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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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,

trek,

jogger,

exercise.

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

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

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

Voice

Voice

Home

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)`

*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

You are learning the free content, however do shake hands with a coffee to show appreciation.

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

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`. 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`. 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. 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?

- 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?

- Practice Saying the Answer

The answer is 'ascending order'.

What does the word 'descending' mean?

- 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?

- 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?

- `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 ""