Fractions

Fractions

Factoring
Prime Number
Composite Number
Greatest Common Factor (GCF)
Least Common Multiple (LCM)
Parts of a fraction
Similar and dissimilar fractions
Proper fraction
Improper fraction
Mixed Number
Reciprical of a fraction
Cross multiplying fractions
Order or compare fractions
Reduce fractions
Mixed number to improper fraction
Improper fraction to mixed number

Basic operations with fractions
Add and subtract fractions
   Like denominators
   Unlike denominators
   Borrow
   Mixed numbers
   Whole numbers from mixed numbers
   Fractions from whole numbers
   Fractions from mixed numbers
   Check answers
Multiply and Divide fractions
   Multiply Fractions
   Cancel fractions
   Divide fractions
   Check answers
Simplify complex fractions
Solve word problems with fractions

Factoring
Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite).
Factoring a number means taking the number apart to find its factors--it's like multiplying in reverse.
To factor a number, divide the number continuously by the smallest possible divisor.
Factors and multiples - First Glance
Examples
Workout
Print this page for factoring help

16/2=8/2=4/2=2
Factors of 16 are 2*2*2*2 or 2^4
If you multiply the factors of 16 together, the product will be 16.

2*2*2*2= 16

Prime Number
A prime number has only two factors, one and itself, so it cannot be divided evenly by any other numbers.

PRIME NUMBERS to 100
2,3,5,7,11,13,17,19,23,29,31,37,41,43, 47,53,59,61,67,71,73,79,83,89,97

Composite Number
A composite number is any number that has more than two factors.

COMPOSITE NUMBERS up to 20
4,6,8,9,10,12,14,15,16,18,20

Greatest Common Factor (GCF)
The greatest common factor, or GCF, is the largest number that divides evenly into two numbers.
To find the GCF of 16 and 84:
Find the prime factors of each number by factoring them.
Identify those prime factors that both numbers have in common and multiply them.
Greatest Common Factor (GCF) - First Glance
In Depth
Examples
Workout

16/2=8/2=4/2=2
84/2=42/2=21/3=7
2*2=4
4 is the GCF of 16 and 84.
It is the largest number that 16 and 84 can be evenly divided by.

Least Common Multiple (LCM)
The least common multiple (LCM) of two numbers is the smallest number (not zero) that can be evenly divided by both numbers.
To find the least common multiple of two numbers:
List the prime factors of each number.
Multiply each factor the greatest number of times it occurs in either number.
Least Common Multiple (LCM) - First Glance
In Depth
Examples
Workout

30 = 2 * 3 * 5
45 = 3 * 3 * 5
2 and 5 each occur once in each number, 3 occurs twice in one number so multiply:
2 * 5 * 3 * 3 = 90
So 90 is the LCM of 30 and 45.
It is the least number that both 30 and 45 will divide into evenly.

Parts of a fraction
A fraction is a number used to name a part of a group or a whole.
The number below the bar is the denominator.
The number above the bar is the numerator.
The bar stands for division.
Fractions - Definitions - First Glance
In Depth
Examples
Workout

Similar and dissimilar fractions
If denominators are the same, fractions are similar.

If denominators are different, fractions are dissimilar.
Fractions - Definitions - First Glance
In Depth
Examples
Workout

5/8 and 3/8 are similar fractions.
3/5and 2/3 are dissimilar fractions.

Proper fraction
Numerator is less than denominator.
Fractions - Definitions - First Glance
In Depth
Examples
Workout

Less than one whole (3/5).

Improper fraction
Numerator is greater than or equal to denominator.
Fractions - Definitions - First Glance
In Depth
Examples
Workout

Equal to one whole (5/5)
Greater than one whole (7/5).

Mixed number
Numbers with a whole number and a fraction.
Fractions - Definitions - First Glance
In Depth
Examples
Workout

More than one whole.
1 2/5

Reciprical of a fraction
The multiplicative inverse of a number.
The recipricol is obtained by turning the fraction over, flipping it.
Two numbers are recipricols if their product is 1.
To find the recipricol of a whole number, write the number in fraction form, then invert.
5 = 5/1 so it's recipricol is 1/5.

Reciprical of 2/3 is3/2
2/3 * 3/2 = 6/6 = 1
Reciprical of 7is1/7
7/1 * 1/7 = 7/7 = 1

Cross multiply fractions
To cross multiply fractions, multiply the extremes and multiply the means.
Extremes are the two outside terms (the first and fourth term).
Means are the two inside terms (the second and third term).

Order or compare fractions
Two fractions are either equivalent (they represent the same number) or the first fraction is greater than > or less than < the second fraction.
If fractions have the same denominator, the one with the highest numerator is larger.
If fractions have the same numerator, the one with the higher denominator is smaller.
If fractions have different numberators and denominators, cross multiply numerators and denominators.
If products are same, fractions are equal.
If product of extremes is greater, first fraction is greater than second fraction.
If product of means is greater, first fraction is less than second fraction.

