Proportional Relationship Study Guide
7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
Unit Rate / A unit rate compares two quantities where the second quantity is 1.How do I find a unit rate?
Step 1: Draw a big fraction bar.
Step 2: Write the units of the problem in the correct place based on what the question is asking.
Step 3: Place numbers from problem with correct units.
Step 4: Divide to solve
Ex. I travel 180 miles in 3 hours. If I am traveling at a constant speed, what is my miles per hour?
Rate: : Unit Rate
Complex Fraction / A complex fraction is a fraction where the numerator is a fraction (, the denominator is a fraction (, or both the numerator and the denominator are fractions (). You solve these by dividing. Re-write the problem using division.
Ex. () =
Better Buy / Comparison of two unit rates to determine the better deal.
Step 1: Set up rates and find the unit rate for each item.
Step 2: Determine which is cheaper to find the better buy.
Ex. Which is the better buy, 24 grams of turkey for $10.08 or 9 grams of turkey for $4.77?
1.An orange juice container starts with 6 cups of juice. How much orange juice is left after three 1 cup servings are poured?
2.At a farmers’ market, 4 apples can be purchased for $3.00. What is the unit price of an apple at the farmers’ market?
3.
7.RP.A.2 ecognize and represent proportional relationships between quantities.
How can I determine if two quantities are in a proportional relationship?
Table / GraphIf there is a constant of proportionality, then it is in a proportional relationship. If there is not a constant, then it is not proportional.
Ex.
X / 1 / 2 / 3 / 5
y / 6 / 12 / 18 / 30
Yes; this is a proportional relationship because all of the x-values can be multiplied by 6 to get the y-values. / To be proportional, the graph must be a straight line through the origin (0,0).
Proportional Non-proportional
How can I identify the constant of proportionality (unit rate) in tables, graphs, or equations?
Tables / Graphs / EquationsIf you know it is proportional and you have the x-value of 1 in your table, then the y-value that goes with the 1 is the unit rate. (Look below, I have the set (1,6). This means that 6 is the constant.
If you don’t have the x-value of 1 listed,
determine if there is a constant, k, by using the equation k = or determine what they multiplied all of the x values in the table by to get the y values.
Ex.
X / 1 / 2 / 3 / 5
y / 6 / 12 / 18 / 30
/ Find the point (1,r) on the graph if available. If this point is unclear on the graph, choose a point on the graph that is clear and divide the y-value by the x-value.
Since I can’t use the point (1,r), I need to pick another point, (4,6) or (6,9) or (10,15).
/ The constant in an equation is the coefficient (number attached) with the x variable in the format y=kx.
Examples:
Y=4x; constant = 4
Y= ¼x; constant = ¼
Y= constant = 1/5
How can I represent proportional relationships with equations?
*An equation that is proportional is in the format y=kx. The constant, k, can be positive or negative and can be a decimal, fraction, or whole number.
Proportional Examples: y=4xy= which can also be written y= y= -2.3x
Not proportional examples: y= x + 2y= y= 3x – 8y=
What does a point (x,y) on a graph represent with special attention to the points (0,0) and (1,r)?
*Look at the x and y axis labels to know what the points represent.
*(1,r) shows the unit rate on a graph
*(0,0) shows if you don’t put anything into something then you don’t get anything out. Ex. If you go 0 miles then you use 0 gallons of gas.
Ex. The point (6, 96) means if you use 6 cups of flour it will make 96 cookies.
7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Percent set up: Once set up, cross multiply and divide.
Ex:What percent of 55is 34?
55x = 3400 x= 61.
Tax / Find the percent of the number and ADD it to the original priceMarkups and Markdowns / Find the percent of the number and ADD it to the original price if it is a markup but SUBTRACT if it is a markdown
Gratuities or tips / Add all of the items together and find the percent of the sum. Then, ADD that to the sum.
Commissions / Find the percent of the total to find the commission.
Fees / Find the percent of the total and ADD the fee to the total.
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3. If the wholesale price of an item is $250 and the markup is 20%, find the retail price of the item.
4. You go to a restaurant and order $137.61 worth of food. You decide to tip the waiter 18%. You also have to pay a tax of 6.5% on the original bill. What is the final cost of the meal?