An Introduction to Ratios and Rates

1
An Introduction to Ratios and Rates

• Today you will learn to
• write ratios as fractions in simplest form.
• determine unit rates and unit prices.
• M07.A-R.1.1.6
• Use proportional relationships to solve
  multi-step ratio and percent problems.
• M07.A-R.1.1.1
• Compute unit rates associated with ratios of
  fractions, including ratios of lengths, areas,
  and other quantities measured in like or
  different units.

2
What are Ratios?

• A ratio is a comparison of two quantities by
  division. You can write a ratio three ways
• 5 to 24 524 5/24
• Two quantities that name the same amount are
  equivalent ratios. For example, 524 and 1048
  are equal ratios.
• One way that you can determine if two ratios are
  equal through division. For example, 5 24
  0.21 and 10 48 0.21.
• Another way to determine if two ratios are equal
  is write them as fractions, and simplify them
  (use a calculator).

3
Ratios

• Click on the link below to Khan Academy...
• Introduction to Ratios
• While there, watch the following videos
• Introduction to Ratios
• Ratios as Fractions in Simplest Form
• Simplifying Rates and Ratios
• Complete the activity Expressing ratios as
  fractions
• Watch the next video
• Describing ratios exercise
• Complete the activity Describing ratios

4
What are Rates?

• A rate is a ratio of two measurements having
  different kinds of units. For example, suppose
  you ran a marathon in two hours. Your running
  rate would be 26.2 miles/2 hours.
• The rate for one unit of a given quantity is
  the unit rate. To find the unit rate, divide the
  first quantity by the second quantity. For
  example, a running rate of 26.2 miles/2 hours,
  the unit rate is 13.1 miles per hour.

5
How do I determine Unit Rates?

• To determine unit rates, divide the first term
  in the rate by the second term.
• You can express speed as a unit rate involving a
  unit of time. However, there are times when the
  time is given in more than one unit, such as
  minutes and seconds. Convert the time to a
  single unit, such as seconds, to find the speed.

6
How do I determine Unit Prices?

• A unit rate that gives the cost per unit is a
  unit price. To find the unit price, divide the
  total price of the item by the size of the item
  or the number of units of the item.

7
Unit Rates and Unit Prices

• Watch the following videos (4) and complete the
  exercises (2) from the Khan Academy on Unit rates
  and Unit Prices.
• Finding Unit Rates and Unit Prices