Class 6 Maths - ICSE
Proportion
The chapter 'Proportion' in Class 6 ICSE Mathematics builds directly upon the concepts of ratio, teaching students how to compare four quantities to see if they are in equal relation. Students learn to identify proportions, understand the properties of extremes and means, and solve word problems using the unitary method and cross-multiplication. This chapter is vital for ICSE board exams as it forms the foundational building block for advanced topics like percentage, profit and loss, speed-distance-time, and algebraic variations in higher classes. Board exams frequently test these concepts through direct numerical problems and practical real-life word problems.
Start Learning FreeKey Concepts
Meaning of Proportion
An equality of two ratios is called a proportion. If two ratios a:b and c:d are equal, we write a:b :: c:d, meaning 'a is to b as c is to d'.
Terms of a Proportion
In a proportion a:b = c:d, the first and fourth terms (a and d) are called extremes, while the second and third terms (b and c) are called means.
Product of Extremes and Means
Four numbers are in proportion if the product of the extremes equals the product of the means, which means a × d = b × c.
Continued Proportion
Three quantities a, b, and c are said to be in continued proportion if a:b = b:c, which can also be written as b squared equals a times c.
Unitary Method
A technique used to find the value of a required number of units by first finding the value of a single unit.
Important Formulas
Board Exam Info
In ICSE Class 6 Mathematics examinations, the chapter on Proportion usually carries around 5 to 8 marks. Common question types include checking whether four given numbers are in proportion, finding a missing term in a proportion, word problems based on direct proportional scaling, and finding the third proportional in continued proportion.
Frequently Asked Questions
What is the difference between ratio and proportion?
A ratio compares two quantities of the same kind using division, whereas a proportion states that two ratios are equal to each other.
How do I check if four numbers are in proportion?
Multiply the first and fourth numbers (extremes) and the second and third numbers (means). If both products are equal, the numbers are in proportion.
Does the order of numbers matter in a proportion?
Yes, the exact order matters because a:b :: c:d means that ratio a:b must equal ratio c:d, and changing the order alters the relationship.
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