Multistep Equations: Fractions and Decimals SWBAT solve multistep equations involving fractions and decimals; solve equations with variables in the denominator

Equations with Decimals When solving an equation with terminating decimals, you can multiply each side by a power of 10 to form an equivalent equation with only integers Count the greatest number of decimal places and use that power of ten to multiply

Equations with Decimals Two decimal places Multiply by 100 (102) 100(1.12c + 2.06) = 100(9.90) 112c + 206 = 990 Solve as usual 112c = 789 C = 7 -206 -206 112 112

Equations with Fractions When solving an equation involving fractions, you can multiply each side by the least common denominator of the fraction to form and equivalent equation with only integers

Equations with Fractions 1½x + 25/6 = -12/3 First change all fractions into their improper form 3/2 x + 17/6 = -5/3 Find the LCD 6 Multiply the both sides by 6 6(3/2 x + 17/6 ) = 6(-5/3)

Equations with Fractions 6(3/2 x + 17/6 ) = 6(-5/3) 6/1*3/2 x + 6/1*17/6 = 6/1*-5/3 Remember to cancel out first to make your job easier 9/1 x + 17/1 = 10/1 9x + 17 = 10 Solve as usual 3 2

Variables in the Denominator When a variable appears in the denominator of an equation you can use cross products to solve the equation

Variables in the Denominator -36 2 n 5 Re-write the mixed number as an improper fraction -36 12 n 5 Cross multiply -36(5) = 12n Solve as usual = 2 =

Examples 0.2x + 1.4 – 0.5x = 2.2 – 0.1x 2n/3 + 3 – n/5 = n – 5 -1.5 + 0.3r = -4.2 m/8 – 2½ = -4 4.8/a = -0.3 7 + 3y -y 4 8 =

Examples -s/3 – 4 = -10 5y – 1 – 3y = 5 1/5 7 35 a 60 0.06t – 2.9 = 7 7 35 a 60 0.06t – 2.9 = 7 =