How to Solve These Math Problems

[marielstepniewski]

1.)

3/5+6/10+9/15+12/20+18/30
_________________________ =
5


2.) If -8 < x < 2 and -4 < y < 10, what is the range of all possible values of xy?

[varun7686]

Hi,

For 2.) i think that..

The minimum value xy can result into is when x = -7 and y = 9 hence xy = -63

The maximum value xy can result into is whn x = -7 and y = -3 hence xy = 21

Therefore -63 <= xy <= 21

For 1.)

Find LCM of the fractions in the numerator, which is 60, therefore numerator becomes (36+36+36+36+36) / 60

the overall fraction can then be written as

5 X 36
-------
5

And the answer is 36.

[gbd97]

1.for 1 just simplify .....you will get the answer.

2.for 2
maximum range of xy is -8*-4=32
minimum range of xy is -8*10=-80

so the ans is -80<xy<32
i think u got your answer.

[tommywallach]

Hey Guys,

Just thought I'd weigh in on these myself. One quick thing: in the future, please only post one question per thread. It makes things way less confusing for people, trust me!

1.)

3/5+6/10+9/15+12/20+18/30
_________________________ =
5

I would do this by quickly noticing that every fraction on top is 3/5ths. There are five of them. So the numerator is just (3/5) * 5. When you divide by 5, the 5s just cancel, so the answer is 3/5.

2.) If -8 < x < 2 and -4 < y < 10, what is the range of all possible values of xy?

For these questions, the safest thing is just to test all of the limit values. In other words:

(-8) * (-4) = 32
(-8) * 10 = -80
2 * (-4) = -8
2 * 10 = 20

This is how you can avoid the error that you saw someone make, where they thought the maximum was 20 (the product of the two GREATEST positive numbers), because they missed the product of the two SMALLEST negative numbers.

-t

P.S. Don't forget that the ranges are technically LESS than 32 and MORE than -80!