This document contains a review worksheet for algebra with 44 questions covering topics like: 1) Properties of numbers that are divisible by 3 or 5 2) Prime and composite numbers 3) Simplifying expressions with fractions, adding, subtracting, multiplying, and dividing fractions. 4) Working with signed numbers and solving equations using properties of equality.

1. Name _____________________________ Date __________________________
Algebra 1B Worksheet Fall Semester Review Part A
1. If a number is divisible by 3 then _________________________________________
__________________________________________
2. If a number is divisible by 5 then _________________________________________
__________________________________________
3. List the PRIME numbers. ________________________________________________
4. What is a composite number? ____________________________________________
5. Find the prime factorization of each number using factor trees. ( Show all work )
a. 140 b. -18
a. ___________ b. _____________
4x
6. Circle the numerator of the fraction
9a 2
7. What does the denominator of a fraction tell us? _______________________________
_____________________________________
8. What does the numerator of a fraction tell us? _________________________________
______________________________________
9. How do we reduce a fraction?
___________________________
___________________________
___________________________
1

2. Find the equivalent ( equal ) fraction, show the factoring and the dividing out in the
middle blank.
12
10. _______________________
30
− 14
11. _______________________
21
18ab 2
12. _______________________
24a 3c
− 10
13. _______________________
− 25
14. List the steps we should go through to multiply fractions.
____________________________
____________________________
____________________________
Multiply the following:
25 . 14
15. ____________________ ___
28 35
5 . −9
16. ____________________ ___
6 10
10 x . 3y 3
17. ____________________ ___
9y 2 25
− 9z . 10a 3
18. ____________________ ___
16a 3z 2
2

3. Divide the fractions. Be sure to reduce all answers to lowest terms. ( Show your work )
Multiplication Problem Factoring Answer
15 10
19. ÷ ____ . ____ _________________________ ___
8 3
11 33
20. ÷ ____ . ____ _________________________ ___
15 5
5 3
21. ÷ ____ . ____ _________________________ ___
28 14
Divide the following:
7
22. ÷ 14 _________________________ ___
15
6 −5
23. ÷ _________________________ ___
21 9
4x 3 − 12x
24. ÷ _________________________ ___
15a 2 5a
Add the fractions and reduce your answers to lowest terms.
1 5 1 3
25. + 26. +
14 6 6 8
_________ + __________ _________ + __________
____________ ____________
_____ _____
3

4. 2 5 a a
27. + 28. +
8 22 4 6
_________ + __________ _________ + __________
____________ ____________
_____ _____
−3 7 7 1
29. - 30. -
20 30 10 5
31. List the rules we use to add signed numbers
32. Add the following:
A. 4 + (-6) B. –9 + (-16) C. –40 + (-9)
D. – 3 + 3 E. –5 + 3¼ F. –11.3 + (5.2)
33. List the rule we use to change subtraction into addition.
34. Subtract:
A. 4 – 9 B. 23 - (-9) C. –6 – 7
D. –15 – (–6) F. 180 - ( 64 - 27 )
35. Evaluate a – b –c for a = 9, b = -2, and c = 6. (Show work)
4

5. 36. List the rules we use to multiply ( or divide ) signed numbers
37. Multiply the following:
A. (5)(-2) B. -3 (-6) C. (-7)(-3) D. (-2) 3
38. Evaluate a(b) – c for a = 8, b = -2, and c = 5. (Show work)
39. Evaluate for k = -1, m = 3, and n = 0. (Show work)
A. (-k) 5 B. –17n C. kmn
40. Simplify or Evaluate - show your work.
A. 5 - 7² B. – 2x for x = - 8 C. Find 7a – 5 b for a = 3, b = -2
D. Find 3a ² + b for a = -1, b = -9 E. Find –4(x – y)² for x = -2, y = 4
3a − b
F. Find for a = 6, b = -4 G. Find a ³ - b for a = -2, b = -3
a +b
40. Define “like” terms of an expression:
41. Simplify:
A. –5x + 12x B. –3y – y C. 7y + 4x + 2y + 7x
D. 6 – 3z – 5z – 1 E. –3x + 4y + 3x + 4y F. 4a – 5.2a
5

6. 42. Simplify then Evaluate:
A. 8y + 4x + 2y + 7x B. 2 c – 3 ( 6 c + 7) for c = -3
for x = -2 and y = 3
43. Simplify:
A. – ( 4 x + 2 y ) B. –3 ( x + y ) + ½ ( x – 14y )
C. – 4 ( 3 z – 4 ) D. –10 – [ 2 ( 4 x + 5 ) – ( 2 x – 1 ) ]
E. – 4 x – ( 9 – 5 x ) + 2
44. Evaluate:
A. – ( 5 z – 4 ) – 2 ( 3 – 4 z ) for z = 2 B. 4 ( -3 a + 1 ) – 4 a for a = ½
45. List the steps we use to solve equations. (hint: they are posted on the walls in Burd’s room)
46. State the properties of equality.
47. Use the properties of equality to solve the following equations:
a. 2x = 14 c. 13 = a – 3
b. x + 5 = 17 b
d. = 11
8
6

7. e. 20 = 6x + 8 i. 3n – 21 = 2n
f. 15 – 4g = -33 j. 3k – 5 = 7k + 7
t k. 3( z – 2 ) + 6 = 5 ( z + 4 )
g. –17 + = 3
5
l. 6r + 5 = 8 ( r + 2 ) – 2r
5+r
h. = -6
−2
7