grade 8 fractions math help

Otis

Elite Member
Joined
Apr 22, 2015
Messages
4,320
… 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

Elite Member
Joined
Oct 27, 2017
Messages
2,525
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
Joined
Jan 17, 2023
Messages
2
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
Joined
Apr 22, 2015
Messages
4,320
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]
 

mather332

New member
Joined
Jan 17, 2023
Messages
2
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
Joined
Apr 22, 2015
Messages
4,320
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
Joined
Nov 24, 2012
Messages
2,968
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
Joined
Dec 30, 2014
Messages
13,417
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....
You can always think about this while you spend sometime in the corner.
 

Steven G

Elite Member
Joined
Dec 30, 2014
Messages
13,417
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!
 
Top