Ratio Notation and Relationships
Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
What a learner can do afterwards
- Explain why 'for every 2 red beads there are 5 blue beads' can be written as 2:5 or as 2/5 of the blue count
- Identify the multiplicative relationship in a table of values (e.g. y is always 3 times x)
- Connect the ratio a:b to the fraction a/b and to the linear function y = (a/b)x
The lesson
You already write ratios like 2:5 and turn one amount into a fraction of another. Now connect the two ideas: a ratio doesn't just compare two amounts once, it tells you the fixed multiplier between them every time. That fixed multiplier is exactly what a fraction shows, and exactly what a straight line through zero shows on a graph.
Look at a table of x and y values: when x is 1, y is 3. When x is 2, y is 6. When x is 3, y is 9. Every single time, y is 3 times x. That constant relationship is the ratio y:x = 3:1, the fraction 3/1, and the line y = 3x passing through (0, 0).
To turn a ratio a:b into a graph rule, just divide: a/b is the number you multiply x by to get y. That number is also the line's steepness.
A ratio a:b is the same as the fraction a/b, and it draws a straight line through zero with that fraction as its steepness.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.