Definition; a fraction is defined as a part of the whole.
example: 1/4. where; 1- is the numerator &
4 - is the denominator
There are 3 types of fractions
1). proper fractions. the best way to remember is the numerator is smaller than the denominator. eg; 1/2. 1/8, 1/3, 3/4, 4/5. etc.
2).improper fractions.the best way to remember is the numerator is bigger than the denominator. eg; 5/2. 5/4, 3/2. etc
3). mixed fractions. is the combination of whole number and a proper fraction. eg. 1 1/4.
2 3/8, 21 4/5, etc.
[interesting learning point 1:we always say I ate 1 1/4 pizza instead of saying 5/4 pizza.though the value of the fractions are same. we always use mixed fraction in spoken language.
learning point 2.; if you remember the definitions it is very easy to compare fractions. eg which is greater 1/2 or 5/4 - improper fractions are bigger than proper fractions. ]
Decimals, fractions and percentages.
decimals,fractions and percentages are just a representation of the same value.
A half can be written as...
As a fraction; 1/2
As a decimal; 0.5
As a percentage; 50%
A Quarter can be written as.....
As a fraction; 1/4
As a decimal; 0.25
As a percentage; 25%.
Conversions
To convert a fraction to a decimal. to convert a fraction to a decimal: simply divide the numerator by the denominator.
eg. 2/5; divide 2 by 5.
answer 2/5 = 0.4 [now practice from your book]
To convert a decimal to a fraction. it is a three step process.
eg. convert 0.5 to a fraction. first step; place the decimal over 1 {where 1 is the denominator.}
0.5/1
second step; multiply the numerator & denominator by 10 or 100
depending on the numbers after the decimal. (1 number
after the decimal by 10, 2 numbers after the decimal by 100
3 numbers after the decimal by 1000 etc.)
0.5/1 = 0.5 x 10 / 1 x 10
= 5/10
third step; simplify the fraction.
5/10= 1/2.
answer; 0.5= 1/2. [now practice from your book]
To convert a decimal to a percentage. it is very easy,just multiply by 100 and add % sign.
eg. convert 0.125 to a percentage.
0.125 x 100 (move decimal point to 2 places to the right) = 12.5
then add % to 12.5.= 12.5%.
answer; 0.125 = 12.5% [now practice from your book]
To convert a percent to a decimal. it is the opposite. divide by 100 and remove % sign.
eg. convert 75 % to a decimal.
75/100 ( move the decimal 2 places to the left) = 0.75
answer; 75% = 0.75. [now practice from your book]
To convert a fraction to a percentage. this is a 3 step process. simplify the fraction(divide the numerator by the denominator) multiply by 100 and then add % sign.
eg. convert 3/8 to a percent.
step 1. simplify the fraction. 3/8 = 0.375.
step 2. multiply by 100. 0.375 x 100. = 37.5
(remember,move the decimal 2 places to the right)
step 3. add % sign to the answer. 37.5%
answer; 3/8 = 37.5% [now practice from your book]
To convert percentage to a fraction. first convert to a decimal (refer percentage to decimal)
eg. convert 80% to a fraction.
step 1. convert it to a decimal. 80/100 = 0.8(refer percentage to decimal
step 2. place decimal over 1; 0.8/1 (refer decimal to fraction step 1.)
step 3. multiply the numerator & denominator by 10 or 100
depending on the numbers after the decimal. (1 number
after the decimal by 10, 2 numbers after the decimal by 100
3 numbers after the decimal by 1000 etc.)
0.8 x 10 / 1 x 10 = 8/10 ( refer 2nd step in decimal to fraction)
step 4. simplify the fraction. 8/10 = 4/5.
answer; 80% = 4/5. [now practice from your book]
SIMPLIFYING FRACTIONS.
why simplify fractions? because it simplifies your life.
eg. it is awful to tell your friend " I ate 4/8 of pizza". If you simplify that fraction(4/8) it is same as 1/2(half).so it sounds as good as it tastes to let your friend know that you ate 1/2 pizza.
SIMPLIFYING FRACTIONS.
why simplify fractions? because it simplifies your life.
eg. it is awful to tell your friend " I ate 4/8 of pizza". If you simplify that fraction(4/8) it is same as 1/2(half).so it sounds as good as it tastes to let your friend know that you ate 1/2 pizza.
what is the easiest way to simplify fractions? by knowing greatest common factor.
eg. greatest common factors of 12 and 16.
Factors of 12: 1, 2, 3, 4, 6, 12. Numbers in color are the common factors.
Factors of 16: 1, 2, 4, 8, 16. but 4 is the greatest common factor.
so, 12 and 16 are commonly divisable by 4, which is the greatest common factor.
let us say solve the fraction 12/16.
Answer; 12 / 16 = 3 / 4.
{learning point: knowing greatest common factor will help you simplify the fraction and also helps you to compare fractions to find out which fraction is greater or smaller.}
Another important tool is to find the least common Multiple.(LCM)
Least; the lowest.
Common; the multiple that is common between two numbers.
Multiple; what you get when you multiply with 1,2,3,4,5,... etc.
let us understand with an example. find the least common multiples of 3 & 5.
multiple of 3 are: 3, 6, 9, 12, 15, 18,...... etc.
multiples of 5 are: 5, 10, 15, 20, 25,....etc.
the least common multiple (LCM) is 15.
{how is it useful: it is easy to compare fractions.}
Comparing Fractions. sometimes we are to compare fractions to find out which fraction is smaller or greater.
There are two methods to compare fractions.
first method: to convert each fraction to decimals
eg. which is greater 3/8 or 5/12
3/8 = 0.375.
5/12 = 0.416..
answer 5/12 is greater.
second method: to make the denominators of the given fractions same.
eg.1. which is smaller 3/8 or 5/8
answer; 3/8
[since the denominators are same, compare numerators, 3 is smaller than 5]
eg.2. which is greater 3/8 or 5/12
{make the denominators same.how can you make denominators same? by finding out the LCM}
factors of 8: 8, 16, 24, 32, ...etc ( 8 x 3= 24)
factors of 12: 12, 24, 36,...etc (12 x 2 = 24)
LCM = 24
remember to do the same thing to the numerator & denominator
so multiply numerator & denominator of each fraction to make the denominators same.
3 x 3 / 8 x 3 = 9/24.
5 x 2 / 12 x 2 = 10/24
since the denominators are same, compare numerators to find out which is greater.
