Proportional Relationships
A proportion states that two ratios are equal. Cross-multiply to solve!
Core Concept
A PROPORTION is an equation showing two equal ratios: 2/3 = 8/12. To solve for unknowns, CROSS-MULTIPLY: if 3/4 = x/20, then 3x20 = 4x, so 60=4x, x=15. Proportional relationships have a constant rate: if y=3x, then y is always 3 times x. On a graph, proportional relationships make a straight line through the origin. The CONSTANT OF PROPORTIONALITY is the unit rate (k in y=kx).
Examples
2/5 = x/15: cross multiply 2x15=30, 5x=30, x=6. If 3 shirts cost $45, 7 shirts cost $105 (k=$15).
If 2/3 = x/12, what is x?
Going Deeper
Proportions solve real problems: scaling recipes, map distances, similar figures.
Scale Drawing
Measure your room. Create a scale drawing where 1 cm = 1 foot. Use proportions to convert.
Proportion Relay
Teams race to solve proportion problems. Each correct answer unlocks the next. First team done wins!
In y=5x, what is the constant of proportionality?
Proportional graphs always pass through?
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