MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
In multi-step equations with the variable in the numerator of a fraction, start by isolating the fraction. This means eliminate everything else on that same side of the equal sign using inverse operations. Remember that in a fraction, the numerator is being divided by the denominator. Once the fraction with the variable in the numerator has been isolated, multiply both sides of the equation by the number in the denominator of the fraction in order to eliminate the denominator. We do this because multiplying is to opposite of dividing. Continue using inverse operations until you find the value of the variable. Don't forget to check your answer by substituting the value back into the original equation.
This is the kind of equation that you might not have ever seen before. We have this kind of gnarly fraction that for most students this is the first time in their Math careers where they see like where you're doing some subtraction and it's also involved in a fraction. It's like this weird looking thing that most people haven't seen before. But don't freak out. If you guys just keep in mind what a fraction means; it means dividing, you'll be able to solve this problem.
So first thing I want to do is get that nasty fraction all by itself by subtracting 4 from both sides of the equation so I'll have m minus 3 divided by 2 is equal to 6. This is where knowing how fractions means dividing is really important. What this means is some number take away 3 then divided by 2 gives you the answer 6 and the way to undo that fraction is to multiply both sides by 2. Instead of dividing by 2 I want to multiply both sides by 2. So what I'll have is m take away 3 is equal to 12, fraction gone, yes! That's the most important part. That's the thing that trips up a lot of students or makes them want to skip this problem on their homework is when they see that big fraction.
Okay now I can do it though m take away 3 equals 12, so add 3 to both sides, and I'll get m is equal to 15. Please be sure to check your work especially on a problem like this that's kind of challenging and where you might have made a mistake in one of these steps going along. The way you check your work is to substitute 15 back in to this original problem where you see m. So I'll do this 15 now take away 3 divided by 2 plus 4 I'm hoping is equal to 10. Let's see 15 take away 3 is 12, 12/2 plus 4 we hope is equal to 10, 12/2 reduces to 6, 6 plus 4 equals 10, yes! I rock. The way you know that's correct is because both sides are equal to each other, 6 plus 4 is indeed equal to 10.
So guys I want to make sure when you come to these problems on your homework you just don't go ahead and skip them. These big weird fractions are intimidating but you can do it. Just keep in mind this means dividing by two so when you're solving you're going to do the opposite which is multiplying.
