Submarine maths quest: ratio

Quick answer

You can use ratios to compare quantities and solve problems in real life, like mixing ingredients for submarine food or scaling drawings for underwater maps.

Learning outcome

By the end of this page, you will be able to use ratios to compare quantities and solve simple problems using real-life examples like submarine food recipes and underwater maps.

• You can identify what a ratio shows about how two amounts relate
• You can use ratios to share or mix things fairly
• You can solve simple problems using ratios in everyday situations
• You can create simple ratio problems with real-life examples

Why this matters

Ratios help you understand how things compare and how to share or mix them fairly. In a submarine, ratios are important for making sure the food tastes right, the maps are drawn to scale, and everything works together properly. You use ratios every day when you share snacks, follow recipes, or help with cooking!

How it works

Ratios show how two or more amounts relate to each other. You can write them as:

• 3 to 5 (written as 3:5)
• 3:5
• 3 over 5 (as a fraction 3/5)

When you have a ratio like 3:5, it means for every 3 of one thing, there are 5 of another. For example, if you mix 3 cups of flour with 5 cups of sugar, the ratio is 3:5.

Let's say you want to make a submarine snack that needs 2 parts of fish to 3 parts of vegetables. This is a ratio of 2:3. If you use 4 fish pieces, you need 6 vegetable pieces to keep the same taste.

Examples you can see

Let's go on a submarine adventure to understand ratios!

Submarine Food Mixing

Imagine you're a submarine chef making a special fish and chips recipe. The recipe says you need 2 cups of fish to 3 cups of chips.

This means the ratio of fish to chips is 2:3. If you want to make more food, you need to keep this same ratio. For example, if you use 4 cups of fish, you need 6 cups of chips.

Underwater Map Scaling

When drawing a map of the ocean floor, you might use a scale of 1:100. This means 1 cm on the map represents 100 cm in real life.

If a submarine is 200 cm long, on your map it would be 2 cm long.

Let's look at a simple example:

• Real submarine length: 200 cm
• Map scale: 1:100
• Map length: 200 ÷ 100 = 2 cm

Submarine Crew Sharing

There are 12 crew members on the submarine. The captain wants to divide 30 sandwiches between the crew so everyone gets the same amount.

So the ratio of sandwiches to crew members is 30:12.

But we can simplify this ratio to make it easier to understand:

• 30 ÷ 6 = 5
• 12 ÷ 6 = 2

So the simplified ratio is 5:2, which means 5 sandwiches for every 2 crew members.

Try it as a mini adventure

Let's go on a submarine quest to find the secret underwater treasure map!

Step 1: Find the Depth Ratio

You need to dive to a depth where the pressure is 15:5 times the surface pressure. Simplify this ratio.

Step 2: Mix the Secret Recipe

The treasure map is hidden in a special underwater soup. The recipe says 3 parts of seaweed to 7 parts of salt. If you have 9 cups of seaweed, how many cups of salt do you need?

Step 3: Scale the Map

Your treasure map is drawn at a scale of 1:50. If the real distance between two underwater caves is 250 meters, how far apart are they on your map?

Step 4: Share the Treasure

You found 48 gold coins. You want to share them between 8 crew members. What is the ratio of coins to crew members?

Step 5: Complete the Mission

After solving all the ratios, you discover that the treasure is hidden where the ratio of red shells to blue shells is 4:6. Simplify this ratio to find the exact location.

Common mistakes

• Mistake: Thinking 15:5 means 15 is bigger than 5, so it's 15 ÷ 5 = 3
  Why it happens: Confusing the ratio with a division problem
  Fix: Remember ratios show the relationship between amounts, not just division
• Mistake: Forgetting to simplify ratios
  Why it happens: Not knowing that 10:15 can be simplified to 2:3
  Fix: Always look for common factors to simplify your ratios
• Mistake: Mixing up the order of a ratio
  Why it happens: Not paying attention to what each part represents
  Fix: Always check which item comes first in the problem
• Mistake: Using ratios to add amounts instead of comparing them
  Why it happens: Not understanding that ratios show relationships, not totals
  Fix: Remember ratios compare how much of one thing there is compared to another

Parent and carer guide

Help your child understand ratios by using everyday examples:

• When cooking, ask them to help measure ingredients using ratios (e.g., 2 cups of flour to 1 cup of sugar)
• Use maps to show how ratios work with scales (e.g., 1 cm on map = 100 m in real life)
• Share snacks using ratios (e.g., 3 cookies for every 2 crackers)
• Play games involving ratios (like sharing toys or cards fairly)
• Ask questions like: "If we have 6 apples and 9 oranges, what's the ratio?"
• Remember to praise effort, not just correct answers
• Use visual aids like drawings or objects to show the ratios
• Encourage them to explain their thinking to you
• Keep practice fun and low-pressure
• Watch for confusion about simplifying ratios

Practice questions

1. What is the ratio of 12 to 18? Simplify it.
   Answer: 2:3
2. If you have 8 fish and 12 vegetables, what is the ratio of fish to vegetables?
   Answer: 2:3
3. A map uses a scale of 1:200. If a submarine is 400 cm long, how long is it on the map?
   Answer: 2 cm
4. You have 15 sandwiches and 5 crew members. What is the ratio of sandwiches to crew members?
   Answer: 3:1
5. If 5 cups of flour are mixed with 10 cups of water, what is the ratio of flour to water?
   Answer: 1:2
6. A treasure map shows 15 red shells to 25 blue shells. Simplify this ratio.
   Answer: 3:5
7. If you use 3 cups of salt with 7 cups of seaweed, what is the ratio?
   Answer: 3:7
8. How many times does 6 go into 18?
   Answer: 3 times
9. If you have 20 coins and 4 crew members, what is the ratio?
   Answer: 5:1
10. A submarine is 300 cm long. On a map with scale 1:100, how long is it?
    Answer: 3 cm

FAQ

What is a ratio?

A ratio is a way to show how two or more amounts are related to each other. For example, if you have 3 red marbles and 5 blue marbles, the ratio of red to blue is 3:5.

How do you simplify a ratio?

To simplify a ratio, find a number that divides both parts evenly. For example, 6:8 can be simplified by dividing both by 2 to get 3:4.

Why do we use ratios in real life?

Ratios help us share things fairly, mix ingredients correctly, and understand how things relate to each other in maps, recipes, and many other situations.

Can ratios be more than two numbers?

Yes! Ratios can compare three or more amounts. For example, if you mix 2 cups of flour, 1 cup of sugar, and 3 cups of milk, the ratio is 2:1:3.

How are ratios used in submarines?

Ratios help submarines mix food correctly, draw accurate maps, share supplies fairly, and understand how pressure and depth relate to each other.