Learn Class 8 Math - Direct and Inverse Variations

Inverse Proportions

If the cost of variable decreases or increases upon corresponding growth or lower within the cost of variable, then we will say that variables are in inverse proportion.

In simple words, variables or portions are proportional to every difference. If one is varied, then the alternative also adjusts using a hard and fast amount.

This belonging of variables is named proportionality, and the image used to symbolize the proportionality is "∝."

There are forms of proportionality of variables. They are:

  • Directly Proportional
  • Inversely Proportional

Relation for Inverse Proportion

Considering variables and establishes the relation for inverse proportionality among and, in which is a constant.

Direct Proportion

Direct share is a mathematical assessment among numbers in which the ratio of the 2 numbers is identical to a steady value. The share definition says that once ratios are equivalent, they're in share.

The symbol used to narrate the proportions is "∝".

Relation for Direct Proportion

Considering variables x and y, frac = k or x=ky establishes the easy relation for direct share among x and y, in which ok is a constant.

Learning Videos for 8th Grade Math - Direct and Inverse Variations

Direct and Inverse Variations Sample Questions for Class 8

Question 1

Kaila just got hired by a company in the big city, but she lives in the suburbs. To get to work everyday, she has to drive from her house to a parking garage where she then takes city transit to a stop 3 miles from her office building. From there, she takes a taxi the rest of the way. If the car drive is 3/5 of the trip and the transit ride is 1/4 of the trip, what is the total distance from her house to work?
A. 50 mi
B. 35 mi
C. 20 mi
D. 42 mi

Question 2

Each car traveling on the highway carries 2 people. Which graph describe this scenario?
A.
B.
C.
D.

Question 3

The weather was observed for 30 days. Each day was classified as sunny or cloudy, and also classified as windy or not windy. The results are shown below:Sunny - 5 days windy, 15 days not windyCloudy - 4 windy, 6 not windyWhich of the following statements is NOT supported by the data?
A. 25% of the sunny days were also windy.
B. 29% of the not windy days were also cloudy.
C. 40% of the cloudy days were also windy.
D. 50% of the windy days were also sunny.

Question 4

What is the distance between (1, 2) and (3, 8)?
A. 6.3
B. 4.5
C. 3.0
D. 6.0

Question 5

A flagpole casts a shadow 27 feet long. A person standing nearby casts a shadow 8 feet long. If the person is 6 feet tall, how tall is the flagpole?
A. 20.25 feet
B. 13.5 feet
C. 48 feet
D. 24 feet