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Mrs. T's Math 7
Vocabulary for Review
| Term | Definition |
|---|---|
| Sum | The answer/solution to an addition problem |
| Quotient | The answer/solution to a division problem |
| Product | The answer/solution to a multiplication problem |
| Difference | The answer/solution to a subtraction problem |
| Natural Numbers | The set of numbers (counting numbers) beginning with the number 1. Example: 1,2,3,4,5... |
| Whole Numbers | The set of natural numbers and zero. Example: 0,1,2,3,4,5... |
| Integers | The set of whole numbers and their opposites (positives and negatives). Example, -5,-4,-3,-2,-1,0,1,2,3,4,5... |
| Zero Pair | A positive unit and a negative unit together that cancels one another out resulting in a value of zero. |
| Coordinate Plane (Rectangular Coordinate System/Grid) | The grid that is created by the x and y axis, each having a positive and negative side. Ordered pairs (coordinates) can be plotted within the Coordinate Plane using the grid created by the integers on each axis. |
| x-axis | The horizontal (from left to right) axis within the Coordinate Plane. |
| y-axis | The vertical (up and down) axis within the Coordinate Plane |
| The Origin | The point within the Coordinate Plane in which the x and y axis intersect. The coordinates of THE ORIGIN are (0,0). |
| Ordered Pair | The set of coordinates (one x value and one y value) that provides the exact location of a point within the Coordinate Plane. Remember, in the alphabet x comes before y (w,X,Y,z), and it is the same in an ordered pair (x,y). |
| Value | what a number is worth |
| Absolute Value | The number of steps an integer is away from zero. Example: The absolute value of -4 is 4. This is ALWAYS a positive value, and is indicated by a line before and after an integer. |
| The Inverse Property of Multiplication A.K.A. The Multiplicative Inverse Property | The mathematical property that says that any number multiplied by its inverse (opposite) equals 1. Example: 3/4 x 4/3 = 12/12 = 1 |
| opposites | Two integers that are located at opposite positions on a number line. Example. -4 and 4 are opposites, and both are 4 steps away from zero (absolute value of each is 4). |
| operator | The symbol that is placed between numbers that tell us which operation (add, subtract, multiply, divide)to carry out. |
| number sentence | A relatively simple equation or expression that consists of numbers and operators (this term is normally used only in lower levels of math). example: 4+5=9, or 2x6 |
| equation | A number sentence in which numbers and operators (and variables)are set equal to other numbers and operators. We typically think of an equation as having variables within it, but it doesn't have to contain them. Example (with variables): 2x +5 = 11 |
| expression | A mathematical phrase in which numbers and operators (and variables)are NOT set equal to something (no equal sign). Example: 2x+5 |
| variable | a letter used to represent and unknown value in an equation or expression |
| coefficient | The number that is next to and just before the variable in an equation or expression. Example: in the equation 2x+5=11 the coefficient is 2 |
| terms | Terms are the part of an equation or expression that are found BETWEEN the operators (they are separated by the operators) Example: in the equation 2x+5=11, there are three terms, which are 2x, 5, and 11 |
| What is the shortcut for adding integers with the SAME signs? | Add the two integers together and keep the same sign. |
| How do you multiply two integers with the same signs? | Multiply the two integers and the product (answer) will ALWAYS be POSITIVE. Ex. -5 x -2 = +10 |
| How do you divide two integers with the same signs? | Divide the two integers and the quotient (answer) will ALWAYS be POSITIVE. ex. -10/-2 = +5 |
| How do you multiply two integers with different signs? | Multiply the two integers and the product will ALWAYS be NEGATIVE. ex. -5(+2)= -10 |
| How do you divide two integers with different signs? | Divide the two integers and the quotient will ALWAYS be NEGATIVE. ex. +10/-2 = -5 |
| What is the shortcut for adding integers with DIFFERENT signs? | SUBTRACT the two integers (biggest minus smallest), and keep the sign of the biggest integer. Ex. -6 + 10 = ? subtract: 10-6 = 4 keep sign of biggest number (here it is 10, which was positive in the original number sentence): +4 So.... -6 + 10 = +4 |
