Grade 6 Math Fractions

Introduction for grade 6 math fractions:

A fraction is a part of a whole. Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. The numerator of a fraction is the number that shows how many equal parts of the, whose are taken.

Numerator
denominator

A mixed number is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+"; for example:

2 + `3 / 4` = 2 `3/4`

An improper fraction as a way to write a mixed number, consider the 2 `3/4` . A complex fraction is a fraction in which one or both of the terms are fraction or mixed number, as in example `3/4` / 6

(Source: Wikipedia)


Grade 6 math fractions – Mixed number as improper fraction and examples:


Grade 6 math fractions - Express mixed number as improper fractions:

Procedure: To express a mixed number as an improper fraction

Multiply the whole number by the denominator.
Add the numerator to obtain the numerator of the improper fraction.
The denominator is the same as that of the original fraction.
Example problems:

Express 5 `2/3 ` as an improper fraction

Solution:

Multiply the whole number by the denominator.

Add the numerator to obtain the numerator for the improper fraction.

= `(5*3+2)/3` = `(15 + 2) / 3`

The denominator is the same as that of the original fraction.

Answer = `17 / 3`

Grade 6 math fractions - Expressing improper fraction as mixed numbers:

Procedure: To express an improper fraction as a mixed number

Divide the numerator by the denominator
Example problems:

Express the following improper fractions as mixed numbers

`13 / 4` = 3 `1/4`
`46 / 3` = 14 `4/3`
`522 / 8` = 65 `2/8`

Grade 6 math fractions - Adding, subtracting fractions and unlike denominator:


Grade 6 math fractions - Adding and subtracting fractions steps:

Steps for adding and subtracting fractions:

To add and subtract algebraic fraction, follow these steps:

Write the given fraction make sure the fraction have common denominator.
Add or  subtract the numerators values.
The result give Solution for the problem
Adding fraction -Example:

(`3 / 2` ) + (`7 / 2` )

= `(3 + 7) / 2`

= `10 / 2`

= 5

Subtracting fraction - Example:

(`9 / 4` ) – (`3 / 4` )

= `(9 - 3) / 4`

=  ` 6 / 4`

=  `3 / 2 `

Grade 6 math fractions – Adding and subtracting unlike denominator fraction steps:

To adding and subtracting fraction that have unlike denominator, follow these steps:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD) (the least numbers into which the denominator of two or more fractions will go evenly).

2. Add and subtract the numerator and place the sum over the lowest common denominator.

Adding unlike denominator fraction -Example:

`7 / 4 ` + `8 / 2 ` =?

Solution:

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

` 7 / 4` = `1 / 4`

` 8 / 2 ` = `16 / 4`

` 7 / 4 ` + `16 / 4 ` = `(7 + 16) / 4`

Answer = `23 / 4`

Subtracting unlike denominator fraction - Example:

`11 / 4` – `3 / 2` =?

Solution:

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

`11 / 4` = `11 / 4`

`3 / 2 ` = `6 / 4`

(`11 / 4` ) – (`6 / 4` ) =  ` (11-6)/4 `

Answer = `5 / 4` .