FUNBRAIN - Fresh Baked Fractions

Change fraction to equal fraction
Sometimes fractions must be converted to equivalent fractions in order to to add or subtract them.
Fractions can be converted to equivalent fractions by multiplying the numerator and denominator by the same number.

2/3 * 3/3 = 6/9
2/3 and 6/9 = 18/18
Product of extremes and means
is the same so fractions are =

Reduce fractions
Fractions are reduced to their lowest terms, or simplified, by finding a common factor. If both the numerator and denominator can be divided by the same number, leaving no remainder, they can be reduced.

Reducing fractions
In Depth
Examples
Workout

Mixed number to improper fraction
To change a mixed number to an improper fraction:
Numerator = denominator * whole number + numerator
Denominator = original denominator

Improper fraction to mixed number
To change an improper fraction to a mixed number:
Numerator / denominator
Whole number = whole number
Numerator = remainder
Denominator = original denominator

Basic operations with fractions

Add and subtract fractions

Fractions - Adding and Subtracting fractions - First Glance In Depth Examples Workout

Like denominator
Add or subtract the numerators and keep the same
denominator.
The resulting fraction (answer) must then be simplified and/or changed to a mixed number.

2/5 + 1/5 = 3/5
add numerators 2+ 1=3
keep denominator 5

Unlike denominators
To add:
Product of Extremes + Product of Means
Denominator * Denominator
To subtract:
Product of Extremes - Product of Means
Denominator * Denominator
The resulting fraction (answer) must then be simplified and/or changed to a mixed number.

Mixed numbers
Add or subtract fractions with fractions and whole numbers with whole numbers.
If result is an improper fraction, change it to a mixed number, add resulting whole number to the existing whole number and keep the fraction.
Adding and subtracting mixed numbers
In Depth
Examples
Workout

7 2/3 fractions added below
+ 3 3/4
10 17/12 = 10+1 5/12 = 11 5/12

2/3+3/4=2*4+3*3=8+9=17= 1 5/12
3*4 12 12

Borrow
If you need to borrow, subtract 1 from the whole number and add 1 to fraction, creating an improper fraction.

Subtract 1 from 5 making it a 4. Add 1 in form of 5/5 to 2/5 making the top fraction 4 7/5, then subtract fractions.
5 2/5 = 4 7/5 (2/5+5/5)
3 3/5 = 3 3/5
1 4/5

Whole numbers from mixed numbers
Subtract whole numbers. Carry down fraction.

7 2/5
-4
3 2/5

Fractions from whole numbers.
Borrow from whole number if necessary. Subtract. Simplify and/or change to a mixed number

Borrow 1 from the whole number and write as a fraction with the same denominator.
6 - 2/3 =
6 = 5 3/3
- 2/3 = 2/3
5 1/3

Fractions from mixed numbers

Add or subtract fractions. Keep whole number

6 7/8
- 2/3
65/24

7/8-2/3=7*3-8*2=21-16= 5
8*3 24 24

Checking answers
To check addition, subtract either addend from sum and result should be other addend.
To check subtraction, add minuend to difference and result should be minucand.

3/7+2/7=5/7 Check 5/7-2/7=3/7
7/8-3/8=4/8=1/2 Check 3/8+4/8=7/8

Multiply and Divide Fractions

Cancel fractions
See if the any numerators and denominators can be divided by the same factor. Divide each by that factor.
Continue to cancel until no numerators or deniminators have the same factors.

Multiply fractions
Change mixed numbers to improper fractions.
Multiply numerators.
Multiply denominators.
Reduce and/or change to a mixed numeral.
When fractions are multiplied, product will be greater than either fraction.
Multiplying fractions - First Glance
In Depth
Examples
Workout

2/5 * 5/8 = 10/40 = 1/4

1 2/3 * 3 5/8 =
5/3 * 29/8= 145/24 = 6 1/24

Divide fractions
Change mixed numbers to improper fractions.
Change division sign to multiplication sign.
Flip second fraction.
Multiply numerators.
Multiply denominators.
When fractions are divided, product will be smaller than either fraction.
Dividing fractions - First Glance
In Depth
Examples
Workout

2 2/5 / 1 2/3 = 12/5 / 5/3 =
12/5 * 3/5 = 36/25 = 1 11/25

Checking answer
To check multiplication and division answers:
Divide product by one fraction and answer should be other fraction.
Multiply quotient by divisor and answer should be other fraction.

Multiply2/3*3/5=6/15
Check6/15/3/5=6/15*5/3=30/45=6/9=2/3
Divide 3/4/2/3=3/4*3/2=9/8= 1 1/8
Check 2/3*1 1/8=2/3*9/8=18/24= 3/4

Simplify complex fractions
A fraction that contains one or more simple fractions is a complex fraction.
2/3
4/5
Multiply each numerator and deniminator by the LCM of the denominators of the simple fraction. Reduce answer and/or change it to a mixed number.

2/3 = 2/3 x 4/5 = 8/15
4/5

Solve word problems with fractions

Hosted by www.Geocities.ws