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Algebra - Mixed Practice (Pre-Algebra)

Lesson Plans > Mathematics > Algebra > Mixed Content

Algebra - Mixed Practice (Pre-Algebra)

Recently I was talking to a student who was working with me on solving systems of rational equations, and he commented that he gets through the "hard" parts of the problem, and then draws a blank on where to go from there. I see students doing this all the time; they get so focused on the complex stuff they've been working on in April and May that they forget the things they learned back in September.

x + 3
12
-
x - 3
15
=
3
5
and when they've finished finding a common denominator and clearing the fractions, they're left with 5x + 15 - 4x + 12 = 36, and they have no idea what to do next, even though they've been doing it all year long.

I told my student that his brain has different "gears" and he needs to "shift gears" when he gets to the easy stuff. These mixed practice sheets are designed to give students a review of subjects covered throughout the year, so they're more likely to remember "what to do next." Many math curricula don't do a good job of reviewing previous concepts, so these are intended to supplement that lack.

This first batch of worksheets focuses entirely on Pre-Algebra concepts. No equations, variables, or algebraic expressions are involved.

Worksheet 1.1

• Prime factorizations
• GCF
• LCM
• Fraction operations
• Order of Operations (no exponents, no nested parentheses)

Worksheet 1.2

• GCF and LCM
• basic operations with positives and negatives
• Order of operations (including nested parentheses and exponents)
• Percentages

Worksheet 1.3

• turning phrases into arithmetic expressions and evaluating
• percentages
• fractions
• positives and negatives
• ages
• prices

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

Lesson by Mr. Twitchell

Mixed Practice 1.1

1. Find the prime factorization of 72

2. Find the prime factorization of 4725

3. Find the prime factorization of 2000

4. Find the GCF of 72 and 2000

5. Find the GCF of 4725 and 2000

6. Find the GCF of 72 and 4725

7. Find the LCM of 72 and 2000

8. Find the LCM of 4725 and 2000

9. Find the LCM of 72 and 4725

10. 2
3
·
6
11
=

11. 1
5
÷
21
20
=

12. 1
3
+
1
5

13. 2
9
+
3
21

14. 10
3
-
5
6

15. 1
4
-
2
3

16. 3 + 7 · 2 - 11 =

17. 2 + 3(5 - 1) - 10 =

18. 9
8
-
1
3
·
1
4

19. 3(
1
2
-
1
3
) =

20. 1
2
(3 -
1
4
) =

Mixed Practice 1.1: Answer Key

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Mixed Practice 1.2

1. Find the GCF and LCM of 138 and 60

2. Find the GCF and LCM or 40 and 90

3. 3 + (-5) =

4. · (-2) =

5. -3 + (-2) =

6. -3 · (-4) =

7. 4 - (-2) =

8. -3 - (-5) =

9. 12 ÷ (-2) =

10. -24 ÷ (-3) =

11. 2 + 3(-5 + 2) - 1 =

12. 3[2 + (-4 - 1) + 1] - 2 =

13. 4 +
1
3
(-
1
2
+
10
3
) =

14. 5
11
[3 - 2(1 -
1
5
) + 1) =

15. 32 + 2(1 - 23) =

16. 23 - 32[52 - 42 - 2(22 + 1) + 1] =

17. 5% of 80 =

18. 120% of  45 =

19. 35 increased by 10% =

20. 81 decreased by 10% =

Mixed Practice 1.2: Answer Key

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Mixed Practice 1.3

Instructions: convert each phrase to an arithmetic expression and evaluate

1. One third of thirty-three

2. Two more than negative seventeen

3. Five less than twelve

4. Two less than twice six

5. The sum of negative eight and negative seven

6. Five less than the product of negative five and three

7. The ratio of ten to two, plus eight

8. Three more than half of eighteen

9. Two fifths of the sum of three and two

10. Twenty percent of the difference between 55 and 25

11. A ten percent increase over twice the sum of one hundred and negative ten

12. Henry's age nine years ago, if he is thirteen years old now

13. Vinnie's age six years ago, if he will be 23 in five years

14. The cost of 10 pencils, if each costs \$0.32

15. The cost of a crayon, if a dozen crayons costs \$2.88

16. The ratio of the cost of a pencil to the cost of crayon in the previous problems

17. The temperature today, if it is 10 degrees warmer than yesterday's high of 72 degrees

18. A ten percent discount on 3 books and 4 notebooks, if a book costs \$8.00 and a notebook costs \$2.50

19. 80% of the cost of 2 pizzas and 3 sodas, if a pizza costs \$15, and a soda costs \$1.50

20. Half of a third of the sum of negative one third and four thirds

Mixed Practice 1.3: Answer Key

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