Mid-Unit 5 Test: Ratios, Rates, and Unit Rates

Mid-Unit 5 Test: Ratios, Rates, and Unit Rates

NEED TO KNOW INFORMATION

- A ratio is a relationship between TWO quantities.

- A ratio can be written three different ways: 1:5 1/5 1 to 5

- To find out if sets of ratios are proportional:

• CROSS MULTIPLY. If the products (answers) are the same on both sides, then they are proportional (equivalent). If they are not, then they are NOT proportional.
• REDUCE EACH RATIO TO LOWEST TERMS. If they are the same ratio in lowest terms, then they are proportional (equivalent).
• MULTIPLY OR DIVIDE LEFT TO RIGHT (mental math). If you can multiply/divide each quantity in the ratio by the same POSTIIVE number and the products are the second ratio, then you have proportional relationship.
• FIND THE UNIT RATE OF EACH. If the unit rates are the same, then they are proportional (equivalent).

- A PROPORTION is made up one TWO EQUAL RATIOS. It is easiest to write out your proportions as fractions and then compare them using one of the ways listed above.

* To solve a proportion when you are missing a value:

Examples:

- To find a UNIT RATE , divide the numerator (top number) by the denominator (bottom number). That answer becomes the numerator and your denominator is ALWAYS a ONE for Unit Rates! Always make sure to include your units!

Example: 200 miles/2 hours = 100 miles/1 hour

- To find the UNIT PRICE, divide the price by the number of units.

***Unit Price is exactly like Unit Rate, except it only deals with money!

Apples cost $0.96 for 4 apples. $/# of units = $0.96/4 = $.24/apple

**TO FIND THE BETTER BUY, FIND THE UNIT PRICE OF EACH ITEM. (HOW MUCH DOES IT COST FOR ONE ITEM?) THEN COMPARE THE PRICES of ONE item. The one that is the “Better Buy” is the smaller number or the cheapest price.

- Graphs and charts are proportional when you have a constant of proportionality. If you DO NOT have a constant, then they are NOT PROPORTIONAL!

K = constant; y = the y-value, and x = the x-value

To find the constant of proportionality (k), use k = y/x

To write the equation of a proportional relationship in a chart/graph: y = kx

(Remember k is the constant)

In order for a group of ratios to be proportional, they must all have the same constant! I they do not, then they are NOT PROPORTIONAL!

A graph is proportional only if it does TWO THINGS:

1) the line must be perfectly straight

2) the line must start and go through the origin (0,0)

**If it does not do BOTH of these things, then the graph is not proportional!

To find the constant of proportionality from a graph (once you have determined it is a straight line that goes through the origin), find a point on the line and get the ordered pair from that point.

Example: A point is sitting on (5,8) ---that means x = 5 and y = 8

So, to find the constant of proportionality : k = y/x = 8/5 So, k = 8/5 or 1.6

Reminder: On tables, the TOP and LEFT SIDE numbers are always your x-value.

The BOTTOM and RIGHT SIDE numbers are always your y-value.