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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

In this page, specifying ratio of two quantities is explained. For example, the number `24` is double of `12`. These two quantities are in the ratio `2` to `1`. The symbols `:` is introduced to specifying a ratio, eg `2:1`.



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Comparing two numbers `p=120` and `q=240`

Apart from saying `q` is greater, which of the following comparison helps to understand the numbers better?

  • `q` is double of `p`
  • `q` is double of `p`
  • `q` is greater than `p`

The answer is "`q` is double of `p`". If `p` is multiplied by `2`, we get `q`.
`120 xx 2 = 240`

Comparing two numbers `p=120` and `q=240`. It is noted that `q` is double of `p`

The comparison in magnitude is specified by ratio.
Ratio of `p` to `q` is `120:240`. To convey the comparison in magnitude, the common-factors are canceled.

`120:240`
(by dividing the two numbers by common factor `120`.
`rArr 1:2`

The ratio of `p` and `q` is `1:2`. This comparison is easier to understand.

Which of the following is a meaning for the word "ratio"?

  • relation between two amounts giving the number of times one quantity is to the other quantity
  • relation between two amounts giving the number of times one quantity is to the other quantity
  • a fixed amount officially distributed to each person

The answer is "relation between two amounts giving the number of times one quantity is to the other quantity".

What is the term used to refer "relation between two amounts, giving the number of times one quantity, to the other quantity"?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is "ratio".

Two numbers are in ratio `2:3`, how is the `:` pronounced?

  • is-to
  • is-to
  • colon

The answer is "is-to"

How is the given ratio `2:3` pronounced?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is "2-is-to-3".

Ratio : comparison of two quantities given as "magnitude of one" to "magnitude of another".

Consider an example `2:3` ratio. This is given as two numbers.

The first number (`2` in the example) is called the first term.

The other number (`3` in the example) is called the second term

Given two ratios `2:3` and `3:2`. Do these two ratios represent the same?

  • Yes. Both have numbers `2` and `3`
  • No. In a ratio, the order of the number is important.
  • No. In a ratio, the order of the number is important.

The answer is " In a ratio, the order of the number is important."

In a basket, there are `20` apples and `30` oranges.

The ratio of apples to oranges is `2:3`. It is not `3:2`.

The ratio of oranges to apples is `3:2`.

The ratio `2:3` is not same as `3:2`.

Solved Exercise Problem:

Time required to travel by train is `1` hour and time required to travel the same distance by car is `50`mins. What is the ratio of the two time periods?

  • `1:50`
  • `60:50` which is simplified to `6:5`
  • `60:50` which is simplified to `6:5`

The answer is "`6:5`". Note that the quantities have to be converted to the same units to workout the ratio.

Solved Exercise Problem:

Simplify the ratio `30:90`

  • `30:90`
  • `1:3`
  • `1:3`

The answer is "`1:3`". The two terms of a ratio can be divided by any common factors to simplify the ratio.

Solved Exercise Problem:

Simplify the ratio `1/6:1/12`

  • ratio with fractions cannot be simplified
  • `2:1`
  • `2:1`

The answer is "`2:1`". The two terms of a ratio can be multiplied by a number to simplify the ratio given in fractions.

Solved Exercise Problem:

In a basket, the ratio of apples to oranges is `1:3`. Which of the following is correct about the given basket?

  • For every `1` apple there are `3` oranges
  • For every `2` apples there are `6` oranges
  • For every `9` oranges there are `3` apples
  • all the above
  • all the above

The answer is "all the above".

Solved Exercise Problem:

In a basket, the ratio of apples to oranges is `1:3`. If the number of oranges in the basket is `27`, how many apples are in the basket?

  • `1`
  • `9`
  • `9`

The answer is "`9`".

In a basket, the ratio of apples to oranges is `1:3`. If the number of oranges in the basket is `27`, how many apples are in the basket?

Solution:

Number of apples in the basket `= 1/3 ` of number of oranges.
The number of oranges `= 27`

The number of apples
`= 1/3 xx 27`
`= 9`

Solved Exercise Problem:

In a basket, there are `40` apples. Divide the apples to a brother and a sister in `2:3` ratio. How much does the brother get?

  • `16` apples
  • `16` apples
  • `2` apples

The answer is "`16` apples".

The total number of apples is `40`
The ratio is `2:3`

Number of apples brother get is
`= 2/(2+3) xx 40`
`=16` apples

Solved Exercise Problem:

In a basket, there are `120` apples. Divide the apples to a brother and a sister in `1/3 : 1/5` ratio. How much does the brother get?

  • `40` apples
  • `75` apples
  • `75` apples

The answer is "`75` apples".

The total number of apples is `120`
The ratio is `1/3:1/5`

Number of apples brother get is
`= 120 xx 1/3 -: (1/3+1/5)`
`=40 -: 8/15` apples
`=40 xx 15/8` apples
`=75` apples

Solved Exercise Problem:

In a basket, there are `120` apples. Divide the apples to a brother and a sister such that they get `1/3` and `1/5` respectively. How many does the brother get?

  • `40` apples
  • `40` apples
  • `75` apples

The answer is "`40` apples". Note that this is a problem in fractions.

The total number of apples is `120`
Brother gets `1/3` of the apples

Number of apples brother get is
`= 120 xx 1/3 `
`=40` apples

                            
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