Download 7th Grade Math - Study Sheet for End-of

7th Grade Math - Study Sheet for End-of-Quarter Test
(3rd Quarter)
Associative Property (addition and multiplication) - it doesn’t matter how you group the
numbers when adding or multiplying (the parentheses can move)
Ex: 3 + (1 + 4) = (3 + 1) + 4, (2 x 7) x 5 = 2 x (7 x 5)
Commutative Property (addition and multiplication) - you can rearrange the terms (the
numbers move)
Ex: 6 + 3 + 5 = 5 + 6 + 3,
4x6x2=4x2x6
Distributive Property (multiplication)
- you ‘distribute’ the number outside the
parentheses to every term inside the parentheses
Ex: 4(2 + 3x - 5y) = (4 x 2) + (4 x 3x) - (4 x 5y), or 8 + 12x - 20y
Combining Like Terms/Simplifying Expressions:
Like terms are terms that have the exact same variable, or no variable.
n, 2n, and - 6n are like terms. 5, -17, and 33 are like terms. n and n2 are NOT like terms.
Ex: 3a + 5a + 6b - 3 - b can be simplified to 8a -5b - 3 by combining like terms (hint: rearrange
the terms to make them easier to work with…..3a + 5a + 6b – b – 3)
Expressions - mathematical phrases
Ex: 4 + 7 or 3d - 5 or 8m/6
Algebraic Expressions - contain at least one variable
Ex: m + 7 or 7n/3 - 5
Equations - mathematical sentences - they contain an equal sign with expressions on both
sides
Ex: 3n - 7 = 14
27/3 = 9, 15 + 7 = 22, 4p + 7x + 4 = 92
Writing Algebraic Expressions:
Changing words into numbers, variables, and operation signs
Ex: a number minus nine can be written as n-9; the product of 17 and a number can be written
as 17n; the sum of a number and 8, divided by 6 can be written as (n+8)/6
Solving 1-Step and 2-Step Algebraic Equations - isolate the variable by
‘undoing’ what has been done to it - remember that whatever you do on one side of the equation
also has to be done on the other side of the equation.
Ex: 2p = 6; to isolate the variable, divide both sides by 2; p = 3
Ex: 4s + 5 = 17; to isolate the variable, first subtract 5 from both sides of the equation, and then
divide both sides by 4; s = 3
Remember to check your answer by substituting your answer for the variable and making sure
the equation is correct.
Graphing and interpreting inequalities on a number line:
Symbols to remember:
To graph n > 2, we need to show all the numbers greater than 2 on the number line. We do
that by putting an open circle on the 2, and making an arrow that extends to the right on the
number line:
To graph n
2, we need to show 2 and all the numbers greater than 2 on the number line, so
we make a closed circle on the 2, and make an arrow that extends to the right on the number
line:
More ex:
Graphing and identifying ordered pairs on a coordinate plane:
Vocabulary:
Coordinate plane - the plane containing the x and y axes
Quadrant - one of the four sections of the coordinate plane
x-axis - the horizontal reference line on the coordinate plane
y - axis - the vertical reference line on the coordinate plane
Origin - the intersection of the x and y axes (0,0)
Ordered pair - two numbers that represent a specific point on the coordinate plane - the first
number refers to the corresponding value on the x axis, the second number refers to the
corresponding value on the y axis) (x,y)
In the illustration below, L is at (2,4) and W is at (-1,-2)
Unit Rate/Constant of Proportionality/Determining if values in a table
or on a graph are proportional
A proportional relationship is one in which the ratios are equal. 2 boys/3 girls, 4 boys/6 girls, 10
boys/15 girls are equal ratios, so those values are proportional. 1 boy/2 girls, 2 boys/3 girls, 3
boys/4 girls are not equal ratios, so those values are not proportional.
A ratio that compares two quantities with different kinds of units is a rate. Ex. A heart is beating
160 beats in 2 minutes. The ratio 160 beats/2 minutes is a rate.
When the rate is simplified so that the denominator is 1, it is called a unit rate. Ex: the ratio of
160 beats/2 minutes can be simplified (reduced) to 80 beats/1 minutes. The unit rate is 80
beats per minute, or 80.
The next example shows a table with the cost of muffins. The unit rate is 50 cents (it costs 50
cents for 1 muffin). Since the price increases by 50 cents for each muffin, the values in the
table are proportional, and 50 is the constant of proportionality - it is the constant number that
is multiplied by the x value (the number of muffins) to get the y value (the total cost of the
muffins). NOTE: the unit rate and the constant of proportionality are the same number.
Number of Muffins (x)
Cost (y)
1
.50
2
1.00
3
1.50
4
2.00
5
2.50
If you were to graph the values from the muffin table, you’d start the graph at (0,0) - because if
you didn’t buy any muffins, you wouldn’t spend any money. The x value, number of muffins,
would be 0, and the y value, cost, would be 0.
Since the points on the graph could be connected by a straight line that goes through the
origin (0,0), you can see that the graph represents a proportional relationship.