Name: ____________________________
CHAPTER 1 NOTES FOR TEST
1-1 EVALUATING ALGEBRAIC EXPRESSIONS:
To evaluate an algebraic expression, substitute a given number for the variable. Then use the order of operations to find the value of
the resulting numerical expression.
Example: Evaluate the expression for the given value of the variable
2𝑎 + 3 𝑓𝑜𝑟 𝑎 = 4
2(𝟒) + 3
𝑐
= 11
1-2 WRITING ALGEBRAIC EXPRESSIONS:
Word Phrases
+
 Add 5 to a number
 Sum of a number and 5
 5 more than a number
 Subtract 11 from a number
 Difference of a number and 11
 11 less than a number
 A number minus 11
×
 3 multiplied by a number
 Product of 3 and a number
÷
 7 divided into a number
 Quotient of a number and 7
Expression
𝑛+5
𝑥 − 11
3 · 𝑚 𝑜𝑟 3𝑚
𝑎
𝑜𝑟 𝑎 ÷ 7
7
1-3 INTEGERS AND ABSOLUTE VALUE:
A number’s absolute value is the distance from 0 on a number line. Absolute value of a nonzero number is always positive because
distance is always positive. “The absolute value of -4 is written as |−4| = 4.
1-4 ADDING INTEGERS:
Adding Two Integers
If the signs are the same…
If the signs are different…
…find the sum of the absolute values. Use the same sign …find the difference of the absolute values. Use the sign
as the integers.
of the integer with the greater absolute value.
1-5 SUBTRACTING INTEGERS:
Words
To subtract an integer, add its
opposite.
Subtracting Two Integers
Numbers
3 − 7 = 3 + (−7)
5 − (−8) = 5 + 8
Algebra
𝑎 − 𝑏 = 𝑎 + (−𝑏)
𝑎 − (−𝑏) = 𝑎 + 𝑏
1-6 MULTIPLYING AND DIVIDING INTEGERS:
If the signs are the same, the sign of the answer is positive.
If the signs are different, the sign of the answer is negative.
Example:
5(−8) = −40 {𝑠𝑖𝑔𝑛𝑠 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑠𝑜 𝑎𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒}
−8
= 1 {𝑠𝑖𝑔𝑛𝑎𝑠 𝑎𝑟𝑒 𝑠𝑎𝑚𝑒 𝑠𝑜 𝑎𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒}
−8
1-7 SOLVING EQUATIONS BY ADDING OR SUBTRACTING
Identity Property of Addition
Words
Numbers
5+0 =5
The sum of any number and zero is
−2 + 0 = −2
that number.
Properties of Equality
Algebra
𝑎+0 =𝑎
Words
Addition Property of Equality:
You can add the same number to
both sides of an equation, and the
statement will still be true.
Subtraction Property of Equality:
You can subtract the same number
to both sides of an equation, and
the statement will still be true.
Numbers
2+3 =5
+4 +4
2+7 =9
4 + 7 = 11
−3 −3
If x=y, then 𝑥 − 𝑧 = 𝑦 − 𝑧
4+4 =8
1-8 SOLVING EQUATIONS BY MULTIPLYING OR DIVIDING:
Identity Property of Multiplication
Words
Numbers
5·1=5
The product of any number and one
−2 · 1 = −2
is that number.
Words
You can divide both sides of an
equation by the same nonzero
number, and the statement will be
true.
Algebra
If x=y, then 𝑥 + 𝑧 = 𝑦 + 𝑧
Division Property of Equality
Numbers
4 · 3 = 12
÷ 2 ÷2
Algebra
𝑎·1=𝑎
Algebra
If 𝑥 = 𝑦 𝑎𝑛𝑑 𝑧 ≠ 0
𝑥
𝑦
Then =
𝑧
𝑧
12
=6
3
1-9 SOLVING TWO-STEP EQUATIONS:
Equations that contain two operations require two steps to solve. Identify the operations and the order in which they are applied to
the variable. Then use inverse operations to undo them in reverse order.
Example:
6𝑥 − 2 = 10
Equation Steps:
1. Frist X is multiple by 6
2. Then 2 is subtracted
Solving Steps:
1. Add 2 to both sides of the equation
2. Then divide both sides by 6
6𝑥 − 2 = 10
+2
+2
6𝑥 = 12
÷6 ÷6
𝑥 = 22
Decimals/Fractions/%:
Fraction to Decimal:
Decimal to Fraction:
Percent to Decimal:
{Tip: You can also think of moving the decimal 2 places to the left}
Decimal to Percent:
{Tip: You can also think of moving the decimal 2 places to the right}
Percent to Fraction:
Fraction to Percent: