Constant of Proportionality
Identify the constant of proportionality (unit rate) in this situation: 6 pounds of apples cost $9.
$1.50 per pound
Solve: If 4/5 = x/20, what is x?
x = 16
Simplify the expression: 3x + 2x
5x
Solve: x + 7 = 15
x = 8
What is the absolute value of -8?
8
A table shows (x, y) pairs: (1, 4), (3, 12), (5, 20). Is this proportional? If so, what is the constant of proportionality?
Yes, c.o.p. = 4
A map has scale 1 inch : 50 miles. How many miles are represented by 3.6 inches?
180 miles
Combine like terms: 5a + 3 - 2a + 7.
3a + 10
Solve: 3x = -21
x = -7
Compute: (-3) × 7
-21
The graph of a relationship is a line through the origin with point (1, 2.5). What is the constant of proportionality?
2.5
Sarah can type 45 words per minute. At that rate, how many words can she type in 2 1/2 minutes?
112.5 wpm
Write an expression for: "7 less than three times a number n."
3n - 7
Solve: 4x + 5 = 29
x = 6
Divide: 3/4 ÷ 1/8
6
Write an equation that represents the proportional relationship where y varies directly with x and the constant of proportionality is 7. Then find y when x = 3.
y = 7x, (3,21)
A bag of trail mix weighs 750 g for 5 servings. How many grams for 12 servings?
1800g
Rewrite the expression 4(x - 5) by expanding.
4x - 20
Solve the equation: 2(x + 3) = 16.
x = 5
Convert the fraction 7/20 to a decimal.
0.35
A recipe uses 2 cups of flour for every 3 cups of sugar. Give the constant of proportionality that expresses cups of flour per cup of sugar, and write the proportional equation relating flour F to sugar S.
c.o.p. = 2/3, f = (2/3)s
Solve this percent problem using proportional reasoning: A jacket is originally $120 and is on sale for 25% off. What is the sale price?
$90
Given the expression 2(3x - 4) + 5x, rewrite it in its simplest equivalent form.
11x - 8
A word problem: A concert ticket and a program together cost $18. The program costs $2 less than half the ticket price. Let t be the ticket price. Write an equation.
1.5t - 2 = 18
Evaluate (−3/4) × (−8/9) ÷ (2/3) and explain the sign of the result.
Sign is Positive because even number of negative factors.
(4/9) or 0.444444444444...