Understanding Fractions

7UnderstandingFractions

Ms. Taylor

Fraction

A fraction is the quotient of two rational numbers.

Numerator

Denominator

Classification of Fractions

Proper FractionImproper FractionMixed Number

Classification of Fractions

A proper fraction is a fraction with the numerator less (smaller) than the denominator.

An improper fraction is a fraction with the numerator great (larger) than or equal (the same) to the denominator.

A mixed number has a fraction and a whole number.

Proper Fractions

3

4

1

2

Improper Fractions

7

5

9

9

Mixed Number

1 4

3

Equivalent Fractions

A equivalent fraction is a fraction that names the same fraction.

These are equivalent fractions.

6 1

18 3

,

Order Fractions

To order fractions with like denominators:

First look at the numerator s.

Place the fractions with the lowest numerator first.

Place the second lowest numerator next.

Keep doing this until there are no more fractions.

Ordering Fractions

Order the following fractions:

2 1 3

4 4 4

The answer:

1 2 3

4 4 4

, ,

,,

Ordering Fractions

To order fractions with unlike denominators.

First find a common denominator, which is smallest whole number that is divisible by each of the denominators.

You find a common denominator by finding the Least Common Multiple (LCM) for whole numbers.

Least Common Multiple (LCM)

Method 1

List the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.

Example

1/5, 1/6, and 1/15

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 45

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Multiples of 15: 15, 30, 45

LCM

The LCM of 5, 6, and 15 is 30; so the common denominator would be 30.

* 6 =

* 6 = You continue with the other two

fractions.

15

630

Ordering Fractions

Now that you have a common denominator. You put the fractions in order from LEAST TO GREATEST!

6 5 2 2 5 6

30 30 30 30 30 30

, , = ,,

Terrific

LCM

Method 2:

Factor each of the denominators into primes.

Then count the number of times each prime number appears in each of the factorizations.

For each prime number, take the largest of these counts. Write down that prime number as many times as you counted.

The product of all the prime numbers written down is the least common denominator.

Method 2

Factor each of the numbers into primes.

Count the number of times each prime number appears in each of the factorizations.

For each prime number, take the largest of these counts.

Write down that prime number as many times as you counted for it in step 2.

The least common multiple is the product of all the prime numbers written down.

Method 2

Example: Find the LCM of 5, 6, and 15.

Prime factorization of 5 is 5.

One five

Prime factorization of 6 is 2 x 3.

One 2 and one 3

Prime factorization of 15 is 3 x 5.

One 3 and one 5

Method 2

The largest count of 2s is one

The largest count of 3s is one

The largest count of 5s is one

So, we simply take 2 x 3 x 5 = 30

Therefore, 30 is the LCM of 5, 6, and 15.

Awesome job!

References

Help with Fractions http://www.helpwithfractions.com/least-common-denominator.html