Name __________________________________________________________
Date ____________________
Order of Operations: PEMDAS
It’s important to follow the order of operations when evaluating an expression. Otherwise, you might get the
wrong answer! You can remember the order of operations using the acronym PEMDAS:
1.
Parentheses, and other grouping symbols
2.
Exponents
3.
Multiplication and Division, from left to right
4.
Addition and Subtraction, from left to right
If your problem doesn’t have one of these steps,
move on to the next step!
Let’s try an example. Use the order of operations to evaluate 4 × 6 + 2² − (4 + 3).
4 × 6 + 2² − (4 + 3)
First, simplify what’s inside the parentheses: 4 + 3 = 7.
4 × 6 + 2² − 7
Then, evaluate the exponent: 2² = 4.
4 × 6 + 4 − 7
Next, multiply: 4 × 6 = 24.
24 + 4 − 7
Then, add: 24 + 4 = 28.
28 − 7 = 21
Finally, subtract 28 − 7 to get the answer, 21.
Evaluate each expression using the order of operations.
9+7×8
46 + 19 − 4²
16 ÷ 4 + 7
10² × 2 + 40 ÷ 8
8 × 12 ÷ (30 − 6)
64 − (8 + 12) × 3
21 ÷ (3 + 4) × 6
(9 − 5) × 7 − 2 × 8
48 ÷ 6 × 2² − (3 + 5)
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SOLVING EQUATIONS WITH SQUARE ROOTS
Taking the square root of a number is the opposite, or inverse, of squaring it.
So, you can solve some equations using square roots.
Let’s try it! Solve x2 = 9.
x2 = 9
x2 =
9
x = ±3
Take the square root of both sides of the equation.
2
2
Since 3 = 3 · 3 = 9 and (–3) = (–3) · (–3) = 9, both 3 and –3 are square
roots of 9. You can write this as ±3.
In the example above, you can simplify the square root of 9 to get ±3 since 9 is a perfect square.
Consider solving an equation like x2 = 11. Because 11 is not a perfect square, you would need to write your
answer using the square root symbol. So, the exact solution of x2 = 11 is x = ± 11.
Try it yourself! Solve each equation for the variable. Don’t forget to check if you’re taking the square root
of a perfect square or not!
a² = 36
m² = 4
g² = 68
j² = 16
q² = 20
b² = 144
r² = 55
d² = 81
s² = 225
f ² = 141
w² = 100
h² = 200
c² = 289
y² = 400
z² = 180
v² = 900
k² = 625
p² = 250
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Name
Date
FRACTION BASICS:
Converting Fractions
and Decimals
Fractions and decimals both represent parts of wholes. You can convert between fractions
and decimals. Look at the examples below to see how. Think about place value charts to help you!
Converting Fractions to Decimals
Convert
1
10
1
10
Converting Decimals to Fractions
to a decimal.
Convert 0.8 to a fraction.
is 1 out of 10, or one tenth:
ones
0
tenths
.
1
1
10
0.8 is the same as eight tenths:
ones
= 0.1
0
53
tenths
.
8
0.8 =
8
10
Convert 100 to a decimal.
Convert 0.72 to a fraction.
53
100
0.72 is the same as seventy-two hundredths:
is 53 out of 100, or fifty-three hundredths:
ones
0
53
100
tenths hundredths
.
5
3
ones
= 0.53
0
tenths hundredths
.
7
0.72 =
2
72
100
Write each fraction as a decimal.
5
10
45
100
2
10
=
=
=
63
100
=
92
100
40
100
=
7
10
99
100
=
6
10
4
10
=
=
3
10
=
=
81
100
=
=
Write each decimal as a fraction.
0.4 =
0.11 =
0.9 =
0.67 =
0.91 =
0.2 =
0.55 =
0.23 =
0.3 =
0.52 =
0.19 =
0.08 =
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Expression vs. Equation
An expression is a mathematical phrase that
contains numbers, variables, or both. Expressions
never have an equal sign.
An equation states that two expressions are equal.
Equations always have an equal sign.
2f + 7
2f + 7 = 31
Expressions and equations are made of different parts. Take a closer look at each part of the
expression below.
Variable: a letter that
represents an unknown
}
first
term
Constant: a number
without a variable
}
2f + 7
Coefficient: the
number multiplied
by a variable
second
term
Expressions and equations
can also include factors,
or numbers you multiply to
get another number.
In 2f + 7, the first term has
two factors: 2 and f.
Term: a part of an expression
that is separated by + or −
Directions: Draw a circle around each expression. Draw a rectangle around each equation.
6 + k = 14
(6 + 9) × 4
2
1
÷
3
7
0.25g × 0.76h
8w - 3w = 20
3 = (2p + 7) ÷ 5
2m + 7n = 14n - 1
3 + 2j
10
Directions: Answer the questions about the following expressions.
10x - y + 3.5
3a + 6 + b
How many terms does the expression have? ______ How many terms does the expression have? ______
What is the coefficient of the first term? ______
What are the variables? _________________
What is the constant term? ______
What are the factors of 3a? _________________
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Parts of an Expression
Variable: a letter that
represents an unknown
An expression is a mathematical
phrase that contains numbers,
variables, or both. An expression
8n − 3
Coefficient: a number
multiplied by a variable
does not have an equal sign.
Constant: a number
without a variable
first term second term
Expressions can have different
Term: a part of an expression
that is separated by + or –
parts. Let's look at an example.
Answer the questions about the following expressions.
7g − 5 + 3h
–7a − 5b + 8
How many terms does this expression have?
How many terms does this expression have?
What are the variables?
What is the constant term?
and
What is the coefficient of the third term?
What is the coefficient of the first term?
2 32 −
–2.5r + 7.2s + 0.8
1 2
1 2
+
j
4
2k
What is the constant term in this expression?
What is the constant term in this expression?
What are the variables?
What are the variables?
and
What is the coefficient of the second term?
and
What is the coefficient of the last term?
Write an expression for each of the following descriptions.
Write an expression with two terms. The second
term should be a constant.
Write an expression with three terms. The first term
should have a negative coefficient. The second term
should have n as a variable and a coefficient of 8.
Write an expression with three terms. The first term
should be a constant. The last term should have a
coefficient of 2.5.
Write an expression with three terms. The first term
should have a coefficient of – 45 . The last term
should be a constant.
Write an expression with two terms. The first term
should have a coefficient of 7.
Write an expression with four terms. The first term
should be a constant. One term should include the
variable z. One term should have a coefficient of 81 .
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Math
Algebra
Writing Expressions
With Variables
#1
An expression in math is a sentence containing numbers and the operations. Below are
examples of expressions:
2+ 3
17 - 16 + 2
2
6
x
5
6
(3 x 5) - (6 x 2)
6
y - 20
A variable represents the unknown number in the expression or equation.
For example, 4 x t = 12. The letter “ t ” represents the number which multiplies
by 4 to equal 12.
Read the sentences below and write an expression. See the example.
Robin has 10 chocolates and Martin has m chocolates. Write an expression of chocolates
that Martin and Robin have together.
Robin has 10
Martin has m
The expression is 10 + m
Bobby grows 20 carrots and Tommy grows k carrots. Write the expression of carrots that
both Bobby and Tommy have.
Julie has 7 jelly beans. She gave y jelly beans to Susie. Write the expression of jelly beans
that she has left.
Sally ate 2 pieces of cake in the morning and n pieces in the evening. Write the expression
for the amount of cake she had today.
Ronny had 12 paper clips. He lost p of them. Write the expression of paper clips Ronny has left.
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