Ratios with More Than Two Quantities
Ratios with More Than Two Quantities extends ratio notation to three or more quantities written as a:b:c, where the order of the numbers must match the order of the quantities described. Covered in Illustrative Mathematics Grade 6, Unit 2: Introducing Ratios, this concept helps Grade 6 students describe multi-part relationships — like mixing three colors of paint or dividing money among three people — and scale them proportionally. Students learn to interpret, write, and use three-part ratios in real-world contexts.
Key Concepts
A ratio can be used to compare three or more quantities. The relationship is written in the form $a:b:c$, where the order of the numbers matches the order of the quantities being compared.
Common Questions
What is a three-part ratio?
A three-part ratio compares three quantities in the form a:b:c. The order matters — the numbers must match the quantities in the same order they are listed.
How do you use a three-part ratio to find actual amounts?
Identify the total parts (a + b + c) and the total quantity. Find the value of one part by dividing the total by the number of parts, then multiply each ratio number by that value.
Can a three-part ratio be simplified?
Yes. Divide all three numbers by their GCF (greatest common factor) to write the ratio in simplest form.
Where are ratios with more than two quantities in Illustrative Mathematics Grade 6?
This topic is in Unit 2: Introducing Ratios of Illustrative Mathematics Grade 6.
How is a three-part ratio different from two fractions?
A three-part ratio a:b:c compares all three quantities simultaneously, while separate fractions compare pairs of quantities. The three-part ratio captures the complete relationship.