1C Algebraic Expressions
Symbol / Words that have the same meaning as the operation symbol+ / and, increased by, more than, plus, add, addition, sum of, the quantity, combine, total
- / decreased by, less than, minus, subtract, subtraction, difference of, take away, deduct, how much more?
x / times, multiply, multiplication, product, multiplied by, double, triple, quadruple
÷ / division, divide, divided by, quotient, over(fraction)
= / equals, same as, as much as, equal to, is, identical
Hints: Use ( ) when there is subtraction or the word “Sum”
Ex: The difference of x + 2 and x – 3 (x +2) – (x - 3)
Ex: 5 times the sum of a number and 3 5(x +3)
Switch the order when there is a “than” and it means subtraction
Ex: Jack is 4 years younger than Sam J = S – 4
Ex: The length is 5 less than the width L= w - 5
Examples:
Write an algebraic expression for each verbal expression.
a)Four more than a number n
n + 4
b)9 less than a number n
n - 9
c)3 times the sum of 15 and a number n
3(15 + n)
d)One-half a number n
n/2
e)3 less than 5 times a number n
5n - 3
f)Jane has $10. Frank has x + 2. How much more does Jane have than Frank?
10 – (x + 2)
g)The length is four less than twice the width
L= 2w – 4
h)There are twice as many fish as cats
f = 2c
i)The quotient of a number and 6
x/6
j)The number of burritos and hamburgers is 10
b + h = 10
Practice. Write algebraic equations for the following:
1) 7 less than the product of 4 and a number x.
2) The difference of 4 and x squared.
3) 15 decreased by twice the sum of x and 3.
4) Jack’s is twice as old as Sally.
5) The width is five more than the length.
6) Sally weighs thirty pounds less than Jackson.
7) There are three times as many cats as dogs.
8) How much more is Sally’s age than twice Thomas’s age?
9) Jane is three years younger than Tom.
10) Mary’s number is 15 less than twice Sally’s number.
11) The difference of twice the number of cats and three times the number of dogs is 17.
12) There are twice as many children as adults.
13) The number of adults and children attending the play is 100.
14) The number of cats and dogs is 120.
15) A child’s ticket is $3 and an adult’s ticket is $7. The total amount of ticket money was $80.
16) Lorenzo bout several pounds of honey roasted peanuts and gave the cashier a $20 bill. Write an expression for the amount of change he will receive if p is the cost of the peanuts.
17) A bakery sells a dozen bagels for $8.50 and a dozen doughnuts for $3.99. Write an expression for the cost of buying b dozen bagels and d dozen doughnuts.
18) A small dog’s age in human years(for dogs older than 2) is equivalent to four times the years increased by 16.
19) Each person in the United States produces approximately 3.5 pounds of trash each day. Write an expression representing the pounds of trash produced in a day by a family with m members.