Adding Mixed Numbers Simplify Subtract Equivalent Fractions The

Adding Mixed Numbers Simplify Subtract Equivalent Fractions

The top number of a fraction is the Numerator The bottom number of a fraction is the Denominator 3 4

To change an improper fraction into a mixed number divide the numerator by the denominator; whatever is left over is the new numerator…keep the same denominator. For Example: 11 4 11 divided 4 equals 2; there is 3 left over. 2 34

To change a mixed number into an improper fraction get MAD…Multiply – Add – Put over Denominator 4 x 2 = 8 8 + 1 = 9 4 1 = 2 9 2

Least Common Multiple Least Common Denominator

Multiples ►A multiple is formed by multiplying a given number by the counting numbers. ► The etc. counting numbers are 1, 2, 3, 4, 5, 6,

Least Common Multiple (LCM) ► The least common multiple is the smallest number that is common between two lists of multiples.

Example: List the multiples of 4: ► 4 x 1=4 ► 4 x 2 = 8 ► 4 x 3 = 12 ► 4 x 4 = 16 ► 4 x 5 = 20 ► 4 x 6 = 24 Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.

EXAMPLE: Find the LCM of 12 and 18 The multiples of 12: The multiples of 18: • 12 x 1 = 12 • 18 x 1 = 18 • 12 x 2 =24 • 18 x 2 = 36 • 12 x 3 = 36 • 18 x 3 = 54 • 12 x 4 = 48 • 18 x 4 = 72 • 12 x 5 =60 • 18 x 5 = 90

EXAMPLE: Find the LCM of 12 and 18 12, 24, 36, 48, 60 18, 36, 54, 72, 90 The first number you see in both lists is 36 The least common multiple of 12 and 18 is 36

Equivalent Fractions

Equivalent fractions A fraction can have many different appearances, these are called equivalent fractions In the following picture we have ½ of a cake because the whole cake is divided into two equal parts and we have only one of those parts. But if we cut the cake into smaller equal pieces, we can see that = Or we can cut the original cake into 6 equal pieces,

Equivalent fractions A fraction can have many different appearances, these are called equivalent fractions Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same. Therefore, = = If you don’t like this, we can cut the original cake into 8 equal pieces,

Equivalent fractions A fraction can have many different appearances, they are called equivalent fractions Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same. Wow, that’s confusing! Therefore, = = =

Equivalent Fractions One Whole or 1

Equivalent Fractions 1 2 Cut them in half

Equivalent Fractions This shape shows one half shaded. NUMERATOR DENOMINATOR 1 2 How many pieces shaded How many pieces it’s cut into

Equivalent Fractions I cut my shape again 1 4 1 4 I still show 1 1 4 But I also show 2 2 4

We need a common denominator to add these fractions.

We need a common denominator to add these fractions. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 7, 14, 21, 28, 35…

2, 4, 6, 8, 10, 12, 14, 16, 18, 20 7, 14, 21, 28, 35… The first number IN COMMON that appears on both lists becomes the common denominator

x 7 7 X 7 14 x 2 6 x 2 14 13 14 7 + 6 = 13

We need a common denominator to add these fractions. 3, 6, 9, 12, 15, 18, 21, 24, 27 5, 10, 15, 20, 25, 30, 35, 40, 45

x 5 10 X 5 15 x 3 9 15 10 – 9 = 1

The numbers you multiply together to get a product

THINK. . . • Greatest. . . The biggest possible • Common. . . They both have it • Factor. . . A factor of both numbers

List the factors of 8 List the factors of 16 What is the biggest number In both lists? This is the GCF.

GREATEST COMMON FACTOR (GCF) GREATEST COMMON FACTOR Helps Simplify fractions

This fraction is not in simplest form. As long as there is a number that you can divide the numerator and denominator by (other than 1) The fraction is not in simplest form. 6 12

Simplifying Fractions GREATEST COMMON FACTOR 6= 12 ? What’s the GCF? ? • What factors do they share? • Which of those factors is the largest? 6 12

Now divide both the Numerator and denominator By the GCF 6 ÷ 6 12 ÷ 6 = 1 2

HINT The GCF will ALWAYS be EQUAL to Or SMALLER than the smallest of the numbers

To simplify a fraction you must divide the numerator and the denominator by the Greatest Common Factor. The Greatest Common Factor is the biggest number you can divide both the numerator and denominator by. 4÷ 4 8÷ 4 = = 1 2 Greatest Common Factor is 4