Understand ratios and ratio language · lesson

Ratios as equal groups

💡 A ratio like 3 to 5 is one group; count how many groups you have, then scale the other amount.

A ratio of 3 to 5 means for every 3 of one thing there are 5 of the other. You can write it as 3 : 5, 3 to 5, or 3/5.

Think of the ratio as one small group. A bigger amount is just many copies of that group.

To find a missing amount, first find how many groups there are. Then multiply the other part of the ratio by that number.

🧠 Let's work it out

A team has 2 coaches for every 11 players. There are 44 players. How many coaches?

What do you think comes next?

💡 Dividing both parts of a ratio by the same number gives an equal ratio, and the smallest whole numbers give simplest form.

You can divide both parts of a ratio by the same number. The ratio stays the same. Only the group size changes.

A ratio is in simplest form when no number bigger than 1 divides both parts. To get there fast, divide by the greatest common factor.

The order matters. "Girls to boys" puts girls first, or on top of the fraction.

🧠 Let's work it out

A club has 15 cats and 35 dogs in its photos. Write cats to dogs in simplest form.

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💡 When a ratio compares two parts, add the parts to get the size of one whole group.

Some ratios compare two parts, like red beads to blue beads. The total is both parts together.

If a problem gives the total, add the ratio parts first. That tells you how many things are in one group.

A part-to-whole ratio puts one part on top and the total on the bottom.

🧠 Let's work it out

Red beads and blue beads are in the ratio 3 : 4. There are 28 beads in all. How many are red?

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💡 If you know how far apart two amounts are, find how far apart one group is, then count groups.

Some problems tell you the difference between the two amounts, not the amounts. Each group adds the same difference.

Find the difference inside one group. Divide the full difference by it to get the number of groups.

For leftovers, use up all of one thing first. Then see how much of the other thing you needed. Subtract that from what you have to get the leftover.

🧠 Let's work it out

Kim and Lu share cards in the ratio 3 : 7. Lu gets 20 more cards than Kim. How many does Kim get?

What do you think comes next?