Free Fractions Study Guide

Free Fractions Study Guide:

These articles we are discussing about free fractions study guide solving problems. 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 were the common or "vulgar" fractions which are still used today (1/2, 5/8, 3/4 etc.) and which consist of a numerator and a denominator. (Source – Wikipedia)

Free fractions study guide problems solve for simple addition fraction, multiplication fraction, subtraction fraction and dividing fraction.


Free fractions study guide-Example problems:


Example 1:

Add the fractions `8/20` + `7/20`

Solution:

The given two fractions are `8/20 ` + `7/20`

Here both the fractions have equal denominators, so take the common denominator, here 20

= `8/20` + `7/20`

Add the numerators directly = 8+7 = 15.

= `15/20`

The addition fraction solution is `3/4` .

Example 2:

Subtract the fractions `4/5 ` – `3/4`

Solution:

The denominator is different so we have to take least common denominator (lcd).

LCD = 5 x 4 = 20

`(4 xx 4)/ (5 xx 4)` = `16/20` and `(3 xx 5)/ (4 xx 5)` =` 15/20`

`16/20` – `15/20`

The denominators are equals

So subtracting the numerator directly = `(16-15)/20`

Simplify the above equation we get =` 1/20`

Therefore the final answer is `1/20`

Example 3:

Multiply the fractions` 2/3` x `6/3`

Solution:

The given two fractions are `2/3` x `6/3`

Multiply the numerators; we get 2 x 6 = 12

Multiply the denominators; we get 3 x 3 = 9

= `12/9`

The multiply fraction solution is `4/3`

Example 4:

Dividing fraction:

`4/2` divides `2/4`

Solution:

First we have to take the reciprocal of the 2nd number, and then multiply with the second one

Reciprocal of `2/4` = `4/2`

`4/2` x `4/2`

Multiply the numerator and denominator

`(4 xx 4)/ (2 xx 2)`

Simplify the above equation we get

= `16/4`

Therefore the final answer is 4

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Free fractions study guide-practice problems:

Problem 1: Add the two fraction `6/15` +` 4/15`

Solution: `2/3`

Problem 2: Subtract two fractions `5/5` –` 2/5`

Solution: `3/5`

Problem 3: multiply two fractions` 3/4` x` 3/4`

Solution: `9/16`

Problem 4: Dividing two fractions` 3/2` and `4/2`

Solution:` 3/4`

Free Online Math Games

Math games are very helpful to lot of children’s. Mostly many children’s do not interest to do math. So entertaining games have been introduced to kids. It helps the children to play and they learn math. Imagine that the kids are very busy to do math games. It is very helpful to the kids, because math is applicable in our practical life and all fields. The math is most powerful. Imagine the kids couldn’t stop to do math. This online math games are available for all categories of students, which includes: free online math games for kids, 1st graders to higher level and also for college students. There are also free online math games for adults. This free online math games make learning fun and interesting for students. The free online math games are useful not only for the students but also for the teachers and parents.

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SOME VARIETIES OF FREE ONLINE MATH GAMES


Free Math Games includes an Order Of Operations game, two "Secret Number" puzzles, and other fun ways to practice math facts and math principles.

Some of the free online math games include: Entrapment, Math Tutoring Service, One to Ten, Math Scramble, Side by Side, Secret Number, Subtraction Triangles, Magical Squares, Adders, Secret Numbers, Zap, Fraction Concentration, Fractional Hi-Lo, Guess It.



ENTRAPMENT

Trap the computer's red dots between our gray dots to solve this mind bender.  There are over two thousand puzzles under this category.

MATH TUTORING SERVICE

The Problem Site's administrator, Douglas Twitchell provides math-tutoring services for high school students.

ONE TO TEN

Use four single-digit integers and the standard arithmetic operations to create all the numbers from one to ten.

MATH SCRAMBLE

Fill in the blanks in an addition problem or a multiplication problem to obtain the correct solution!

SIDE BY SIDE

A set of three math puzzle games in which we are given a list of seven numbers in a row, and we must rearrange the numbers according to the rule of the game.

SECRET NUMBER

The computer picks a random number between 10 and 99. We must ask questions to determine what the secret number is.

SUBTRACTION TRIANGLES

This puzzle is a bit like a Pascal's Triangle, except the numbers subtract to the values above them, instead of adding to the numbers below.

MAGICAL SQUARES

Select an "Easy", "Moderate", or "Challenge" game, and then place numbers in the square grid so they add up to the right sum for each row and column.

ADDERS

Refresh our memory on basic math facts by racing a snake around the game, gobbling up correct answers and avoiding running into walls.

SECRET NUMBERS

A variation on 'My Secret Number'. The number has three digits, and the computer tells us all the information we need to determine the number.

ZAP

A math game that just might give us brain cramps. It's a sliding tile puzzle that forces us to do mental arithmetic while racing against the clock.

FRACTION CONCENTRATION

Test our memory while evaluating and reducing fractions to find equivalent fractions. This game can be played as a one-player game or a two-player game.

