# Ratios, rates, & percentages

Contents

Ratios, rates, and percentages are some of the most useful math concepts in real life (and what is REAL life anyway, huh?). From baking recipes to sports, these concepts wiggle their way into our lives on a daily basis.

## Intro to ratios

Ratios show up everywhere in life—sports, finance, medicine, cooking, you name it! In this tutorial, we learn what ratios are and how to use them.

Intro to ratios

Learn how to find the ratio between two things. In this video, we find the ratio of apples to oranges.

Intro to ratios

Learn how to find the ratio between two things given a diagram.

Ratios as fractions

How are fractions and ratios the same? How are they different? Is 2:5 the same as 2/5?

Basic ratios

Choose the ratio that goes with a picture of two quantities like apples and bananas.

Ratio tables

Learn how to fill out tables of equivalent ratios.

Ratio tables

Practice filling out tables of equivalent ratios.

## Ratio word problems

Practice solving ratio word problems like, "If 60 cherries go in 3 pies, how many cherries go in 9 pies?"

Ratio word problem: centimeters to kilometers

Sal uses ratios to figure out how far apart two cities should be on a map.

Ratio word problems

Practice solving ratio word problems like, "If Ben reads 10 pages in 15 minutes, how long does it take him to read 40 pages?"

Ratio word problem: boys to girls

Sal solves a tricky ratio word problem.

## Intro to rates

Learn about a special type of ratio called a rate. A rate is the ratio of two measurements that have different units such as 10 kilometers per hour or 12 hot dogs per minute!

Intro to rates

Sal introduces rates using examples like 35 miles per hour and 10 dollars per hour.

Solving unit rate problem

Jayda takes 3 hours to deliver newspapers on her route. What is the rate per hour at which she delivers the newspapers?

Solving unit price problem

Miranda's Maid Service charges $280 to clean 8 offices. What is the company's price for cleaning a single office?

Rate problems

Use rates to solve word problems. For example, Charlie can type 675 words in 9 minutes. How many words can Charlie type in 13 minutes?

Comparing rates example

Sal puts three fish tanks in order by volume of water per fish.

Comparing rates

Example problem: Three different stores are offering a deal on pencils. Which store has the lowest price per pencil?

## Intro to percents

Percent literally means "per cent" or "per hundred". Learn how to rewrite fractions as percents and vice versa.

The meaning of percent

Let's think about what percent really means by looking at a 10 by 10 grid.

Meaning of 109%

Percents are parts per hundred. So, how does this work for percents greater than 100% like 109%?

Converting percents to decimals & fractions example

Sal writes 18% as a decimal and as a fraction.

Converting percents & fractions

Practice writing percents as fractions and fractions as percents. For example, convert 30% to a simplified fraction.

## Percent-decimal conversions

Decimals and percents are two ways of expressing the same number. For example, 0.5 and 50% mean the exact same thing. Learn how to convert decimals to percents and vice versa.

Converting decimals to percents: 0.601

Sal converts 0.601 to a percent.

Converting decimals to percents: 1.501

Sal converts 1.501 to a percent.

Converting decimals to percents

Practice expressing a decimal like 0.546 as a percent.

Converting percents to decimals: 59.2%

Sal converts 59.2% to a decimal.

Converting percents to decimals: 113.9%

Sal converts 113.9% to a decimal.

Converting percents to decimals

Practice expressing a percent like 12.3% as a decimal.

Converting between percents, fractions, & decimals

For example, learn how 50%, 1/2, and 0.5 are all equivalent.

## Percent problems

Learn how to solve percent problems like these: What is 80% of 25? Three is what percent of four?

Finding a percent

Fractions are our friends as we use them to find a percentage. You'll also see a couple of different ways to arrive at the answer.

Percent of a whole number

There are several different ways to solve problems involving percentages, decimals, and fractions. Watch as Sal finds the percentage of a whole number.

Finding percents

Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.

## Percent word problems

Learn how to solve a variety of word problems involving percentages.

Percent word problem: 100 is what percent of 80?

This word problem is expressed simply which can be confusing to some. Take your time and focus on the what is being asked for.

Percent word problem: 78 is 15% of what number?

In this example, you working with us to find the number that is expressed as a given percentage. We'll create a simple algebraic equation to solve!

Percent word problem: guavas

We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem.

Percent word problem: recycling cans

It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division!

Percent word problem: penguins

You're given the percent in this example and asked to find the whole number represented by the percent.

Percent word problems

Practice solving word problems involving percents.