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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.continue
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



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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.multiplication 1 * 1/4

The multiplication `1 xx 1/4` is illustrated. multiplication 1 * 1/4 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.multiplication 2 * 1/4

The multiplication `2 xx 1/4` is illustrated. multiplication 2 * 1/4 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.multiplication 1 * 3/4

The multiplication `1 xx 3/4` is illustrated. multiplication 1 * 3/4 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.multiplication 2/3 * 1/4

The multiplication `2/3 xx 1/4` is illustrated. multiplication 2/3 * 1/4 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.multiplication 2/3 * 3/4

The multiplication `2/3 xx 3/4` is illustrated.multiplication 2/3 * 3/4 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`'

                            
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