a number that divides another number with a remainder of zero
variable
Distributive Property
like terms
coefficient
factor
constant
A factor is a number that divides another number with a remainder of zero.
A variable is a symbol that represents a quantity that can vary or change.
The Distributive Property is a property of multiplication over addition or subtraction, which states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding or subtracting the results.
Like terms are terms that have identical variables raised to the same exponent. They can be combined by adding or subtracting their coefficients.
A coefficient is the numerical factor that is multiplied by a variable in a term.
A constant is a term that has no variable part. It is a fixed value that does not change.
You and your three friends are going to the State Fair. It costs $5 per person for admission into the fair and $3 for each ride. Which algebraic expression represents the TOTAL amount of money it will cost for you and your three friends to get into the fair and ride "x" amount of rides? (2 points)
Responses
5x + 3
5x + 3
3x + 5
3x + 5
15x
15x
3x + 20
To find the total amount of money it will cost for you and your three friends to get into the fair and ride "x" amount of rides, you would need to multiply the cost of admission per person ($5) by the number of people (4), and add it to the cost of each ride ($3) multiplied by the number of rides ("x").
Therefore, the algebraic expression that represents the total cost would be:
4 * $5 + $3 * x
Simplifying this expression, we get:
20 + 3x
So the correct answer is:
3x + 20
At the fair there are two bean bag toss games. You gain 3/4 of a point for each bean bag that you get on the target and you lose 1/2 point for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 3/4h - 1/2g. In a different bean bag toss game you gain 7/8 points for each bean bag that get on the target and you lose 3/4 points for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 7/8h - 3/4g. You can figure out the total number of points earned by simplifying this expression: (3/4h - 1/2g) + (7/8h - 3/4g). What would this expression be simplified? (Hint: Combine like terms!) (2 points)
Responses
10/14h - 4/6g
10/14h - 4/6g
15/8h + 5/4g
15/8h + 5/4g
1 5/8h - 1 1/4g
1 5/8h - 1 1/4g
1 1/2h - 1 3/4g
To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), we need to combine like terms.
First, let's simplify the terms with "h":
(3/4h + 7/8h)
To add these two fractions, we need to find a common denominator, which in this case is 8. So, we need to express 3/4h as an equivalent fraction with a denominator of 8:
(3/4h) = (3/4 * 2/2 = 6/8h)
Now we can add the two fractions:
(6/8h + 7/8h) = 13/8h
Next, let's simplify the terms with "g":
(-1/2g - 3/4g)
To subtract these two fractions, we need to find a common denominator, which in this case is 4. So, we need to express -1/2g as an equivalent fraction with a denominator of 4:
(-1/2g) = (-1/2 * 2/2 = -2/4g)
Now we can subtract the two fractions:
(-2/4g - 3/4g) = -5/4g
Combining the simplified terms, the expression becomes:
(13/8h - 5/4g)
So the correct answer is:
15/8h + 5/4g
omplete this fill-in-the-blank problem. (4 points)
When you evaluate an expression, you substitute a number in for a
. For example, to evaluate the expression 4y+3 for y=6, you would substitute 6 for "y". You would then solve using the Order of Operations. So, 4(6)+3=
. You can also simplify algebraic expressions without knowing what the variables equal. For example, in this expression, (6k+5)+(3k-7). You would add together the coefficients (numbers) in front of "k" and add together the constants or numbers. Adding or subtracting the same variables together is called combining
. So, you would combine 6k + 3k which would equal 9k and you would combine the constants, 5 + -7 which would equal
.
When you evaluate an expression, you substitute a number in for a variable. For example, to evaluate the expression 4y+3 for y=6, you would substitute 6 for "y". You would then solve using the Order of Operations. So, 4(6)+3=
27.
You can also simplify algebraic expressions without knowing what the variables equal. For example, in this expression, (6k+5)+(3k-7). You would add together the coefficients (numbers) in front of "k" and add together the constants or numbers. Adding or subtracting the same variables together is called combining like terms. So, you would combine 6k + 3k which would equal 9k and you would combine the constants, 5 + -7 which would equal -2.