Definitions
A symbol (like x) that represents an unknown or changeable numerical value.
variable
The sum of 9, y, and 4 is what number.
13 + y
The product of 7 and x.
7x
or 7*x
or (7)(x)
BUT NOT 7xx
The power problem equivalent to 6 * 6 * 6 * 6 * 6.
65
The value of 5x + 4 if x is 8.
44
The mathematical rule that the order of operands does not change the result of an operation.
Commutative property
Daily Double: What mathematical operations are commutative?
The difference between y and x.
The quotient of 8 and 2.
4
The power problem equivalent to y * y * y * y * y * y * y.
y7
The value of x4 - x if x is 5.
620
The mathematical rule that multiplying a number by a sum or difference is equivalent to multiplying the number by each term individually and then adding or subtracting the results. i.e. a(b+c) = ab + ac
Distributive Rule
The perimeter of a rectangle with sides of x and 6.
2x +12
The volume of a rectangular box 6 feet long, 3 feet wide, and 4 feet high.
72 cubic feet
The power problem equivalent to 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 (10 of them).
310
The value of (3 * 4)2.
144
The answers to each type of calculation (1) addition, (2) subtraction, (3) multiplication, and (4) division are what.
(1) sum, (2) difference, (3) product, (4) quotient
Each week, Dashing Dan jogs one mile farther than he did the week before. If he jogs 18 miles this week, how far will he jog next week?
18 miles + 1 mile = 19 miles
A rectangle has an area of 63 square meters. One side is 9 meters long and the other side is this length.
7 meters
The multiplication problem equivalent to x5.
x * x * x * x * x
The expression for (y - 4)5 as a difference. Hint: use the distributive rule.
5y - 20
State the order of operations.
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
A log is cut into two pieces. If the log was 12 feet long and one piece is x feet long, then the other pieces is this number of feet.
12 - x feet
The members of the River City School band march in a rectangular array of rows and columns. If there are x rows and y columns, then there are this number of people in the band.
xy people
Dividing zero by another number makes sense, but dividing a number by zero does not make sense for this reason.
If we divide 3 by 0, then 3/0 would be the number that is multiplied by 0 to give 3...but there is no such number.
Alice's Restaurant sells coffee for 40 cents a cup. One week, they sell x cups and the next week they sell y cups. An expression for the total amount charged for these two weeks is this.
40 (x + y)
Or, 40x + 40y