Ratios & Rates

What is a ratio? A ratio is the comparison between two quantities Have we studied anything that would be considered a ratio? Fractions are ratios. Fractions compare two quantities. That's why numbers that can be written in fraction form are called rational numbers

Ratios & Rates What do ratios look like? A ratio can be written in the following forms…Fraction "to" Colon "out of"

Ratios & Rates What is a rate? A rate is a ratio that compares quantities of different types of measure. What are different types of measure? Different types of measure are measures that measure different types of things.

Ratios & Rates Examples of Different Types of Measures feet and minutes are different types of measures. ft measures a distance or length min measures time How many feet are in a minute? How many minutes are in a foot? We can't answer these questions, the units are not the same type of measurement.

Ratios & Rates Examples of the Same Type of Measurement gallons and quarts are the same type of measurement. gal measure a liquid capacity qt measure a liquid capacity How many gallons in a quart? How many qt in a gal? We can answer these questions, the units can be converted to each other. Though, its probably easiest to convert quarts to gallons.

Ratios & Rates Are the following pairs of units the same type or different types? ft & mi $ & cents gal & mi $ & h cm & min & lb yd & s Abbreviation Key ft: feet yd: yard mi: mile in: inch cm: centimeter m: meter gal: gallon lb: pound h: hour min: minute s: second $: dollar The circled pairs are the same type of units.

Ratios & Rates What do rates look like? A rate can be written in the following forms…Fraction "per"

Ratios & Rates Which are rates, which are just ratios? The circled pairs are the rates.

Ratios & Rates Simplifying Ratios & Rates Many times we need to simplify ratios and rates. How do you simplify a ratio? Since a ratio can be written as a fraction, and since we reduce to simplify a fraction, we will also reduce in order to simplify a ratio.

Ratios & Rates Simplifying Ratios 1. Write the ratio as a fraction 2. Reduce

Ratios & Rates Simplifying Ratios 1. Write the ratio as a fraction 2. Reduce

Ratios & Rates Simplifying Ratios 1. Write the ratio as a fraction 2. Reduce Sometimes, we make sure the units are the same!

Ratios & Rates Simplifying Ratios & Rates How do you simplify a rate? Since a rate is a ratio, you can simplify a rate as it was a ratio – reduce.

Ratios & Rates Simplifying Rates 1. Write the rate as a fraction 2. Reduce

Ratios & Rates Simplifying Ratios & Rates How do you simplify a rate? Since a rate is a ratio, you can simplify a rate as it was a ratio – reduce. A rate can also be simplified by writing it as a unit rate.

Ratios & Rates What is a unit rate? A unit rate is a rate that is written in terms of 1 unit. A unit rate is a rate whose denominator is 1 unit. The following are unit rates…

Ratios & Rates How do you write a rate as a unit rate? Writing a unit rate is quite simple. Remember, a fraction is a division problem. To get 1 in the denominator, we simply divide. Divide the numerator by the denominator.

Ratios & Rates Writing a unit rate 1. Write the ratio as a fraction 2. Divide numerator by denominator

Ratios & Rates Writing a unit rate 1. Write the ratio as a fraction 2. Divide numerator by denominator

Ratios & Rates Writing a unit rate 1. Write the ratio as a fraction 2. Divide numerator by denominator