Pre-Requisires
Test & Enrich
Direct and Inverse Proportions | Speed Notes
Notes For Quick Recap
Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down to continue …)
Study Tools
Audio, Visual & Digital Content
Direct Variation or Direct Proportion:
Extra:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains
constant. That is if
=k [k is a positive number, then x and y are said to vary directly.
In such a case if y1, y2 are the values of y corresponding to the values x1, x of x
respectively then = .
If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.
Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are
written as
. Symbol
stands for ‘is proportion to’.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy
= k, then x and y are said to vary inversely. In this case if y1, y2 are the values of y
corresponding to the values x1, x2 of x respectively then
x1, Y1 = x2, y2 or
=
When two quantities x and y are in inverse proportion (or vary inversely), they are
written as x
. Example: If the number of workers increases, time taken to finish
the job decreases. Or If the speed will increase the time required to cover a given distance decreases.
1. Distance and Time
| Time (hours) | Distance (km) | Formula |
|---|---|---|
| 0 | 0 | |
| 1 | 60 | |
| 2 | 120 | |
| 3 | 180 |
2. Cost of Groceries
| Number of Apples | Total Cost ($) | Formula |
|---|---|---|
| 0 | 0 | |
| 1 | 2 | |
| 2 | 4 | |
| 5 | 10 |
3. Cooking Ingredients
| Number of Servings | Amount of Flour (cups) | Formula |
|---|---|---|
| 0 | 0 | |
| 4 | 2 | |
| 6 | 3 | |
| 8 | 4 |
4. Speed and Fuel Consumption
| Distance (km) | Fuel Consumed (liters) | Formula |
|---|---|---|
| 0 | 0 | |
| 15 | 1 | |
| 30 | 2 | |
| 45 | 3 |
5. Salary and Hours Worked
| Hours Worked | Total Earnings ($) | Formula |
|---|---|---|
| 0 | 0 | |
| 1 | 15 | |
| 5 | 75 | |
| 10 | 150 |
Dig Deep
Topic Level Resources
Sub – Topics
Select A Topic
Topic:
Chapters Index
Select Another Chapter
[display-posts category=”CBSE 8 – Mathematics – Study – Premium” posts_per_page=”25″]
Assessments
Personalised Assessments
