Download Word Problem Notes

M8 - 10.8 - Expressions Notes
Meaning
Common Written Phrase
+
Five more than a number
+5
Difference, Less, Subtract, Decreased, Take away −
Four less than a number
−4
Product, Times, Multiplied
×
A number less than three
Quotient, Divide, Split
÷
Twice a number
2
Half a number
⎯⎯
2
6
⎯⎯
Word
Sum, More, Add, Increased
Six divided by a number
Two thirds of a number
Written Phrase
Algebraic Expression
3−
2
⎯⎯
3
Algebraic Expression
Five more than a number, five added to a number, five more than , plus five, a number
plus five, the sum of a number and five.
+5
Four less than a number, four subtracted from a number, four less than , minus four, a
number minus four, the difference of a number and four, a number decreased by four.
−4
A number less than three, a number subtracted from three, less than three, three minus
, three minus a number, the difference of three and a number, three decreased by a
number.
3−
Twice a number, two times a number, two times ,
number, the sum of two and .
2
times two, the sum of two and a
Half a number, a number divided by two, divided by two, half of , the quotient of a
number and two, a number split into two parts, one half
⎯⎯
2
6
⎯⎯
Six divided by a number, the quotient of six and a number, six divided by , six split into
parts.
2
⎯⎯
3
Two thirds of a number, a number times two thirds, a number divided by three and
multiplied by two.
Three more than a number
+3
Five times a number
5
Eight less than a number
1
⎯⎯
2
2
⎯⎯⎯
3
A number less than four
4−
−8
A third of a number
⎯⎯
3
Equ Page 1
Eight divided by a number
8
⎯⎯
M8 - 10.8 - Create/Solve Equations Notes
Find and Solve the following Equations
Five more than a number is 8. What is the number?
+5 =8
−5
−5
=3
The number is 3.
Three less than twice a number is 7. What is the number?
2 −3= 7
+3
+3
2
10
⎯⎯⎯= ⎯⎯⎯
2
2
=5
The number is 5.
Equ Page 2
M8 - 10.9 - 1 Var Word Problems Notes
"Let" Statements
Choosing a letter that represents the number you need to find.
Bob is 6 years older than Mark. Mark is 30. How old is Bob?
=
+6=
.
′
= +6
= 10 + 6
= 16
+6=
(30) + 6 =
36 =
′
= 10
Substitute
′
= 30
= 36
Nick is two years younger than twice Damon's age. Nick is 28. How old is Damon?
=
2 −2 =
2 −2=
2 − 2 = 28
+2 + 2
2
30
⎯⎯⎯= ⎯⎯⎯
2
2
= 15
Substitute
= 15
Equ Page 3
= 28
6
ℎ
M8 - 10.9 - 1 Var Now/Then Notes
Barb is 3 years older than Mark. In 4 years from now, the sum of their ages will be 21. How old are they now?
=
+3=
′
Then
Now
Barb
+3
( + 3) + 4
Mark
+4
( + 3 + 4) + ( + 4) = 21
+ 7 + + 4 = 21
2 + 7 + 4 = 21
2 + 11 = 21
−11 − 11
2 = 10
2
10
⎯⎯⎯= ⎯⎯⎯
2
2
=5
Mark is 5
+3 =
(5) + 3 = 8
Barb is 8
Stella is 10 years older than Alina. In 5 years from now, Stella will be twice Alina's age. How old is Stella
and Alina?
=
.
Now
Stella
+ 10
Then
( + 10) + 5
+5
Alina
( + 10) + 5 = 2( + 5)
+ 15 = 2 + 10
−
−
15 = + 10
−10
− 10
5=
=5
+ 10
(5) + 10 = 15
Alina is 5.
Stella is 15.
Two consecutive numbers sum to 11. What are the two numbers?
=
+1=
+ ( + 1) = 11
+ + 1 = 11
2 + 1 = 11
−1
−1
2 = 10
2
10
⎯⎯⎯= ⎯⎯⎯
2
2
=5
5 is the smaller number.
Equ Page 4
+1
(5) + 1 = 6
6 is the larger number.