| How do you subtract two integers both with the same signs and with different signs? | Anytime you see subtraction of two integers you must KiSS it. KEEP the first #, SWITCH the MINUS to a PLUS, and SWITCH the 2ND # to its OPPOSITE. it is now an addition problem--follow addition rules to solve. ex. -5 - +10= , KiSS: -5 + -10 = -15 |
| Square Root | The integer that you multiply by itself to get a perfect square. Ex. 4 x 4 = 16 16 is the perfect square 4 is the square root of 16 |
| Radical | A radical is the symbol (looks like a long division symbol with a checkmark on the left side of it) that tells you to find the square root of the number that is given under it. |
| Scientific Notation | A shorter way to express (show) very, very large numbers or very, very small numbers using a number greater than or equal to 1, and less than 10 multiplied by a power of 10. |
| Power of Ten | The integer 10 multiplied by itself a given amount of times. Powers of Ten are usually expressed as a base with an exponent. Ex. 10 x 10 x 10 could be expressed as 10^3, they both equal 1,000 |
| What is the shortcut to find the standard form of the following: 2.5 x 10^8 ? | Since the exponent on the 10 is 8, you will move the decimal 8 places. Because the exponent 8 is POSITIVE you will move the decimal to the RIGHT (the POSITIVE direction on the number line). 2.5 becomes 250,000,000 |
| What is the shortcut to find the standard form of the following 2.5 x 10^-8 ? | Since the exponent on the 10 is 8, you will move the decimal 8 places. Because the exponent 8 is NEGATIVE you will move the decimal to the LEFT (the NEGATIVE direction on the number line). 2.5 becomes .000000025 |
| What is the shortcut to write the following in scientific notation? 7,540,000 | The number is large, so the exponent will be positive. Put a decimal behind the 1st # (7). Count the #'s that are now to the right of the decimal--this is the exponent.Remove all zeros. 7,540,000 7.540000 (6 behind decimal, so 10^6) 7.54 x 10^6 |
| What is the shortcut to write the following in scientific notation? .00000754 | The # is less than 1, so the exp. will be neg Move the decimal to the right so that 1 # with a value (not 0) is left of it. Count the #'s that are now to the left of decimal. Remove zeros. ex. .00000754 000007.54 (moved 6 places) 7.54 x 10^-6 |
| What is the value of a negative exponent? Ex. 10^-4 | It is like saying 1 divided by the positive exponent version. Ex. 10^-4 1/10^+4 = 1/10x10x10x10 = 1/10,000 Decimal Form: .0001 |
| Deposit | To put in, or add to. If I deposit money into my account, I put money into the account. |
| Withdraw | To remover from, or take out. If I withdraw money from my account I am taking money out. |
| Ascending | Ordered in increasing value--least to greatest. **Remember ascending begins with a vowel, and up begins with a vowel. If you count UP, each number gets bigger. The same is true when numbers are listed in ascending order. |
| Descending | Going down in value from greatest to least. **Remember Down and Descending both begin with the letter D. |
| Commute | To move from one place to another. In the commutative property the numbers change places or move. Ex. 4+2+6 is the same as 6+2+4 Note that the order of the numbers changed. |
| Associate | To hang out in groups. In the associative property the groupings change--numbers don't change spaces, only the groups change. Ex. 4+(2+6) is the same as (4+2)+6 Note that the groupings are different, but the order of the numbers stayed the same. |
| Inverse | The opposite of, or to undo an action. In the inverse properties, a numbers inverse, or opposite is used to "undo" something. Ex. 1/4 * 4/1 = 1 (The inverse of 1/4 is 4/1) 4 + (-4) = 0 (The inverse of 4 is -4) |
| Distribute | To spread out evenly. in the distributive property a value is multiplied across a quantity in parenthesis. Ex. 4 (x + 2) is the same as 4x + 4(2) |
| Term(s) (algebraic) | The parts of an equation that are separated by operators. Ex. 4x+2=12 The terms are 4x, 2, and 12 |
| Coefficient | The number next to the variable (number and variable that are being multiplied). Ex. 4x+2=12 The coefficient is 4 |
| Variable | A letter that represents an unknown number or value. Example: 4x+2=12 The variable is x |
| Constant | A value that does not change. Ex: 4x+2=12 The constants are 2 and 12 |
Created by:
Mrs. Thompson
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