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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.

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  think,
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To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

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User Guide    

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

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Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Arithmetics with Fractions

Arithmetics with Fractions

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Comparing Fractions


 »  convert the fractions to like fractions and compare the numerators.
   → `color(coral)(3/4) ? color(darkgreen)(2/3)`
   → `color(coral)(3/4 = 9/12)` and `color(darkgreen)(2/3 = 8/12)`
   → `color(coral)(9) > color(darkgreen)(8)` ` rArr ` `color(coral)(9/12) > color(darkgreen)(8/12)`
   → `color(coral)(3/4) > color(darkgreen)(2/3)`

Comparing Fractions

plain and simple summary

nub

plain and simple summary

nub

dummy

Two fractions can be compared by numerators after converting them into like fractions.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Comparing two fractions of different place values or denominators is explained.


Keep tapping on the content to continue learning.
Starting on learning "Comparing Fractions". ;; Comparing two fractions of different place values or denominators is explained.

Given numbers `7` and `3`, which number is larger?

  • `7`
  • `3`

The answer is '`7`'

Given numbers `4` and `6`, which number is smaller?

  • `6`
  • `4`

The answer is '`4`'

Given numbers `5` and `5`, which number is smaller?

  • One of them has to be smaller
  • The numbers are equal

The answer is 'The numbers are equal'

Given two integers or whole numbers, they can be compared as

 •  greater or larger

 •  smaller or lesser

 •  equal.

Can such comparison be done on two fractions?

Given two fractions `1/8` and `1/12`. comparing 1/8 and 1/12 The figure shows the fractions. `1/8` is shown in brown, and `1/12` is shown in purple color. Which fraction is larger?

  • `1/8`
  • `1/12`

The answer is '`1/8`'. From the picture it is clear that `1/8` is larger.

Given two fractions `3/4` and `5/8`. Which fraction is larger?

  • comparing numerators `3` and `5`, it is clear that `5/8` is larger
  • considering the place values are different, the fractions cannot be compared without converting them to like fractions

The answer is 'considering the place values are different, the fractions cannot be compared without converting them to like fractions'.

Given two fractions `3/4` and `5/8`. comparing 3/4 and 5/8 The figure shows the fractions. `3/4` is shown in brown, and `5/8` is shown in purple color. Which of the following helps to compare these two fractions?

  • Convert the fractions to like fractions having same place value
  • Convert the fractions to the simplest form

The answer is 'Convert the fractions to like fractions having same place value '.

Given two fractions `3/4` and `5/8`. The fraction `3/4` is converted to `6/8` to make them like fractions.comparing 3/4 and 5/8 Both `6/8` and `5/8` have the same place value `1/8` (ie: same denominator `8`).

In this form, the numerators can be compared and `6/8` is larger, which means its equivalent fraction `3/4` is larger than `5/8`.

Given several fractions, how to find the largest fraction among them?

  • Compare the numerators
  • compare the denominators
  • Convert the fractions to like fractions and compare

The answer is 'Convert the fractions to like fractions and compare'.

What does the word 'ascend' mean? ascending meaning

  • to go up or climb
  • to write a reason for

The answer is 'to go up or climb'.

What is the order called when fractions are ordered from the smallest to the largest?ascending meaning

  • Practice Saying the Answer

The answer is 'ascending order'.

What does the word 'descending' mean? descending meaning

  • to move down
  • to write a reason for

The answer is 'to move down'.

What is the order called when fractions are ordered from the largest to the smallest?descending meaning

  • Practice Saying the Answer

The answer is 'descending order'.

Given several fractions, how to arrange them in ascending order?

  • order them by numerators
  • order them by denominators
  • Convert the fractions to like fractions and order

The answer is 'Convert the fractions to like fractions and order'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Comparing fractions: Given two fractions `p/q` and `l/m`, convert them to the same place value as `(p xx i)/(q xx i)` and `(l xx j)/(m xx j)`, where denominators are equal. Then `p xx i` and `l xx j` can be compared to one of the following.

