Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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.
mathsFractionsArithmetics with Fractions

### Multiplication of fractions

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

•  multiplication in first principles -- repeatedly combining a quantity and measuring the combined and

•  simplified procedure : Multiplying numerators and denominators

click on the content to continue..

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
• 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
• 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
• 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
• 2/12
• 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. 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
• 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.

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/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)

Solved Exercise Problem:

Multiply 14/18 xx 3/4.

• 7/12
• 7/12
• 13/18

The answer is '7/12'

switch to slide-show version