# Algebra Question

November 17, 2012 11:35 AM Subscribe

Can anyone help with an algebra question I am trying to help my neice with her homework.

(9/2m) - (m+4)/4m = 5/36

11th grade algebra- do you multiply entire equation by 2m? lowest common denominator? help. An explanation would be great and also any websites that help with algebra would be great too. Thanks.

(9/2m) - (m+4)/4m = 5/36

11th grade algebra- do you multiply entire equation by 2m? lowest common denominator? help. An explanation would be great and also any websites that help with algebra would be great too. Thanks.

Multiply the whole equation by 4m, that gets rid of the m's in the denominator. Then multiply the whole equation by 36 to get rid of the all remaining denominators. At this point you can simplify the equation to a point where solving it should be easy.

posted by Green With You at 11:42 AM on November 17, 2012

posted by Green With You at 11:42 AM on November 17, 2012

Here we go:

Multiply the top and bottom of the first term on the left hand side by 2 to get:

18/4m -(m+4)/4m = 5/36

So now both term on the left hand side have 4m as the denominator so we can write it as:

(18-(m+4))/4m = 5/36

Expanding the bracket in the numerator on the left hand side we get:

(18-m-4)/4m = 5/36

(14-m)/4m=5/36

Multiply both sides by 4 (to get rid of the 4 and make the denominator on the right hand side more tractable) and we get:

(14-m)/m = (5*4)/36

Now 36 = 9*4

Therefore we can cancel out the 4 in the numerator on the right hand side and change 36 to 9 giving us:

(14-m)/m = 5/9

Now cross-multiply the two sides:

9*(14-m) = 5m

Expanding:

126-9m = 5m

Take the 9m term to the other side:

126 = 14m

Now remember that 126 = 9*14

So m = 126/14 = 9.

posted by peacheater at 11:43 AM on November 17, 2012 [3 favorites]

Multiply the top and bottom of the first term on the left hand side by 2 to get:

18/4m -(m+4)/4m = 5/36

So now both term on the left hand side have 4m as the denominator so we can write it as:

(18-(m+4))/4m = 5/36

Expanding the bracket in the numerator on the left hand side we get:

(18-m-4)/4m = 5/36

(14-m)/4m=5/36

Multiply both sides by 4 (to get rid of the 4 and make the denominator on the right hand side more tractable) and we get:

(14-m)/m = (5*4)/36

Now 36 = 9*4

Therefore we can cancel out the 4 in the numerator on the right hand side and change 36 to 9 giving us:

(14-m)/m = 5/9

Now cross-multiply the two sides:

9*(14-m) = 5m

Expanding:

126-9m = 5m

Take the 9m term to the other side:

126 = 14m

Now remember that 126 = 9*14

So m = 126/14 = 9.

posted by peacheater at 11:43 AM on November 17, 2012 [3 favorites]

FYI you can enter algebra into wolfram-alpha and get a step-by-step solution.

posted by idb at 12:05 PM on November 17, 2012 [3 favorites]

posted by idb at 12:05 PM on November 17, 2012 [3 favorites]

(9/2m) - (m+4)/4m = 5/36

It would sure be great if we didn't have that (1/4m) in there because it's hard to work with. So let's multiple both side of the equation by 4m.

4m((9/2m) - (m+4)/4m) = 4m(5/36)

Which reduces to

18 - m + 4 = (5/9)m

Add m to both sides to get

18 - 4 = (5/9)m + m

Or

14 = (14/9)m

Multiply both sides of the equation by (9/14)

9 = m

posted by deathpanels at 12:36 PM on November 17, 2012 [2 favorites]

It would sure be great if we didn't have that (1/4m) in there because it's hard to work with. So let's multiple both side of the equation by 4m.

4m((9/2m) - (m+4)/4m) = 4m(5/36)

Which reduces to

18 - m + 4 = (5/9)m

Add m to both sides to get

18 - 4 = (5/9)m + m

Or

14 = (14/9)m

Multiply both sides of the equation by (9/14)

9 = m

posted by deathpanels at 12:36 PM on November 17, 2012 [2 favorites]

When I teach this, I have them multiply by the LCD which is 36m.

You get:

162 - 9(m + 4) = 5m

162 - 36 = 9m + 5m

126 = 14m

so m = 9

posted by Obscure Reference at 1:50 PM on November 17, 2012

You get:

162 - 9(m + 4) = 5m

162 - 36 = 9m + 5m

126 = 14m

so m = 9

posted by Obscure Reference at 1:50 PM on November 17, 2012

I actually went with multiplying the first term by 2 (so not changing the number, just how it's represented), which yields 18/4m - (m+4)/4m = 5/36... so 4m = 36... so m = 9... (and also 18-(m+4)=5... so m=9...) which is just a test to make sure the first value is correct.

It's been years since I took algebra so I started off with 1/2 - 1/4 = x (to refresh my memory of the rules of fraction subtraction)... 1/2 is the same as 2/4... so I rewrote as 2/4 - 1/4 = x... and so x is 1/4... realizing that the bottom remains consistent I was able to realize that once you change 9/2m to 18/4m you've got two equations that you can use to test the value...

Perhaps not the *best* way to solve, but just a demonstration that using what you know to figure out what you don't know works, sometimes.

posted by one4themoment at 6:22 PM on November 17, 2012

It's been years since I took algebra so I started off with 1/2 - 1/4 = x (to refresh my memory of the rules of fraction subtraction)... 1/2 is the same as 2/4... so I rewrote as 2/4 - 1/4 = x... and so x is 1/4... realizing that the bottom remains consistent I was able to realize that once you change 9/2m to 18/4m you've got two equations that you can use to test the value...

Perhaps not the *best* way to solve, but just a demonstration that using what you know to figure out what you don't know works, sometimes.

posted by one4themoment at 6:22 PM on November 17, 2012

Also I loved this question, and I spent a few minutes destroying a piece of scrap paper with my scribbles :)

posted by one4themoment at 6:23 PM on November 17, 2012

posted by one4themoment at 6:23 PM on November 17, 2012

Thank you all!

posted by Summer Fall at 6:44 PM on November 18, 2012

posted by Summer Fall at 6:44 PM on November 18, 2012

This thread is closed to new comments.

posted by coolsara at 11:38 AM on November 17, 2012