Transcript 1-1: Writing Expressions and Equations

1-1: Writing Expressions and
Equations
Lesson Opener
• ? represents a number.
• That number plus ten
equal 14.
• How do we represent
the number
algebraically?
WHAT YOU’LL LEARN
Translate words into
algebraic expressions
and equations.
BUILD YOUR VOCABULARY (pages 2–3)
• An algebraic expression contains
numbers and variables along with +, -, x,
and/or ÷.
• A variable is a symbol used to represent
an unknown number.
• A numerical expression contains
numbers along with +, -, x, and/or ÷.
BUILD YOUR VOCABULARY (pages 2–3)
• A factor is a quantity that is being
multiplied.
• A product is the result of numbers that
are multiplied.
• An equation is a mathematical sentence
that contains an equals sign (=).
ORGANIZE IT
In your notes, write
several words or
phrases for each of
the operations,
addition, subtraction,
multiplication, and
division.
Addition
Subtraction
plus
the sum of
increased by
more than
added to
The total of
minus
the difference of
decreased by
less than
fewer than
subtracted from
Multiplication
Division
Times
The product of
Multiplied by
At
Of
Divided by
The quotient of
The ratio of
per
EXAMPLES
Write an algebraic expression for each
verbal expression.
1
the sum of p and 12
p + 12
2
the product of k and q
k  q or kq
Your Turn
Write an algebraic
expression for each verbal expressions
a) b decreased by 6
b–6
b) the product of 9 and z
9  z or 9z
EXAMPLES
A python eats 4 pounds of meat each month.
3 Write a numerical expression to represent
the amount it eats in 5 months.
The numerical expression is 4  5 or 4(5).
4 Write an algebraic expression to represent
the amount it eats in d months.
The algebraic expression is 4  d or 4d.
EXAMPLES
Write a verbal expression for each algebraic
expression.
5 37 + s
the sum of 37 and s .
37 increased by s.
6 5 (b – 3)
5 times the difference of b and 3.
5 multiplied by the difference of b and 3.
Your Turn
Write a verbal
expression for each algebraic expression
a) x ÷ 7
X divided by 7
b) 4 + (2n)
the sum of 4 and the product of 2 and n.
An equation is a mathematical sentence
that contains an equals sign (=). Words
are used to indicate the equals sign.
An equation may contain numbers,
variables, or algebraic expressions.
Equality
Equals
Is equal to
Is
Is the same as
Is equivalent Is as much as
to
Is identical to
EXAMPLES
Write an expression for each sentence.
7 The quotient of t and 8 equals 20.
t ÷ 8 = 20 or t/8 = 20
8
Seven less than three times g is 31.
3g - 7 = 31
Your Turn
Write an expression for
each sentence.
a) A number x increased by 12 is the
same as 27.
X + 12 = 27
b) The product of 8 and d decreased by
9 equals 23.
8d – 9 = 23
EXAMPLES
Write a sentence for each equation.
9 j + 4 = 21
Four more than j is equal to 21.
10 3z – 12 = 11
The product of 3 and z
decreased by 12 equals 11.
Your Turn
equation.
a) r - 10 = 5
Write a sentence for each
Ten less than r is equal to 5.
b)
n
 6  30
3
The quotient of n and 3 increased by
6 equals 30.