The idea
A ratio compares amounts in a stated order. A blue-to-gold ratio of two to three means two equal parts blue for every three equal parts gold. These are five parts altogether, rather than five individual objects.
Before you begin: Multiply, divide and recognise equal parts.
Thirty counters are shared into blue and gold groups in the ratio 2 to 3. Find each group.
Add the parts of the ratio to find how many equal parts make the whole total.
Divide the thirty counters among those five equal parts.
Blue gets two parts and gold gets three parts. Check that the amounts add back to thirty.
The total is right, and dividing both amounts by six recovers the original ratio.
A mistake to avoid
The second ratio number is not the total number of parts. For 2 to 3, blue is two fifths of the total, not two thirds.
Your turn.
Share forty counters in the given blue-to-gold ratio.
Show the solution
There are eight equal parts, each containing five counters. Keep blue and gold in the stated order.