Reciprocal Constants of Proportionality
Reciprocal Constants of Proportionality is a Grade 7 math skill in Illustrative Mathematics, Chapter 2: Introducing Proportional Relationships. Students discover that if y=kx models a relationship, then x=(1/k)y, and understand that the constant of proportionality in one direction is the reciprocal of the constant in the other direction.
Key Concepts
If a proportional relationship between two quantities, $x$ and $y$, has a constant of proportionality $k$ such that $y = kx$, then the relationship can also be expressed as $x = (\frac{1}{k})y$. The two constants of proportionality, $k$ and $\frac{1}{k}$, are reciprocals.
Common Questions
What are reciprocal constants of proportionality?
If y equals kx with constant k, then rearranging gives x equals (1/k) times y. The constant going one direction (k) is the reciprocal of the constant going the other direction (1/k).
How do you find the reciprocal constant of proportionality?
If the constant from x to y is k, the constant from y to x is 1 divided by k. For example, if y equals 3x, then x equals (1/3)y.
What is an example of reciprocal constants of proportionality?
If a car travels at 60 miles per hour, then miles equals 60 times hours. Rearranging: hours equals (1/60) times miles. The constants 60 and 1/60 are reciprocals.
Why are the two constants reciprocals of each other?
Because y equals kx and x equals y/k. Dividing by k is the same as multiplying by 1/k, so the proportionality constant in each direction is the reciprocal of the other.
What chapter covers reciprocal constants of proportionality in Illustrative Mathematics Grade 7?
Reciprocal constants of proportionality are covered in Chapter 2: Introducing Proportional Relationships in Illustrative Mathematics Grade 7.