Exercise 33 Page 113

We want to factor out the coefficient of the variable term — 38. Let's rewrite each term as a product of 38 and some other factor. To do so, we need to think of a number that gives 1 when multiplied by 38. We can find it by dividing 1 by 38. 1 = 3/8 * ? ⇔ 1 ÷ 38 = ? The quotient equals 83, which means that 1 is 38 times 83. Now we can write each term as a product of two factors. 1{\dfrac{3}{8}z &= {\color{#FD9000}{\dfrac{3}{8}}} \cdot z \\[0.5em] 1 &= {\color{#FD9000}{\dfrac{3}{8}}} \cdot \dfrac{8}{3}} Finally, we will use the Distributive Property to factor the expression. Let's go!

3/8z +1

SplitIntoFactors

Split into factors

3/8 * z +3/8 * 8/3

FactorOut

Factor out 3/8

3/8(z+8/3)