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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsCommercial ArithmeticsComparing Quantities

Ratio & Fraction Differences

Ratio and Fraction are two methods to specifying relative magnitude of quantities. Eg: `12` and `24` are in `1:2` ratio

OR `12` is `1/2` of `24`.

Understanding the differences in these two representation is explained.



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What is a ratio?

  • comparison of two quantities given as magnitude of one to magnitude of another
  • comparison of two quantities given as magnitude of one to magnitude of another
  • specification of one quantity that is part of a whole, given as magnitude of the part to magnitude of whole

The answer is "comparison of two quantities given as magnitude of one to magnitude of another"

What is a fraction?

  • comparison of two quantities given as magnitude of one to magnitude of another
  • specification of one quantity that is part of a whole given as magnitude of the part to magnitude of whole
  • fraction can be used both for comparing two quantities and also for specifying one quantity
  • fraction can be used both for comparing two quantities and also for specifying one quantity

The answer is "fraction can be used both for comparing two quantities and specifying one quantity"

Consider `4` apples and `6` oranges. And there are pieces of a cake. The cake was cut into `6` pieces and only `4` pieces are remaining.

 •  ratio of apples to oranges is `4:6` which is equivalently `2:3`

 •  number of apples is `4/6` fraction of number of oranges. which is equivalently `2/3`.

 •  number of cakes is `4/6` fraction of the whole, which is equivalently `2/3`.

Note that the fraction can be used both for comparing quantities and to specify a quantity.

Consider `4` apples and `6` oranges.

 •  ratio of apples to oranges is `4:6` which is equivalently `2:3`

 •  ratio of apples to fruits is `4:10` which is equivalently `2:5`

 •  number of apples is `4/6` fraction of number of oranges. which is equivalently `2/3`.

 •  fraction of apples in the fruit basket is `4/10` which is equivalently `2/5`.

Students should always pay attention to the context under which ratio or fraction is given.

Consider: Distance-to-school is `3`km in the east and distance-to-hospital is `9`km in the north.

 •  ratio of distance-to-school to distance-to-hospital is `3:9` which is equivalently `1:3`

 •  distance-to-school is `3/9` fraction of distance to hospital.

 •  fraction of distance to school to the total distance does not make sense. The distances cannot be added unless specifically required in the given problem.

For example, consider that a person traveled to school first and returned to home. And then he traveled to hospital and returned home. In this case, the total distance traveled can be worked out.

Ratio Vs Fraction : comparison of two quantities given as magnitude of one to magnitude of another is ratio.

Fractions are also used to represent comparison of two quantities given as magnitude of one over magnitude of another.

Fractions specify one quantity that is part of a whole given as magnitude of the part to magnitude of whole.

Solved Exercise Problem:

Convert `2:3` into a fraction.

  • `2//3`
  • `2//3`
  • ratio cannot be converted into a fraction

The answer is "`2//3`"

Solved Exercise Problem:

convert `11/14` into a ratio

  • `11:14`
  • `11:14`
  • it cannot be converted

The answer is "`11:14`".

The fraction `11/14` can mean two possibilities

 •  Two quantities are in `11:14` ratio

 •  one quantity is specified as `11/14` part of the whole.

In the context of ratio, the fraction is taken to be in the form of comparison of two quantities, unless specified in the question.

Solved Exercise Problem:

The number of apples are `2/3` of the number of oranges. What is the ratio of apples to oranges?

  • `2:3`
  • `2:3`
  • `2:1`

The answer is "`2:3`". The given fraction specifies the comparison of apples to oranges.

Number of apples is `2/3` of the number of oranges. Which means, for every orange, there are `2/3` apples.
So the ratio of apples to oranges is `2/3 : 1`, which is equivalently `2:3`

Solved Exercise Problem:

A basket has `2/3` apples and rest oranges. What is the ratio of apples to oranges?

  • `2:3`
  • `2:1`
  • `2:1`

The answer is "`2:1`". The given fraction specifies the quantity of apples.

Quantity of apples `2/3`
Quantity of oranges `1 - 2/3 = 1/3`
So the ratio of apples to oranges is `2/3 : 1/3` which is equivalently `2:1`

                            
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