily flip both fractions to say that

$\displaystyle \displaystyle\frac{\text{units of length}}{\text{units of width}}=\frac{5}{7}.$

You're asked to "convert" from units of width to units of length. Your intuition about multiplication is good. But what will you multiply by? You want the undesired units to cancel, and be left with the desired units.

9. so as its length do you multiply 5.5 by 7?

and if it was width you would multipy 5.5 by 5?

10. im still not sure what to do

11. You want the units to cancel. So multiply by whichever of the two fractions I've provided will do that. This is no different from normal unit conversion. For example, it's a fact that $\displaystyle 2.54\,\text{cm}=1\,\text{in}.$ It follows, then, that

$\displaystyle \displaystyle\frac{2.54\,\text{cm}}{1\,\text{in}}= \frac{1\,\text{in}}{2.54\,\text{cm}}=1.$

Therefore, I may multiply any quantity whatsoever by either fraction, and not change the value. (I'm just multiplying by 1, after all.) So, if I want to convert 3 inches to centimeters, I do this:

$\displaystyle \displaystyle 3\,\text{in}\times\frac{2.54\,\text{cm}}{1\,\text{ in}}=3\times\frac{2.54\,\text{cm}}{1}=3\times 2.54\,\text{cm}=7.62\,\text{cm}.$

Yes, units can cancel just like that. So, you pick whichever fraction will get the undesired units to cancel, so that you're left with the units you want.

Now, in the problem you have, you have units of width, but you want units of length. Which fraction would you pick to multiply your 5.5?

12. umwould you use the second fraction?

13. Right. And why would you pick that one?

14. no actually the first one because its cm

15. Darn. I wasn't clear. Post # 11 is mostly an example to show you how unit conversion works. The question at the end of Post # 11 is referring back to Post # 8. So, to rephrase: which of the two fractions in Post # 8 do you want to multiply your 5.5 units of width by? Don't worry about cm to in conversion in this problem. The cm, in your problem as posted in Post # 5, will just come along for the ride.

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