# Lesson 113 – Doodles Do Algebra

Today your child learns to solve a first degree equation, well the first step anyway.

Solving simple equations involves three steps, the first of which is clearing the equation of fractions by multiplying through by the least common multiple.

The Least Common Multiple is a term your child learned a number of lessons ago and practiced quite a bit so she probably will remember it. If not, just explain that it is the smallest number that can be divided by two (or three or more) numbers. So the least common multiple of 2 and 3 is 6 and the least common multiple of 4 and 5 is 20 because 20 is the smallest number that is divisible by both 4 and 5 evenly. Things only get tricky when you find the least common multiple of three or more terms. So the least common multiple of 2 and 3 and 4 is 12 (not 24, that is a common multiple but not the least one) because 12 is divisible by 2 and 3 and 4 evenly.

So in the example by DoodlePoodle, the first step of solving the simple equation

$x/2+x/3=5$ is to multiply through by 6 (the least common multiple of 2 and 3)

Make sure that your child remembers to multiply through every single term in the equation (on both sides) because you need to maintain an Identical Equation (a term from Lesson 112’s vocabulary exercises).

So in our example, we multiply through by 6 and get $6x/2+6x/3=5*6$ which can be reduced to $3x+2x=30$ and that is where your child can stop for today. The goal for today is to get her to find the least common multiple and use it to clear the equation of any fractions. If she naturally continues on and solves the equation, don’t stop her – just emphasize the first step of solving the equation and let her skip some of the next lessons that deal with the final two steps of solving simple equations.

I have found that the moment you slow a child’s natural progress in learning a subject, she will instantly get bored and tune out and actually not learn what she was learning so rapidly before. In homeschooling, my biggest challenge is negociating the balancing act of teaching my twins the same material when one of them zooms through the information and the other one needs more practice with something. Flexibility is key to good teaching.

3. $2(2x-4)-15=10b$ or $4x-8-15=10b$ if she goes one step further. (least common multiple is 10)
4. $ad*a+ac*b-cd*c=acdx*d$ (least common multiple is acdx)