Sec 4-2D. Solve Equations with Rational coefficients Pg. 221 - 226

Multiplicative Inverses or Reciprocals Two numbers with a product of 1 are called MULTIPLICATIVE INVERSES or RECIPROCALS. 2 and ½ are multiplicative inverses. 3 5 𝑎𝑛𝑑 5 3 are another pair. 2 1 ∗ 1 2 =1 3 5 ∗ 5 3 =1

Find Multiplicative Inverses What is the multiplicative inverse of 7 8 ? 8 7 What is the multiplicative inverse of 5 1 2 ? 5 1 2 = 11 2 2 11 7 8 ∗ 8 7 =1 11 2 • 2 11 =1

Decimal and Rational Coefficients Sometimes the coefficients of a term in a multiplication equation are rational numbers. If the coefficient is a decimal, divide each side by that coefficient. 0.45x = 2 0.45𝑥 0.45 = 2 0.45 x = 4.44

Decimal and Rational Coefficients If the coefficient is a fraction, multiply each side by the reciprocal of the coefficient. 3 4 𝑥=5 4 3 ∙ 3 4 𝑥=5∙ 4 3 x = 20 3 x = 6 2 3

Word Problem John told Sam that he needed 1 7 8 feet of wire to build one robot. Sam has 30 feet of wire. How many robots can John build with that much wire? 1 7 8 𝑛=30 15 8 𝑛=30 8 15 ∙ 15 8 𝑛=30∙ 8 15 n = 2 • 8 = 16