Solve for m in Algebra Equation: m/3 - m/5 = 4

[Jenninifer]

Homework Statement

"m" over 3 minus "m" over 5 equals 4. find m

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

$$\frac{m}{3} - \frac{m}{5} =4$$

Find the LCM of 3 and 5, and the multiply the entire equation by that number. Then you can simplify it.

 

[Jenninifer]

I tried that already, i multiplied everything by 15.
but the answer for m i got was 20 and when you substitute it it doesn't work.

 

[rock.freak667]

I tried that already, i multiplied everything by 15.
but the answer for m i got was 20 and when you substitute it it doesn't work.

Try it again. I don't get m=20 when I multiply and then simplify.

 

[Jenninifer]

okay well what do you get when you multipy it?
do you get 15m over 3 and 15m over 5 equals 60?

 

[rock.freak667]

okay well what do you get when you multipy it?
do you get 15m over 3 and 15m over 5 equals 60?

yes that is what you'd get. Now what is 15/3 and 15/5 work out to be?

 

[Jenninifer]

i know it's 5m and 3m right?

 

[rock.freak667]

i know it's 5m and 3m right?

Right, so you are left with 5m-3m=60

 

[berkeman]

okay well what do you get when you multipy it?
do you get 15m over 3 and 15m over 5 equals 60?

You don't multiple each term by 15. You multiple each term by 1, which keeps everything equal. The "1" that you multiply each term on the left by depends on what is in the denominator, because you are trying to get 15 in the denominator of both of the left terms so that you can add them.

What fraction x/x = 1 should you multiply the first term by to get 15 in the denominator?
What fraction y/y = 1 should you multiply the first term by to get 15 in the denominator?


EDIT -- Yikes, you guys type fast! Way ahead of me!

 

[Jenninifer]

yes so 2m = 60,
divide both by 2 and you get 30,
WOW! i cannot believe myself.

 

[HallsofIvy]

You don't multiple each term by 15. You multiple each term by 1, which keeps everything equal. The "1" that you multiply each term on the left by depends on what is in the denominator, because you are trying to get 15 in the denominator of both of the left terms so that you can add them.

You are apparently getting common denominators so you can subtract the fractions:
$$\frac{m}{3}\frac{5}{5}- \frac{m}{5}\frac{3}{3}= 4$$
$$\frac{5m}{15}- \frac{3m}{15}= \frac{5n- 3m}{15}= \frac{2m}{15}= 4$$
And now multiply both sides of the equation by 15 to get 2m= 60.

But it is easier to do what Jennifer and rock.freak667 did: multiply both sides of the equation by 15 right from the start:
$$\frac{m}{3}(15)- \frac{m}{5}(15)= 4(15)$$
$$5m- 3m= 2m= 60$$

Jennifer, in future please show exactly what you did, how you solved the equation and what answer you got in your first post. That will make it easier for us to see how to help you.