Download Lesson 5 Multiplying and Dividing Rational Numbers

Understanding Algebra Word
Problems
*Represent a given situation using algebraic
expressions or equations in one variable.
*Simplify and evaluate algebraic
expressions.
The biggest challenge to solving word problems is
figuring out whether to add, subtract, multiply or
divide.
Words Meaning
Addition
Words Meaning
Subtraction
Words Meaning Words Meaning
Multiplication
Division
and
increased
more
more than
plus
sum
total
decreased
difference
less
less than
left
lower than
minus
double
half (× ½)
product
times
triple
twice
divide into
half (÷ 2)
divide by
divide among
quotient
To solve a word problem, you must first interpret
the action you need to perform and then choose
the correct operation for that action.
Action
Operation
Possible Question Clues
Combine
Add
How many all together?
Combine equal groups
Multiply
How many all together?
Separate
Subtract
How many more? How many less?
Separate into equal groups
Divide
How many equal groups?
Word Phrases
+
–
• a number plus 5
• add 5 to a number
• sum of a number and 5
• 5 more than a number
• a number increased by 5
• a number minus 11
• subtract 11 from a number
• difference of a number and 11
• 11 less than a number
• a number decreased by 11
Expression
n+5
x  11

• 3 times a number
• 3 multiplied by a number
• product of 3 and a number
3m

• a number divided by 7
• 7 divided into a number
• quotient of a number and 7
a
or a  7
7
TEST YOUR SKILL!!
Match the phrase with the
correct algebraic expression.
1) 2 more than y
1. y - 2
2. 2y
3. y + 2
4.
y/
2
2) 16 divided into m
1. 16 - m
2. 16m
3. m + 16
4.
m/
16
3) 2 less than s
1. s - 2
2. 2s
3. s + 2
4.
s/
2
4) Triple John’s age j
1. 3 + j
2. j - 3
3. 3j
4. j ÷ 3
5) Twice the sum of y and 15
1. 2y + 15
2. 2 + y + 15
3. 2 (y + 15)
4. 2(15) + y
6)
n feet lower than than 10
1. 10 - n
2. n - 10
3. n + 10
4. 10 + n
7) The quotient t and 4
4 goes into t
2. t goes into 4
3. Multiply 4 by t
4. Add 4 and t
1.
8) 18 divided by a number, g
1. 18 - g
2. 18 ÷ g
3. g + 18
4. 18 × g
ABC 2.4
Setting Up Algebra Word
Problems
To set up algebra word problems:
To complete an algebra problem, an equal
sign must be added.
2. The words is or are as well as equals tell you
that you should add an equal sign.
1.
Double Jake’s age, x, minus 4 is 22.
2x - 4 = 22
Translate the word problem into an
equation. DO NOT find the solution yet.
1. Triple the original number, n, is 2,700.
3n = 2700
2. The product of a number, y, and 5 is equal to
15.
5y = 15
3. Four times the difference of a number, x, and 2
is 20.
4(x – 2) = 20
4. The total, t, divided into 5 groups is 45.
t ÷ 5 = 45
Translate the word problem into an
equation. DO NOT find the solution yet.
1. The number of pants in the store, p, minus 54
pants sold today is 320.
p – 54 = 320
2. One-half an amount, x, added to $50 is $262.
x/2 + 50 = 262
3. One hundred plants, divided by 5 rows, equals
n number of plants per row. 100 ÷ 5 = n
4. A number, y, less than 50 is 82. y - 50 = 82
Translate the word problem into an
equation. DO NOT find the solution yet.
1. Seventeen more than half a number, h, is 35.
h/2 + 17 = 35
2. The quotient of a number, w, and 4 is 32.
w ÷ 4 = 32
3. Six less a number, d, is 12.
d – 6 = 12
4. Four times the sum of a number, y, and 10 is
48.
4(y + 10) = 48