# 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.

They start with something likeI 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.

**Mixed Practice Overview**- Mixed Practice #1 - Pre-Algebra
- Mixed Practice #2 - Algebraic Expressions
- Mixed Practice #3 - Linear Equations
- Mixed Practice #4 - Polynomial Manipulation
- Mixed Practice #5 - Factoring
- Mixed Practice #6 - Quadratic Equations
- Mixed Practice #7 - Rational Expressions
- Mixed Practice #8 - Systems of Equations
- Mixed Practice #9 - Radical Expressions

## Handouts/Worksheets

## Mixed Practice 1.1

- Find the prime factorization of 72

- Find the prime factorization of 4725

- Find the prime factorization of 2000

- Find the GCF of 72 and 2000

- Find the GCF of 4725 and 2000

- Find the GCF of 72 and 4725

- Find the LCM of 72 and 2000

- Find the LCM of 4725 and 2000

- Find the LCM of 72 and 4725

- ·23=611

- ÷15=2120

- +13=15

- +29=321

- -103=56

- -14=23

- 3 + 7 · 2 - 11 =

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

- -98·13=14

- 3(-12) =13

- (3 -12) =14

## Mixed Practice 1.1: Answer Key

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## Mixed Practice 1.2

- Find the GCF and LCM of 138 and 60

- Find the GCF and LCM or 40 and 90

- 3 + (-5) =

- 4
**·**(-2) =

- -3 + (-2) =

- -3
**·**(-4) =

- 4 - (-2) =

- -3 - (-5) =

- 12 ÷ (-2) =

- -24 ÷ (-3) =

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

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

- 4 + (-13+12) =103

- [3 - 2(1 -511) + 1) =15

- 3
^{2}+ 2(1 - 2^{3}) =

- 2
^{3}- 3^{2}[5^{2}- 4^{2}- 2(2^{2}+ 1) + 1] =

- 5% of 80 =

- 120% of 45 =

- 35 increased by 10% =

- 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

- One third of thirty-three

- Two more than negative seventeen

- Five less than twelve

- Two less than twice six

- The sum of negative eight and negative seven

- Five less than the product of negative five and three

- The ratio of ten to two, plus eight

- Three more than half of eighteen

- Two fifths of the sum of three and two

- Twenty percent of the difference between 55 and 25

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

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

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

- The cost of 10 pencils, if each costs $0.32

- The cost of a crayon, if a dozen crayons costs $2.88

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

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

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

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

- Half of a third of the sum of negative one third and four thirds

## Mixed Practice 1.3: Answer Key

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