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`'

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