REVIEW TEST
Foundations of Algebra Midterm review Foundations of Algebra
Unit 1: The Real Number System Key Ideas: Classifying Numbers Operations on Rational Numbers (Converting decimals, fractions, percents) Comparing Numbers Rounding Estimating Radicals Simplifying Radicals Operations on Radicals Pythagorean Theorem
Classifying Numbers Irrational Rational Real Integer Whole Natural Examples - Classify into as many categories as possible: -6 2.7 3/4 52
Fractions, Decimals, and Percents Convert ¾ to a decimal. Convert .0923 to a percent.
Operations with Rational Numbers Read the problem, then determine the operation you should use (addition, subtraction, multiplication, or division). Four out of every five students enrolled in Algebra feel prepared for their final. If there are 250 students, how many feel ready for their exam?
Compare Rational Numbers Convert to decimals and then compare 3.7 ____ _____
Rounding Look at the place value (tenth, hundredth, thousandth) Then, look at the next number If it’s 5 or more, round up If it’s 4 or less, round down Round 1/13 to the hundredth place Round √7 to the thousandths place
Simplify Radicals Write out prime factorization, circle pairs, take one out Even exponent: take half out Odd exponent: leave one, take ½ of the rest
Operations with Radicals You can only add or subtract if the radicand is the same. Try to simplify first. Simplify again at the end. To multiply, multiply Outside by Outside and Inside by Inside. Simplify at the end.
Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2 Find the missing side, a=5, b=12, c=? Find the missing side, a=?, b=6, c=10