1. Sec 4-2D. Solve Equations with Rational coefficientsPg

2. 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 are another pair.
2 1 ∗ 1 2 =1
3 5 ∗ 5 3 =1

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

4. 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 =
x = 4.44

5. 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

6. Word Problem
John told Sam that he needed 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