Fraction Strips for Math

Introduction to fraction strips for math:

Fractions:

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development was the common or "vulgar" fractions which are still used today (`1/2` , `2/3` , `3/4` , etc.) and which consist of a numerator and a denominator. (Source: Wikipedia)

Objective of fraction strips for math :

The main objective of this article is to learn the fraction strips for math. This article gives you types of fractions , some solved math problems on fraction strips .

Types of Fraction Strips in Math:

The following are three types of fractions in math,

Proper fraction

Improper fraction

Mixed fraction

Proper fraction:

Fractions are in the form a/b  ( where a, b are the integers), b is always greater than a(b > a) called as proper fractions.

Example: `7/8` , `16/26`

Improper fractions:

The fraction a/b ( where a, b are the integers) a is always greater than b( a > b)  called as improper fractions.

Example: `5/3` ,`12/5` , `156/46`

Mixed fraction:

The fractions are in the form of a b/c ( where a, b ,c are the integers) is called as mixed fraction. Here a is called as quotient, b is known as remainder and c is known as divisor.

Example: 2 `3/4` , 6 `7/5`

Problems on Fraction Strips for Math:

Problem 1:

Add the following negative fractions ` - 3/5 ` and `-9/5`

Solution:

Given, Add` - 3/5` and `-9/5`

That is `-3/5` + `( -9/5)` =  `-3/5 ` - `9/5`

= - ( `3/5 ` + `9/5` )

Here both fractions are have common denominator. So we can add the numerator juat like integers and keep the denominator as it is.

- ( `3/5` + `9/5` ) = - `( 3+9 )/ 5`

= `- 12/5`

Answer: `-3/5` - `9/5` =` - 12/5`

Problem 2:

Add the following negative fractions` -17/15` and `-21/ 26`

Solution:

Given, Add `-17/15` and` -21/ 26`

That is,` -17/15` + (` -21/ 26 ` ) = `-17/15`   `-21/ 26`

= - (`17/15`   +` 21/ 26` )

Here we are going to add `17/15` ,  `21/ 26` . But both fractions have different denominators. We cannot add directly. We need to make common denominator. For that we need to find the lcd of 15 and 26.

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255,…..390............

Multiples of 26 = 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, 338, 364, 390, 416 ...

Here 390 is the least common factor of 15 and 26.

Multiply `17/15` by 26 on both numerator and denominator,

`17/15` = (17 * 26) / ( 15 * 26)

= `442 / 390`

Multiply `21/ 26` by 15 on both numerator and denominator,

`21/ 26` = ( 21 * 15) / ( 26 * 15)

=   `315 / 390`

Now we can add the given fractions,

- (`17/15`   + `21/ 26` ) = - ( `442 / 390 ` + `315 / 390` )

= - `( 442 + 315) / 390`

= -` 757 / 390`

Answer:  -`17/15` + ( `-21/ 26` ) = - `757 / 390`

Problem 3:

Multiply `(x+2)/( y-3)` * `(x)/(5y)`

Solution:

Given, `(x+2)/( y-3)` * `(x)/(5y)`

We can multiply just like integers, But multiply the Both numerator and multiply the both denominator separately.

`(x+2)/( y-3)` * `(x)/(5y)` = `(x(x+2))/(5y(y-3)) ` 

= `(x^2+2x)/(5y^2-15y)`

Answer: `(x+2)/( y-3)` * `(x)/(5y)` =`(x^2+2x)/(5y^2-15y)`