Practice Inverse Quantity in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The reciprocal or multiplicative inverse of a quantity, where multiplying a number by its inverse yields one. Inverse quantities appear whenever two measurements are inversely related, so that doubling one halves the other.
More workers = less time to finish. Double the workers, halve the time.
Showing a random 20 of 50 problems.
Example 1
easyIf workers take days, do workers take more or fewer days?
Example 2
challenge varies inversely with . When , . Find when .
Example 3
medium and when . Find when .
Example 4
challengeShow that if varies inversely with , then varies directly with .
Example 5
easyWhat is the reciprocal of ?
Example 6
hardPipe A fills a tank in hours; pipe B in hours. Working together, how long to fill the tank?
Example 7
mediumThe reciprocal of added to itself: if , find .
Example 8
easyIf speed doubles for a fixed distance, what happens to travel time?
Example 9
challengeTwo workers together finish a job in hours. Alone, the first takes hours. How long does the second take alone?
Example 10
easyFind the reciprocal of .
Example 11
challengeIf , by what factor must change to make five times larger?
Example 12
mediumIf is multiplied by in the relation , by what factor does change?
Example 13
mediumA tank fills in hours with pumps. How long with pumps (same rate each)?
Example 14
mediumDivide using multiplication by the reciprocal.
Example 15
mediumAt constant temperature, . If is reduced from L to L, what is the new pressure?
Example 16
medium identical machines complete a batch in hours. How long would machines take?
Example 17
hardAt constant temperature a gas obeys . Sketch (describe) the graph of vs and state its shape.
Example 18
easyWhat is the reciprocal of ?
Example 19
hardA reciprocal pair: a number plus its reciprocal equals . Find both possible values of the number.
Example 20
easyIf (inverse variation) and , find .