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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

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Multiplication of Fractions

» `a/b xx c/d` `= (ac)/(bd)`

» `color(deepskyblue)(2) xx color(coral)(1/4)`

→ `2` pieces

→ `1/4` of each of those pieces

→ result is count `2` in place value`1/4`

→ `= 2/4`

» `color(darkgreen)(2/3) xx color(coral)(3/4)`

→ `color(darkgreen)(2)` pieces in place value `color(darkgreen)(1/3)`

→ `color(coral)(3/4)` of each of those pieces

→ result is count `6` in place value `12`

→ `= 6/12 = 1/2`

» **Procedural Simplification**: Cancel any common factors.

→ `2/3 xx 3/4`

→ common factors `3` and `2` canceled

→ `= 1/2`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Multiplication is understood in two steps

• The place value of multiplicand is modified by the place value of multiplier.

• The given number of multiplicand is multiplied by the given number of multiplier.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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Fractions are part of whole. Multiplication is repeated addition. In this page, Multiplication of two fractions is explained.

Starting on learning "Multiplication of fractions". ;; Fractions are part of whole. Multiplication is repeated addition. In this page, Multiplication of two fractions is explained.

Multiplication of integers or whole numbers: `4 xx 3 = 12`

• `4` is the multiplicand

• `3` is the multiplier

• `12` is the product

Multiplication is repeating the multiplicand the multiplier times -- to get the product.

`4` repeated `3` times =

`4+4+4 = 12`

Multiplication by a fraction : Consider `1 xx 1/4`

Multiplicand `1` is multiplied by a multiplier `1/4`.

The multiplication process is illustrated in the next page.

The multiplication `1 xx 1/4` is illustrated. The multiplicand is divided into `4` parts (which is the place value of the multiplier) and product is calculated by selecting `1` part (which is the numerator of the multiplier). What is the result as illustrated in the figure?

- `1/2`
- `1/4`

The answer is '`1/4`'

Multiplication by a fraction : Consider `2 xx 1/4`

Multiplicand `2` is multiplied by a multiplier `1/4`.

The multiplication process is illustrated in the next page.

The multiplication `2 xx 1/4` is illustrated. The multiplicand is divided into `4` parts (which is the place value of the multiplier) and product is calculated by selecting `1` part from each (which is the numerator of the multiplier). What is the result as illustrated in the figure?

- `2/8`
- `2/4`

The answer is '`2/4`'.

The answer is not `2/8` as the value of one piece with respect to a whole is `1/4` and `2` pieces are taken. That is, `2 text( pieces of ) 1/4 = 2/4`.

Multiplication by a fraction : Consider `1 xx 3/4`

Multiplicand `1` is multiplied by a multiplier `3/4`.

The multiplication process is illustrated in the next page.

The multiplication `1 xx 3/4` is illustrated. The multiplicand is divided into `4` parts (which is the place value of the multiplier) and product is found by selecting `3` parts (which is the numerator of the multiplier). What is the product as illustrated in the figure?

- `3/4`
- `1/4`

The answer is '`3/4`'.

The product is `3` pieces in the place value `1/4` which is `3/4`.

Multiplication by a fraction : consider `2/3 xx 1/4`

Multiplicand `2/3` is multiplied by a multiplier `1/4`.

The multiplication process is illustrated in the next page.

The multiplication `2/3 xx 1/4` is illustrated. Each part of multiplicand is divided into `4` parts (which is the place value of the multiplier) and product is found by selecting `1` part (which is the numerator of the multiplier) from each. What is the product as illustrated in the figure?

- `2/12`
- `2/8`

The answer is '`2/12`'.

The product is `2` pieces in the place value `1/12` which is `2/12`.

`2/12` can be simplified to `1/6`.

Multiplication by a fraction : Consider `2/3 xx 3/4`

Multiplicand `2/3` is multiplied by a multiplier `3/4`.

The multiplication process is illustrated in the next page.

The multiplication `2/3 xx 3/4` is illustrated. What is the product as illustrated in the figure? The each part of multiplicand is divided into `4` parts (which is the place value of the multiplier) and product is found by selecting `3` parts (which is the numerator of the multiplier) from each. What is the product as illustrated in the figure?

- `6/8`
- `6/12`

The answer is '`6/12`'.

The product is `6` pieces in the place value `1/12` which is `6/12`.

`6/12` can be simplified to `1/2`.

Having understood the first principles of multiplication of fractions, the procedural simplification for the same is :

• Numerators of multiplicand and multiplier are multiplied to numerator of product.

