expressions
Key Terms • Variable: number we don’t know (use a letter) • Expression: mathematical phrase (does not have an equals sign) • Evaluate: Find the answer • Equation: mathematical sentence (HAS an equals sign) • Substitute: replace
Evaluate the following if a = 12 and b = -3.
Example 1: 12
12
1 4
12
1 2
56 8
12
12 56 8
Replace all a’s with 12.
48 12
a
a
6
Evaluate the following if a = 12 and b = -3.
Example 2: 3 21
b 21 2b
2( 3) 24 6
4
Replace all b’s with -3.
Evaluate the following if a = 12 and b = -3.
Example 3: 2
b
2
Replace all a’s and b’s.
5
2a
( 3) 5 2 (12 )
9 5 24
4
2
1
24
24
12
Verbal Phrases (Clues! ) Sum More than Add Increase Plus Positive + Greater Than Subtract Minus Decrease Less - Take Away Less Than Diminished Difference Negative
Divide ÷ Equal By ● Of
Quotient Half Groups Separate
Product
Times
Factor Into
Multiply Double
Twice
Verbal Phrases (Clues! ) IS Equal To Same As = Total Answer Equivalent
35 is a number
Write Algebraic Expressions for These Word Phrases
x+6 • The sum of x and six • Twice a number, minus 11 2y - 11 • The quotient of b and 45 b÷45 • Three times a number 3n • Ten minus, the quantity of the product of y and 3 10 - (y●3) • 3 less than x x-3 • 3 less x 3-x
Write Algebraic Expressions for These Word Phrases • • • •
Ten more than a number A number decreased by 5 6 less than a number A four times a number increased by 8 • The sum of a 3 times a number and 9 • The quantity of x minus 2, (x divided by 10
n + 10 w-5
x-6 4n + 8 3n + 9
– 2)÷10
Write an Algebraic Equation for Equation for These Situations
• Scott’s brother Alan is 2 years younger than Scott
A=S-2
• The sum of two numbers is 12
b + c = 12
• The difference between two numbers is 5
m–n=5
A NUMBER X INCREASED BY 9 X+9
A NUMBER Y DIVIDED BY 8 Y Y / 8 OR 8
ELEVEN LESS B 11 - B
THE MONEY LEFT OVER FROM £10 AFTER SPENDING £J
£(10 – J)
5 LESS THAN X x-5
2/3 OF A NUMBER R MINUS TWENTY-THREE
2/3 R - 23
A NUMBER 21 DIVIDED BY P, PLUS 16
21÷p + 16
THE PRODUCT OF SIX AND Y INCREASED BY FIVE
6Y + 5
THE DIFFERENCE WHEN 32 IS SUBTRACTED FROM Z
Z - 32
Evaluate the following if a = 12 and b = -3.
Example 1: 12
12
1 4
12
1 2
56 8
12
12 56 8
Replace all a’s with 12.
48 12
a
a
6
Evaluate the following if a = 12 and b = -3.
Example 2: 3 21
b 21 2b
2( 3) 24 6
4
Replace all b’s with -3.
Evaluate the following if a = 12 and b = -3.
Example 3: 2
b
2
Replace all a’s and b’s.
5
2a
( 3) 5 2 (12 )
9 5 24
4
2
1
24
24
12
Verbal Phrases (Clues! ) Sum More than Add Increase Plus Positive + Greater Than Subtract Minus Decrease Less - Take Away Less Than Diminished Difference Negative
Divide ÷ Equal By ● Of
Quotient Half Groups Separate
Product
Times
Factor Into
Multiply Double
Twice
Verbal Phrases (Clues! ) IS Equal To Same As = Total Answer Equivalent
35 is a number
Write Algebraic Expressions for These Word Phrases
x+6 • The sum of x and six • Twice a number, minus 11 2y - 11 • The quotient of b and 45 b÷45 • Three times a number 3n • Ten minus, the quantity of the product of y and 3 10 - (y●3) • 3 less than x x-3 • 3 less x 3-x
Write Algebraic Expressions for These Word Phrases • • • •
Ten more than a number A number decreased by 5 6 less than a number A four times a number increased by 8 • The sum of a 3 times a number and 9 • The quantity of x minus 2, (x divided by 10
n + 10 w-5
x-6 4n + 8 3n + 9
– 2)÷10
Write an Algebraic Equation for Equation for These Situations
• Scott’s brother Alan is 2 years younger than Scott
A=S-2
• The sum of two numbers is 12
b + c = 12
• The difference between two numbers is 5
m–n=5
A NUMBER X INCREASED BY 9 X+9
A NUMBER Y DIVIDED BY 8 Y Y / 8 OR 8
ELEVEN LESS B 11 - B
THE MONEY LEFT OVER FROM £10 AFTER SPENDING £J
£(10 – J)
5 LESS THAN X x-5
2/3 OF A NUMBER R MINUS TWENTY-THREE
2/3 R - 23
A NUMBER 21 DIVIDED BY P, PLUS 16
21÷p + 16
THE PRODUCT OF SIX AND Y INCREASED BY FIVE
6Y + 5
THE DIFFERENCE WHEN 32 IS SUBTRACTED FROM Z
Z - 32
