2 Course 2 of 10
Pre-algebra practice
One problem set for every lesson in the course. Problems go from easy to challenging, and each one has a worked solution.
Unit 1 Whole numbers
- 1 Whole numbers and the properties of operations What whole numbers are, how place value works, and the commutative, associative, identity and distributive properties that make mental math easier, plus division with remainders. 9 problems
- 2 The order of operations (PEMDAS) The order of operations explained with PEMDAS, why multiplication and division are done left to right, how to handle nested grouping symbols and fraction bars, and the most common mistakes. 9 problems
- 3 Exponents and the laws of exponents What exponents mean, squares and cubes, why any nonzero number to the zero power is 1, and the product, quotient and power rules for exponents, with examples and common mistakes. 9 problems
- 4 Divisibility rules, prime numbers and prime factorization Factors and multiples, quick divisibility rules for 2, 3, 4, 5, 6, 9 and 10, prime and composite numbers, and how to find the prime factorization of a number with a factor tree. 9 problems
- 5 Greatest common factor and least common multiple How to find the GCF and LCM of two or three numbers by listing and by prime factorization, what relatively prime means, and how to tell which one a word problem needs. 9 problems
Unit 2 Integers
- 6 Integers, absolute value, adding and subtracting What integers are, how to compare them on a number line, absolute value and opposites, and the rules for adding and subtracting positive and negative numbers, including "add the opposite". 9 problems
- 7 Multiplying and dividing integers The sign rules for multiplying and dividing integers, why a negative times a negative is positive, powers of negative numbers, the difference between (-4)² and -4², and the order of operations with integers. 9 problems
Unit 3 Fractions
- 8 Fractions, equivalent fractions and simplest form What a fraction means, proper and improper fractions, mixed numbers, how to find equivalent fractions, how to write a fraction in simplest form and how to compare fractions. 9 problems
- 9 Adding and subtracting fractions and mixed numbers How to add and subtract fractions with like and unlike denominators using the least common denominator, how to work with mixed numbers including regrouping, and negative fractions. 9 problems
- 10 Multiplying and dividing fractions How to multiply fractions and simplify before multiplying, reciprocals, dividing with "keep, change, flip", multiplying and dividing mixed numbers, and powers of fractions including negative exponents. 9 problems
Unit 4 Decimals
- 11 Decimals, repeating decimals and rounding Decimal place value, comparing decimals, converting between fractions and decimals, terminating and repeating decimals, turning a repeating decimal into a fraction, and rounding. 9 problems
- 12 Powers of ten and scientific notation Multiplying and dividing by powers of ten, writing very large and very small numbers in scientific notation, converting back to standard form, and multiplying and dividing in scientific notation. 9 problems
Unit 5 Ratios and percents
- 13 Ratios, rates and proportions How to write and simplify ratios, unit rates and unit prices, what a proportion is, solving proportions with cross products, and using proportions with scale drawings. 9 problems
- 14 Percents, discounts, tax and percent change What percent means, converting between percents, decimals and fractions, finding a percent of a number, the part, the whole or the percent, discounts, sales tax, tips and percent increase and decrease. 9 problems
- 15 Proportional relationships, direct and inverse variation How to recognize a proportional relationship from a table, a graph or an equation, the constant of proportionality in y = kx, inverse variation where xy = k, and solving word problems with each. 9 problems
Work each problem out on paper before you open the solution. If your answer is off, compare the steps and find where you went wrong. If a problem stops you cold, go back to the lesson: every set links to it.