Math for Life: ratios and statistics

Ratios and rates

In simple words

A ratio compares two amounts, like 2 scoops of juice powder for every 3 cups of water. A rate is a ratio with different units, like kilometres per hour.

Key facts

A ratio compares amounts. 12 girls to 18 boys is written 12 : 18.
Simplify a ratio by dividing both numbers by the biggest number that goes into both (like a fraction). 12 : 18 = 2 : 3.
Part to part compares groups (girls : boys = 2 : 3). Part to whole compares a group to everything (girls : class = 12 : 30 = 2 : 5). Part to whole can be written as a fraction or percent: 12 / 30 = 0.40 = 40%.
A rate compares different units: 240 km in 3 hours. A unit rate has 1 in the bottom: 240 / 3 = 80 km per hour.
Order matters. 2 : 3 is not the same as 3 : 2.

Example

Class of 30: 12 girls and 18 boys. Ratio girls : boys = 12 : 18 = 2 : 3. Girls are 12 / 30 = 40%, boys are 18 / 30 = 60%.
A tray of 12 eggs costs $5.40. Unit rate: 5.40 / 12 = $0.45 per egg.

Step by step

Pick a group you know (a class, a team, a family, a shopping basket).
Count two parts and write them as a ratio, with the order you chose first.
Simplify by dividing both numbers by the biggest number that goes into both.
Add the parts to get the whole, then write part : whole as a fraction.
Turn the fraction into a percent: divide top by bottom, then multiply by 100.
For a rate, divide the top amount by the bottom amount to get a unit rate (for example km per hour).
Check: the two percents add to 100, and the simplified ratio times the same number gives the original numbers back.

Watch on YouTube

Introduction to ratiosKhan Academy · YouTube · youtube.com

Solving unit rates problemKhan Academy · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01Ratios and rates

LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:00

Voice

Read the video script

[Screen: 12 girls and 18 boys] "Twelve girls, eighteen boys. The ratio is twelve to eighteen."
[Text on screen: 12 : 18 = 2 : 3] "Divide both by six. Two to three."
[Text on screen: 12 / 30 = 40%] "Girls out of the whole class of thirty is forty percent."
[Text on screen: 240 km / 3 h = 80 km/h] "A rate has different units. Two hundred forty kilometres in three hours is eighty kilometres an hour."

Try it now

Choose a group of 20 to 40 things (your phone apps, a team, a pantry). Write one part-to-part ratio, simplify it, and write one part-to-whole percent. Then find one unit rate from a real price or trip.

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Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

I'm learning "Math for Life: ratios and statistics" on The Future Market. Lesson 1: "Ratios and rates".

What the lesson teaches:
- A ratio compares amounts. 12 girls to 18 boys is written 12 : 18.
- Simplify a ratio by dividing both numbers by the biggest number that goes into both (like a fraction). 12 : 18 = 2 : 3.
- Part to part compares groups (girls : boys = 2 : 3). Part to whole compares a group to everything (girls : class = 12 : 30 = 2 : 5). Part to whole can be written as a fraction or percent: 12 / 30 = 0.40 = 40%.
- A rate compares different units: 240 km in 3 hours. A unit rate has 1 in the bottom: 240 / 3 = 80 km per hour.
- Order matters. 2 : 3 is not the same as 3 : 2.

The exercise I'm working on:
Choose a group of 20 to 40 things (your phone apps, a team, a pantry). Write one part-to-part ratio, simplify it, and write one part-to-whole percent. Then find one unit rate from a real price or trip. ---

I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.

I'm a parent helping my child (about 8 years old) with a lesson called "Ratios and rates" from the course "Math for Life: ratios and statistics".

Here's what the lesson says:
A ratio compares two amounts, like 2 scoops of juice powder for every 3 cups of water. A rate is a ratio with different units, like kilometres per hour.

The activity:
Choose a group of 20 to 40 things (your phone apps, a team, a pantry). Write one part-to-part ratio, simplify it, and write one part-to-whole percent. Then find one unit rate from a real price or trip. ---

Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words.
Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.

Open Claude

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