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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.

User Guide

Welcome to nubtrek.

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.

User Guide

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.

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.

User Guide

trek is the step by step exploration of the concept.

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.

User Guide

jogger provides the complete mathematical definition of the concepts.

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.

User Guide

exercise provides practice problems to become fluent in the concepts.

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.

summary of this topic

### Arithmetics with Fractions

Voice

Voice

Home

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 value1/4
→  = 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

### Multiplication of fractions

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.

Keep tapping on the content to continue learning.
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'

Progress

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"

we are not perfect yet...