Transcript translating expressions and equations ppt

Translating Between
Words and Expressions
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List words that indicate
addition
List words that indicate
subtraction
List words that indicate
multiplication
List words that indicate
division
List words that indicate
equals
Be aware of the difference between "less" and "less than".
For example:
"Eight less three" and "Three less than Eight" are
equivalent expressions. So what is the difference in
wording?
Eight less three:
Three less than eight:
8-3
8-3
When you see "less than", you need to switch the order of
the numbers.
As a rule of thumb, if you see the words "than" or
"from" it means you have to reverse the order
of the two items on either side of the word.
Examples:
·8 less than b means _______________
b-8
·3 more than x means x_______________
+3
·x less than 2 means 2_______________
-x
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The many ways to represent multiplication...
How do you represent "three times a"?
(3)(a)
3(a)
3 a
3a
The preferred representation is 3a
When a variable is being multiplied by a number, the
number (coefficient) is always written in front of the
variable.
The following are not allowed:
3xa ... The multiplication sign looks like another
variable
a3 ... The number is always written in front of the
variable
Representation of division...
How do you represent "b divided by 12"?
b ÷ 12
b ∕ 12
b
12
When choosing a variable, there are some
that are often avoided:
l, i, t, o, O, s, S
Why might these be avoided?
It is best to avoid using letters that might be
confused for numbers or operations. In the
case above (1, +, 0, 5)
TRANSLATE THE WORDS
INTO AN
ALGEBRAIC EXPRESSION
Three times j
Eight divided by j
+
j
-
j less than 7

5 more than j
4 less than j
÷
0
1
2
3
4
5
6
7
8
9
Write the expression for each statement.
Then check your answer.
The sum of twenty-three and m
23 + m
Write the expression for each statement.
Then check your answer.
Twenty-four less than d
d - 24
Write the expression for each statement.
Remember, sometimes you need to use
parentheses for a quantity.
Four times the difference of eight and j
4(8-j)
Write the expression for each statement.
Then check your answer.
The product of seven and w, divided by 12
7w
12
Write the expression for each statement.
Then check your answer.
The square of the sum of six and p
(6+p)
2
100
The quotient of 200 and the quantity of
p times 7
A
B
200
7p
200 - (7p)
C
200 ÷ 7p
D
7p
200
101
35 multiplied by the quantity r less 45
A
35r - 45
B
35(45) - r
C
35(45 - r)
D
35(r - 45)
102 Mary had 5 jellybeans for each of 4 friends.
A
B
C
D
5+4
5-4
5x4
5÷4
103
If n + 4 represents an odd integer, the next
larger odd integer is represented by
A
B
C
D
n+2
n+3
n+5
n+6
From the New York State Education Department. Office of Assessment Policy, Development
and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra;
accessed 17, June, 2011.
104 a less than 27
A
27 - a
B
C
a
27
a - 27
D
27 + a
105
If h represents a number, which equation
is a correct translation of:
“Sixty more than 9 times a number is 375”?
A
B
C
D
9h = 375
9h + 60 = 375
9h - 60 = 375
60h + 9 = 375
From the New York State Education Department. Office of Assessment Policy, Development
and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra;
accessed 17, June, 2011.
Using Numerical and
Algebraic Expressions and
Equations
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We can use our algebraic translating skills to solve other
problems.
We can use a variable to show an unknown.
A constant will be any fixed amount.
If there are two separate unknowns, relate one to the other.
The school cafeteria sold 225 chicken meals today. They
sold twice the number of grilled chicken sandwiches
than chicken tenders. How many of each were sold?
2c + c = 225
chicken
sandwiche
s
chicke
n
tender
s
total
meals
c + 2c = 225
3c = 225
3
3
c = 75
The cafeteria sold
150 grilled chicken
sandwiches and
75 tenders.
Julie is matting a picture in a frame. Her frame is 9 12 inches
wide and her picture is 7 inches wide. How much matting
should she put on either side?
1
1
2m + 7 = 9 2
both sides
of the mat
size of
picture
size of
frame
2m + 7 = 9 2
-7 -7
1
2m = 2 2
2
2
1
m = 14
Julie needs 1 14 inches on
each side.
Many times with equations there will be one number that
will be the same no matter what (constant) and one that
can be changed based on the problem (variable and
coefficient).
Example: George is buying video games online. The cost
of the video is $30.00 per game and shipping is a flat fee of
$7.00. He spent a total of $127.00. How many games did he
buy in all?
George is buying video games online. The cost of the
video is $30.00 per game and shipping is a flat fee of $7.00.
He spent a total of $127.00. How many games did he buy in
all?
Notice that the video games are "per game" so that means
there could be many different amounts of games and
therefore many different prices. This is shown by writing
the amount for one game next to a variable to indicate any
number of games.
30g
cost of
one video
game
number
of
games
George is buying video games online. The cost of the
video is $30.00 per game and shipping is a flat fee of $7.00.
He spent a total of $127.00. How many games did he buy in
all?
Notice also that there is a specific amount that is charged
no matter what, the flat fee. This will not change so it is the
constant and it will be added (or subtracted) from the other
part of the problem.
30g
cost of
one video
game
+7
number
of
games
the cost
of the
shipping
George is buying video games online. The cost of the
video is $30.00 per game and shipping is a flat fee of $7.00.
He spent a total of $127.00. How many games did he buy in
all?
"Total" means equal so here is how to write the rest of the
equation.
30g
cost of
one video
game
+7
number
of games
the cost
of the
shipping
= 127
the total
amount
George is buying video games online. The cost of the
video is $30.00 per game and shipping is a flat fee of $7.00.
He spent a total of $127.00. How many games did he buy in
all?
Now we can solve it.
30g + 7 = 127
-7
-7
30g = 120
30
30
g = 4 George bought 4 video games.
106 Lorena has a garden and wants to put a
gate to her fence directly in the middle of
one side. The whole length of the fence is
1
24 feet. If the gate is 4 2 feet, how many feet
should be on either side of the fence?
107 Lewis wants to go to the amusement park
with his family. The cost is $12.00 for parking
plus $27.00 per person to enter the park.
Lewis and his family spent $147. Which
equation shows this problem?
A 12p + 27 = 147
B 12p + 27p = 147
C 27p + 12 = 147
D 39p = 147
108
Lewis wants to go to the amusement park
with his family. The cost is $12.00 for parking
plus $27.00 per person to enter the park.
Lewis and his family spent $147. How many
people went to the amusement park WITH
Lewis?
109
Mary is saving up for a new bicycle that is
$239. She has $68.00 already saved. If she
wants to put away $9.00 per week, how many
weeks will it take to save enough for her
bicycle? Which equation represents the
situation?
A
B
C
D
9 + 68 = 239
9d + 68 = 239
68d + 9 = 239
77d = 239
110
Mary is saving up for a new bicycle that is
$239. She has $68.00 already saved. If she
wants to put away $9.00 per week, how
many weeks will it take to save enough for
her bicycle?
111
You are selling t-shirts for $15 each as a
fundraiser. You sold 17 less today then
you did yesterday. Altogether you have
raised $675.
Write and solve an equation to
determine the number of t-shirts you
sold today.
Be prepared to show your equation!