1. 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 = 5j
Subtract
– 3j
– 3j 18 = 2j
Divide 2 2 9 = j
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2. 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 =
Substitute 5 3 15
Simplify = 3 5 3 = 3
Check

3. 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

4. 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 =
a a – 2a – 8
Combine 16 =
a a – 8
Subtract
– 16
– 16 =
a a – 24
Factor =
(a + 6)(a – 4)
Zero product property =
a + 6 =
a – 4
Solve
− 6 = a 4 = a

5. 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

6. 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

7. Algebra I Concept Test # 18 – Rational Ex. & Proportions Practice Test
7. Simplify:
y – 3 •
(y – 7)2
Expand
y2 – 10y
y – 3
(y – 7)(y – 7) •
Factor denominator
y2 – 10y
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)

8. 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

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

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

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

12. 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 = 6
Subtract
– 4
– 4
x = 2

13. 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) (x + 1) = 1(x + 1)(x – 2)
Reduce
4x – x = x2 – 2x + x – 2
Multiply

14. 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 – x = 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