7th grade Math
Chapter 7
Notes
Translating in the “math language”
Addition
plus
the sum of
more than
Subtraction
minus
difference of
decreased by
Multiplication
Times
The product of
Multiplied by
increased by
total
added to
fewer than
less than
subtracted
Of
twice
Division
Divided by
The quotient of
Separate into
equal parts
“a number increased by 7”
is written
“x + 7”
“4 increased by a number is 12”
is written
“4 + x = 12”
Terms are parts of an expression that are added together. If terms have
identical variable parts, they are like terms. If a term has a number part
and a variable part, the number part is called the coefficient. A term that
does not have a variable part is called a constant.
An inverse operation is an operation that “undoes” another operation.
Adding and subtracting are inverse operations.
The Addition Property of Equality- adding the same number to each side
of an equation produces an equivalent equation.
x– a = b …… x – a + a = b + a
Multiplication Property of Equality- multiplying each side of an equation by
the same nonzero number produces an equivalent equation.
x/a = b……x/a(a) = b(a)
Division Property of Equality- dividing each side of an equation by the
same nonzero number produces an equivalent equation.
ax = b…….ax/a = b/a
Solving two-step equations:
Our goal is to isolate the variable. When the variable has friends, we have
to see how they are connected, and complete an inverse operation to
get them away from their friends (isolate them). When there are two
friends, disconnect the add/subtract friend first then disconnect the
multiply/divide friend.
2x + 1 = 7
2x + 1 - 1= 7 – 1
2x = 6
2x /2 = 6 /2
x=3
Solving inequalities:
An inequality uses the signs: <, >, ≥, ≤
The solution to an inequality is often an entire group of numbers
(sometimes an infinite amount)
We can graph an inequality to model the numbers.
< and > use open circles
≥, and ≤ used filled in circles
A function is a pairing of each number in one set with a number in
another set. Start with an input, and the number that it connects to is
called the output. All input values are the domain of a function, all output
values are the range of a function. We usually call the input values “x”,
and the output values “y”.
We can graph functions by using the input (x) values and the output (y)
values as ordered pairs describing points on a coordinate plane.
Start by making an xy chart, filling in values for y when the x values are set
at -2,-1,0,1, 2. Next, graph the 5 points that were just created. If it is a
linear function these points will all lie in a line. Connect the dots and
place arrows on each end.
Graph y = x + 2
x
-2
-1
0
1
2
y
0
1
2
3
4
We have created the points: (-2,0), (-1,1), (0,2), (1,3) and (2,4).
Plot these on a coordinate plane and connect them to form a
line.