 •  greater than or larger than

 •  smaller than or lesser than

 •  equal



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `3/4` and `2/3`, Which fraction is smaller?comparing 3/4 and 2/3

  • `3/4`
  • `2/3`

The answer is '`2/3`'. First, convert them to like fractions

`text(LCM)(4,3) = 12`

`3/4 = 9/12`

`2/3 = 8/12`

Comparing the numerators `9` and `8`, it is concluded that `2/3` is smaller.

your progress details

Progress

About you

Progress

Given numbers 7 and 3 , which number is larger?
7
7
3
3
The answer is ' 7 '
Given numbers 4 and 6 , which number is smaller?
6
6
4
4
The answer is ' 4 '
Given numbers 5 and 5 , which number is smaller?
1;has;smaller;to
One of them has to be smaller
numbers;are;equal
The numbers are equal
The answer is 'The numbers are equal'
Given two integers or whole numbers, they can be compared as ;; greater or larger ;; smaller or lesser ;; equal. ;; Can such comparison be done on two fractions?
Given two fractions 1 by 8 and 1 by 12.;; The figure shows the fractions. 1 by 8 is shown in brown, and 1 by 12 is shown in purple color. Which fraction is larger?
eigth;eight;8
1 by 8
12;twelve
1 by 12
The answer is "1 by 8". From the picture it is clear that 1/8 is larger.
Given two fractions 3/4 and 5/8 . Which fraction is larger?
comparing;larger;clear
comparing numerators 3 and 5 , it is clear that 5/8 is larger
taking;place;value;denominator
considering the place values are different, the fractions cannot be compared without converting them to like fractions
The answer is 'considering the place values are different, the fractions cannot be compared without converting them to like fractions'.
Given two fractions 3 by 4 and 5 by 8. The figure shows the fractions. 3 by 4 is shown in brown and 5 by 8 is shown in purple color. Which of the following helps to compare these two fractions?
like;identical;place;value
Convert the fractions to like fractions having same place value
simplest;form
Convert the fractions to the simplest form
The answer is 'Convert the fractions to like fractions having same place value '.
Given two fractions 3 by 4 and 5 by 8. The fraction 3 by 4 is converted to 6 by 8 to make them like fractions. Both 6 by 8 and 5 by 8 have the same place value 1 by 8. That is same denominator 8. In this form, the numerators can be compared and 6 by 8 is larger. Which means that its equivalent fraction 3 by 4 is larger than 5 by 8.
Two fractions can be compared by numerators after converting them into like fractions.
Comparing fractions: Given two fractions p by q and l by m, convert them to the same place value as, p multiplied i by q multiplied i, and l multiplied j by m multiplied j, where denominators are equal. Then p multiplied i and l multiplied j can be compared to one of the following. ; Greater than or larger than. ; smaller than or lesser than. ; equal.
Given 3 by 4 and 2 by 3, Which fraction is smaller?
4
3 by 4
2
2 by 3
The answer is "2 by 3". First, convert them to like fractions. L C M of 4 and 3 is 12. ;; 3 by 4 = 9 by 12 ;; and 2 by 3 = 8 by 12 ;; Comparing the numerators 9 and 8, it is concluded that 2 by 3 is smaller.
Given several fractions, how to find the largest fraction among them?
numerators;numerator
Compare the numerators
denominators;denominator
compare the denominators
convert;fractions;like
Convert the fractions to like fractions and compare
The answer is 'Convert the fractions to like fractions and compare'.
What does the word 'ascend' mean?
go;up;climb
to go up or climb
write;reason
to write a reason for
The answer is 'to go up or climb'.
What is the order called when fractions are ordered from the smallest to the largest?
ascend;ascending
The answer is 'ascending order'.
What does the word 'descending' mean?
move;down
to move down
write;reason
to write a reason for
The answer is 'to move down'.
What is the order called when fractions are ordered from the largest to the smallest?
descend;descending
The answer is 'descending order'.
Given several fractions, how to arrange them in ascending order?
numerators;numerator
order them by numerators
denominators;denominator
order them by denominators
convert;fractions;like
Convert the fractions to like fractions and order
The answer is ""

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