FRACTIONAL HI – LO

Similar to 'Hi-Lo', except that we are guessing fractions between 0 and 1. A bit more challenging, since we are dealing with both numerators and denominators!

GUESS IT!

Professor Puzzler helps young children learn about estimation by guessing amounts, and by recognizing more and less

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ADVANTAGES


Learn math in an fun and interestig way
Creates interest among students in maths
Loss of  fear of Math among students and parents
Helps students to learn Math very easily.
Loss of tension among parents regarding Math.

Math Fractions

Introduction to Math Fractions:
Fraction represents a part  of a whole. A fraction of material or thing is a piece or section of it. It is a quantity

which cannot be represented as a whole number.A fraction has two parts one is numerator and the  other is

denominator.

The rectangular  picture above can be divided into 8 equal parts.

4 parts of total   rectangle is painted  with Brown colour  .Hence brown colour constitutes 4/8 of total.

2 parts of total   rectangle is painted  with Black colour.Hence Black colour constitutes 2/8 of total.

1 part   of total   rectangle is painted  with Blue colour.Hence Blue colour constitutes 1/8 of total.

1 part   of total   rectangle is painted  with Red  colour.Hence Red  colour constitutes 1/8 of total.

MATH FRACTIONS IN DAILY LIFE:-

i)   Grades awarded to students for example (4/5, 5/5).

ii)  To represent  time such as  quarter past the hour.Quarter is nothing but a fraction equivalent to 1/4.

iii)  Percentages which are also fraction .50% is equivalent to 50/100 =1/2.


Math fractions description:

TYPES OF MATH  FRACTIONS :-

i)  Proper fractions:These are the fractions having numerator always less than the denominator

The value of a proper fraction is always less than 1.

Examples:-  1/3  ,5/6 ,7/9

ii)  Improper fractions:These are the fractions having numerator  greater  or equal to denominator

The  value of a improper fraction will be  always greater than or equal  to

Any   whole number can be transformed into a improper fraction.

Examples:-  8/3  , 6/6 , 9/2

iii)  Mixed fractions :Mixed fraction is whole number and fraction together. An improper

fraction  be rewritten as mixed fraction and vice versa.

Examples :-   2`(3)/(7)`,   4`(4)/(11)`

iv) Equivalent fractions :Fraction which  reduce to same number on simplification are called

equivalent fractions.

Examples :- the equivalent fraction of  10/25  is 2/5  as 5 is common factor

in numerator and denominator.

MATH FRACTIONS  OPERATIONS :

i)  Division : Fractions can be divided . Fraction in numerator is multiplied by reciprocal of fraction in

the denominator.

Example :  `(3)/(4)`   `-:`   `(5)/(7)`    =     `(3)/(4)`   `x`   `(5)/(7)`

=   `(15)/(28)`



ii) Subtraction  : Fractions can be subtracted provided the denominators of fractions  are same.For

fractions having unequal denominators ,denominators are to be made same for

subtraction.

Example1 :  `(2)/(9)`   `**`   `(1)/(9)`    =   `(1)/(9)`

Example2 : `(1)/(2)`     -    `(1)/(4)`        =   `(1*2)/(2*2)`   -    `(1)/(4)`      =        `(2)/(4)`  -  `(1)/(4)`      =   `(1)/(4)`



iii) Multiplication: Fractions can be multiplied directly ie numerators with numerators and

denominators with denominators.

Example : `(2)/(9)`   `xx`   `(1)/(9)`    =   `(2)/(81)`

iv) Addition :Fractions can be added provided the denominators of fractions  are same.For

fractions having unequal denominators ,denominators are to be made same for

addition.

Example1 :  `(2)/(9)`   +   `(1)/(9)`    =   `(3)/(9)`

Example2 : `(1)/(2)`     +  `(1)/(4)`        =   `(1*2)/(2*2)`   +    `(1)/(4)`      =        `(2)/(4)`  +  `(1)/(4)`      =   `(3)/(4)`

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More Examples for Math Fractions:


Ex1:

Multiply the fractions is `8/5` and `5/9`

Sol:

Here we can observe than there is a common factor in numerator and denominator which is 5.

so cancelling 5  we will be left with     `(8)/(9)`

Ex2:

Arrange  the following fractions in ascending order     `(3)/(4)`    `(2)/(3)` `(1)/(6)`

Sol:

To compare fractions their denominators should be equal .so least common multiple of 4,3,6 is

12 .So now we make denominators equal

`(3)/(4)`` = ` `(3xx3)/(4xx3) =9/12`

similarly

`(2)/(3)`` = ` `(8)/(12)`

`(1)/(6)``=``(2)/(12)`

Since denominators are equal and so numerators can be compared

so  1/6 ,2/3,3/4 is the required order.

Ex3:

Add the following mixed fractions

i)     `(1)/(3)`  + 5 `(1)/(3)`

`sol:`

`(1)/(3)`  + 5 `(1)/(3)`

=  1+5  +    (1/3)+ (1/3)

` =6 + ``(2)/(3)`

= 6`(2)/(3)`