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The short version Place value is what a digit is worth because of where it sits in a number. The 4 in 40 is worth forty. The 4 in 4,000 is worth four thousand. Every place is 10 times the place to its right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions. Expanded form…
The short version Set notation is the shorthand for writing a collection of things. Curly braces hold the members: A = {2, 4, 6, 8}. Roster form lists every member. Set builder form states the rule instead: {x | x is an even number between 0 and 10}. Union (∪) means everything in either set….
The short version The commutative property says you can swap the order of two numbers in addition or multiplication and the answer stays the same. 7 + 26 = 26 + 7, and 4 × 25 = 25 × 4. It fails for subtraction and division. 9 – 4 = 5 but 4 – 9…
The short version A palindrome is a word, phrase, number or date that reads the same forward and backward. Racecar, level, 121 and 02/02/2020 all qualify. To test a number, write its digits in reverse order and compare. 4,554 reversed is still 4,554, so it’s a palindrome. 1,231 reversed is 1,321, so it isn’t. There…
The short version A conjugate is what you get when you flip the sign between the two terms of a binomial. The conjugate of 5 + √3 is 5 – √3, and the conjugate of 3 + 2i is 3 – 2i. Multiply a pair of conjugates and the middle terms cancel, leaving a² –…
The short version A coefficient is the number multiplying a variable in a term. In 7x the coefficient is 7, and in -3xy it’s -3. When you see no number at all, the coefficient is 1. So x means 1x, and -m means -1m. The sign belongs to the coefficient. In 6x² – 7x +…
The short version The radius goes from the center of a circle to the edge. The diameter goes all the way across, through the center. The diameter is always twice the radius. Circumference is the distance all the way around the outside. It equals π × diameter, or 2 × π × radius. If you…
The short version The symbol > means “greater than” and the symbol < means “less than.” So 7 > 3 reads “seven is greater than three,” and 3 < 7 reads “three is less than seven.” The most reliable trick: the pointy end always points at the smaller number, and the wide open end always…
The short version Brackets group part of an expression so you do that part first. In 4 × (3 + 2), the brackets force the addition ahead of the multiplication, giving 20 instead of 14. Three kinds show up in school math: parentheses ( ), square brackets [ ], and braces { }. For order…
The short version The main types of numbers are natural, whole, integers, rational, irrational, real and imaginary. Most of them sit inside each other like nesting boxes, so one number usually belongs to several types at once. Natural numbers are 1, 2, 3 and up. Add zero and you have whole numbers. Add the negatives…