• Denominators of multiplicand and multiplier are multiplied to denominator of product.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Multiplication of Fractions: ** For two fractions multiplicand `p/q` and the multiplier `l/m`

Every `1/q` part of multiplicand is split into `m` pieces making it `1/(q xx m)` as the modified place value

) From each of `p` parts of multiplicand `l` parts make the product making `p xx l` parts

`p xx l` parts in `1/(q xx m)` place value gives the result `(p xx l)/(q xx m)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Multiply `14/18 xx 3/4`.

- `7/12`
- `13/18`

The answer is '`7/12`'

*your progress details*

Progress

*About you*

Progress

Multiplication of integers or whole numbers : 4 times 3 = 12 ;; 4 is the multiplicand;; 3 is the multiplier ;; 12 is the product. ;; Multiplication is repeating the multiplicand the multiplier times -- to get the product. 4 repeated 3 times equals ;; 4 +4 + 4, = 12.

Multiplication by a fraction : Consider 1 multiplied 1 by 4. ;; Multiplicand 1 is multiplied by a multiplier 1 by 4. ;; The multiplication process is illustrated in the next page.

The multiplication 1 times 1 by 4 is illustrated. The multiplicand is divided into 4 parts; which is the place value of the multiplier; and product is calculated by selecting 1 part; which is the numerator of the multiplier. What is the result as illustrated in the figure?

2

1 by 2

4

1 by 4

The answer is "1 by 4"

Multiplication by a fraction : Consider 2 multiplied 1 by 4. ;; Multiplicand 2 is multiplied by a multiplier 1 by 4. ;; The multiplication process is illustrated in the next page.

The multiplication 2 times 1 by 4 is illustrated. The multiplicand is divided into 4 parts; which is the place value of the multiplier; and product is calculated by selecting 1 part from each; which is the numerator of the multiplier.

8

2 by 8

4

2 by 4

The answer is "2 by 4". The answer is not 2 by 8, as the value of one piece with respect to a whole is 1 by 4 and 2 pieces are taken. that is, 2 pieces of 1 by 4 value equals 2 by 4.

Multiplication by a fraction : consider 1 multiplied 3 by 4. Multiplicand 1 is multiplied by a multiplier 3 by 4. ;; The multiplication process is illustrated in the next page.

The multiplication 1 times 3 by 4 is illustrated. The multiplicand is divided into 4 parts; which is the place value of the multiplier; and product is found by selecting 3 parts; which is the numerator of the multiplier. ;; What is the product as illustrated in the figure?

3

3 by 4

1

1 by 4

The answer is "3 by 4". The product is 3 pieces in the place value 1 by 4 , which is 3 by 4.

Multiplication by a fraction : consider 2 by 3 times 1 by 4. Multiplicand 2 by 3 is multiplied by a multiplier 1 by 4. ;; The multiplication process is illustrated in the next page.

The multiplication 2 by 3 times 1 by 4 is illustrated. ;; Each part of multiplicand is divided into 4 parts; which is the place value of the multiplier; and product is found by selecting 1 part; which is the numerator of the multiplier; from each. What is the product as illustrated in the figure?

12

2 by 12

8

2 by 8

The answer is "2 by 12". The product is 2 pieces in the place value 1 by 12;; which is 2 by 12.;; 2 by 12 can be simplified to 1 by 6

Multiplication by a fraction : consider 2 by 3 times 3 by 4. Multiplicand 2 by 3 is multiplied by a multiplier 3 by 4. ;;The multiplication process is illustrated in the next page.

The multiplication 2 by 3 times 3 by 4 is illustrated. The each part of multiplicand is divided into 4 parts; which is the place value of the multiplier; and product is found by selecting 3 parts; which is the numerator of the multiplier; from each.

8

6 by 8

12

6 by 12

The answer is "6 by 12" The product is 6 pieces in the place value 1 by 12 which is 6 by 12. ;; 6 by 12 can be simplified to 1 by 2.

Having understood the first principles of multiplication of fractions, the procedural simplification for the same is : ;; Numerators of multiplicand and multiplier are multiplied to numerator of product. ;; Denominators of multiplicand and multiplier are multiplied to denominator of product.

Multiplication is understood in two steps ;; The place value of multiplicand is modified by the place value of multiplier. ;; The given number of multiplicand is multiplied by the given number of multiplier.

Multiplication of Fractions: For two fractions multiplicand p by q and the multiplier l by m. Every 1 by q part of multiplicand is split into m pieces making it 1 by q times m as the modified place value ;; From each of p parts of multiplicand l parts make the product, making p times l parts;; p times l parts in 1 by q times m place value gives the result p times l divided by q times m.

Multiply 14 by 18, multiplied by, 3 by 4.

7;12

7 by 12

13;18

13 by 18

The answer is "7 by 12"