Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 1. Solve the proportion using the cross-product property: j + 6 j = Apply cross product property 5 3 3 (j + 6) = 5 • j Distribute 3j + 18 = 5j Subtract – 3j – 3j 18 = 2j Divide 2 2 9 = j © 2007- 09 by S-Squared, Inc. All Rights Reserved.

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 2. Check solution for # 1 j + 6 j = ; 9 = j Equation and solution 5 3 9 + 6 9 = Substitute 5 3 15 Simplify = 3 5 3 = 3 Check

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 3. Solve the proportion using the cross-product property: 2m 8 = Apply cross product property 7 m 2m • m Simplify = 8 • 7 2m2 = 56 Divide 2 2 m2 = + 28 Square Root m = + 4 • 7 Perfect square factor m = + 2 7 Simplify

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 4. Solve the proportion using the cross-product property: 8 a + 4 = Apply cross product property a – 2 2 8 • 2 = (a – 2) (a + 4) Multiply 16 = a2 + 4a – 2a – 8 Combine 16 = a2 + 2a – 8 Subtract – 16 – 16 = a2 + 2a – 24 Factor = (a + 6)(a – 4) Zero product property = a + 6 = a – 4 Solve − 6 = a 4 = a

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 5. Simplify: 32x2 24x * Factor each term into it’s prime factorization 32x2 2 • 2 • 2 • 2 • 2 • x • x 24x 2 • 2 • 2 • 3 • x * Reduce the common factors 2 • 2 • 2 • 2 • 2 • x • x 2 • 2 • 2 • 3 • x 2 • 2 • x 4x 3 3

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 6. Simplify: 3r3 – 6r2 12r * Factor the greatest common factor from the binomial in the numerator r 3r2(r – 2) 12r 4 * A monomial may only reduce with another monomial r(r – 2) r2 – 2r Multiply = 4 4 * Simplify implies that all operations are performed

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 7. Simplify: y – 3 • (y – 7)2 Expand y2 – 10y + 21 y – 3 (y – 7)(y – 7) • Factor denominator y2 – 10y + 21 y – 3 • (y – 7)(y – 7) Reduce (y – 7)(y – 3) * Any binomial term in the numerator may reduce with any binomial term in the denominator (y – 7)

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 8. Simplify: 2w + 9 w – 9 + 21w 21w * Notice, the fractions have like denominators. Add the numerators and place over common denominator 2w + 9 + w – 9 Combine like terms 21w 1 3w Reduce 21w 7 1 7

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 9. Simplify: 5x2 – 5x − 2x2 + 7x – 8 + 2x + 4 2x + 4 * Notice, the fractions have like denominators. Add the numerators and place over common denominator 3x2 + 2x – 8 Factor the numerator 2x + 4 (3x – 4)(x + 2) Factor the denominator 2x + 4 (3x – 4)(x + 2) Reduce 2(x + 2) 3x – 4 2

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 10. Simplify: 7h – 2 2h + 6 – 5h2 + 2h – 16 5h2 + 2h – 16 * Notice, the fractions have like denominators. Subtract the numerators and place over common denominator 7h – 2 – (2h + 6) Combine like terms 5h2 + 2h – 16 5h – 8 Factor the denominator 5h2 + 2h – 16 5h – 8 1 Reduce (5h – 8)(h + 2) h + 2

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 11. Simplify: 5 1 + 5x – x x2 * To add fractions we need common denominators * The common denominator is x2 5 • x 1 + 5x – x • x x2 5x 1 + 5x 5x – 1 – 5x – x2 x2 x2 * The fractions have like denominators, subtract the numerators − 1 x2

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 12. Solve: 1 2 3 + = 2 x x * To solve a fractional equation multiply each term by the LCD 2x * The LCD is 1 • 2x 2 • 2x 3 • 2x + Multiply = 2 x x 2x 4x 6x Reduce + = 2 x x x + 4 = 6 Subtract – 4 – 4 x = 2

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 13. Solve: 4 1 + = 1 x + 1 x – 2 * To solve a fractional equation multiply each term by the LCD (x + 1)(x – 2) * The LCD is 4 (x + 1)(x – 2) 1 (x + 1)(x – 2) + = 1 (x + 1)(x – 2) x + 1 (x – 2) 4(x – 2) + 1(x + 1) = 1(x + 1)(x – 2) Reduce 4x – 8 + x + 1 = x2 – 2x + x – 2 Multiply

Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test 13cont. Solve: 4 1 + Your accomplishments will mold your character = 1 x + 1 x – 2 4x – 8 + x + 1 = x2 – 2x + x – 2 Combine like terms 5x – 7 = x2 – x – 2 Subtract – 5x – 5x − 7 = x2 – 6x – 2 Add + 7 + 7 = x2 – 6x + 5 Factor = (x – 5)(x – 1) Zero product property = x – 5 = x – 1 Solve 5 = x 1 = x