**Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.**

Teacher’s Notes:

Today’s lesson is continued practice in manipulating numbers in algebraic equations, with the aim of solving for an unknown. The only new bit today is understanding that all the rules governing fractions apply when those fractions contain an unknown quantity, or “x”. The “x” just goes along for the ride!

Worksheet:

*Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra“*

Challenge Question Answers:

- 9x/7 = 18, so 9x=18*7 and x=18*7/9, or x=2*7=
**14** - 2x + 3x/7 = 14x/7 + 3x/7 =
**17x/7**(this is just to show your child that the same rules of fractions apply, even when there is an unknown in the problem)

Doodle Dailies Answers:

**x/2****x=2****x=15**- 2x/3 = 8, so 2x=3*8=24, then
**x=12** - Here you have to recognize that Eliza is the older of the sisters, so her age is x. Ruth’s age is 3x/5 (or three fifths that of Eliza’s age). Then the sum of the ages of the sisters is x (Eliza) + 3x/5 (Ruth) and that sum is 24 years. So x + 3x/5 = 24. Then you need to change both fractions so they have a common denominator before you can add them, so 5x/5 + 3x/5 = 24. And then you can add to get 8x/5 = 24, and then 8x=24*5, x=24*5/8=3*5=
**15 So Eliza is 15 and Ruth is 6 (or 3/5 of 15).**

As always, please leave comments when you have them.

Thanks