# grade 8 fractions math help

#### Otis

##### Elite Member
… i keep being careless with my calculations …
Hi Eddy. You might try double-checking what you write, after each step.

Are you still using a calculator? I'd suggest doing arithmetic by hand, followed by checking on a calculator. If they don't match, redo the arithmetic by hand. After you've double-checked enough, your mind will begin to realize some mistakes as you make them. • eddy2017

#### eddy2017

##### Elite Member
honestly, yes. I'm using a calculator
I think that is killing me.
I should do it like you say.
by hand first and the double check itvwith a calc.

#### mather332

##### New member
4.5 hours is a correct answer. You method is okay. But, if you're expected to use exact arithmetic (instead of calculator approximations), there might be an issue with your work on a class assignment.

1/(3/4) is not 1.33 (it's actually 4/3).

1.33 is only a decimal approximation for 4/3.

1.33 is exactly 133/100.

Likewise, 15/3.33 is not 4.5

15/3.33 is actually 500/111. Very good. Here's another way to go.

Mr. J fills a shelf in 3/4 hour.

15 × 3/4 = 45/4

Mr. J completes the job in 45/4 hour.

Mr. H requires 2/3 the time Mr. J does, to complete the job.

2/3 × 45/4 = 15/2

Therefore, Mr. J completes 4/45ths of the job per hour, and Mr. H completes 2/15ths of the job per hour. We combine those reciprocals.

4/45 + 2/15 = 2/9

Working together, they complete 2/9ths of the job per hour, so it takes them 9/2 hour to finish.

9/2 = 4.5 Why did you make the fractions reciprocal.

#### Otis

##### Elite Member
Why did you make the fractions reciprocal.
Hi mather. It's because we're using the number 1 to represent the whole job. In other words, when we multiply [hours to do entire job] times [fraction of job done per hour] we must get 1.

If we do 1/4 of a job per hour, then we need 4 hours to do the job. If we do 1/2 per hour, then we need 2 hours.

Let T = hours to do entire job, with 2/9 of job done each hour:

(T)(2/9) = 1

We can see that T must be the reciprocal of 2/9. For those who don't see it, solve for T by dividing each side by 2/9. Then see note below.

Dividing by a fraction is the same as multiplying by its reciprocal.

(T)(2/9)(9/2) = (1)(9/2)

T = 9/2

NOTE: We always get 1, when we multiply two reciprocals.

EDIT: Let a/b and c/d be two fractions written in lowest terms.

IF (a/b)(c/d) = 1
Then a=d AND b=c
Fractions a/b and c/d are reciprocals [imath]\;[/imath]

• BigBeachBanana and mather332

#### mather332

##### New member
Hi mather. It's because we're using the number 1 to represent the whole job. In other words, when we multiply [hours to do entire job] times [fraction of job done per hour] we must get 1.
If we do 1/4 of a job per hour, then we need 4 hours to do the job. If we do 1/2 per hour, then we need 2 hours.

Let T = hours to do entire job, with 2/9 of job done each hour:

(T)(2/9) = 1

We can see that T must be the reciprocal of 2/9. For those who don't see it, solve for T by dividing each side by 2/9. Then see note below.

Dividing by a fraction is the same as multiplying by its reciprocal.

(T)(2/9)(9/2) = (1)(9/2)

T = 9/2

NOTE: We always get 1, when we multiply two reciprocals.

IF (a/b)(c/d) = 1
Then a=d AND b=c
Fractions a/b and c/d are reciprocals [imath]\;[/imath]
Thank you so much! You are the best. #### Otis

##### Elite Member
Thank you so much!
You are welcome.

Otis said:
IF (a/b)(c/d) = 1
Then a=d AND b=c
Fractions a/b and c/d are reciprocals
I forgot to state that fractions a/b and c/d are written in lowest terms.

EG: (3/4)(8/6) = 1, but 8/6 is not reduced.

After reducing 8/6 to lowest terms, we see the reciprocals.

(3/4)(4/3) = 1
[imath]\;[/imath]

#### MarkFL

##### Super Moderator
Staff member
I would solve this by observing that in 90 minutes, the two of them can fill 5 shelves, or 15 shelves in 270 minutes, which is 4.5 hours.

#### Steven G

##### Elite Member
IF (a/b)(c/d) = 1
Then a=d AND b=c
Fractions a/b and c/d are reciprocals [imath]\;[/imath]
@Otis,
You might want to rethink that statement!
Suppose we have (a/b)[(kc)/(kd)]=1....

• The Highlander

#### Otis

##### Elite Member
Hi Steven! The fraction (kc)/(kd) is not written in lowest terms. It seems like you missed this added post:
I forgot to state that fractions a/b and c/d are written in lowest terms. #### Steven G

##### Elite Member
The fraction (kc)/(kd) is not written in lowest terms. It seems like you missed this added post: OK, we'll see if I get out of corner time with that line next time I make a sloppy error.
Have a great night/day!

#### Otis

##### Elite Member
we'll see if I get out of corner time … next time I make a sloppy error.
You just did! [imath]\;[/imath]