Fractions Math 6

Fraction Basics Fractions

Fractions Basics A fraction is a part of a whole We call the top number the Numerator, it is the number of parts you have. We call the bottom number the Denominator, it is the number of parts the whole is divided into

Fractions Basics Adding Fractions: fractions can be added easily if the denominator s the same:

Equivalent Fractions Fractions

Equivalent Fractions Equivalent Fractions: Some fractions may look different, but are really the same.

Equivalent Fractions

Equivalent Fractions When a fraction is multiplied or divided by the same number, the fraction keeps it's value. The rule to remember is: Change the bottom using multiply or divide, And the same to the top must be applied"

Equivaent Fractions Simplifying (or reducing) fractions means to make the fraction as simple as possible Why say four-eighths (4/8) when you really mean half (1/2)? You should always complete an answer using the simplest form. That is called Simplifying. The fraction is in its Simplest Form

Equivalent Fractions There are two ways to simplify a fraction: Method 1: Divide both the numerator and denominator until you can't divide any more

Equivalent Fractions Method 2: Divide both the numerator and denominator by the Greatest Common Factor Example: The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4. Divide both top and bottom by 4:

Equivalent Fractions You can make equivalent fractions by multiplying or dividing both numerator and denominator by the same amount. NEVER add or subtract, to get an equivalent fraction. (You only multiply or divide) Only divide when the top and bottom would still be whole numbers.

Try This

Try This 198 ÷ 2 = 99 216 ÷ 2 = 108 99 ÷ 9 = 11 108 ÷ 9 = 12 = 11 12

Mixed Numbers and Improper Fractions

Mixed Numbers and Improper Fractions Types of Fractions Proper Improper Mixed (Numbers or Fractions)

Proper Fractions a fraction where the numerator is less than the denominator.

Improper Fraction a fraction where the numerator is greater than or equal to the denominator.

Mixed Numbers (a.k.a . Mixed Fractions) A Mixed Fraction is a whole number and a proper fraction combined.

Mixed Numbers and Improper Fractions

Converting Improper Fractions to Mixed Fractions Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator.

11 4 3 4 2 These fractions are equivalent

Try This Convert 13/5 to a mixed fraction Divide the numerator by the denominator. 13 ÷ 5 = 2 r.3 Write down the whole number answer 2 Then write down any remainder above the denominator. 2 3/5

Converting Mixed Fractions to Improper Fractions Multiply the whole number part by the fraction's denominator. Add that to the numerator Then write the result on top of the denominator.

2 5 3 17 5 These fractions are equivalent

Convert 4 2/3 to a improper fraction Multiply the whole number part by the fraction's denominator. 4 x 3 = 12 Add that to the numerator 12 + 2 = 14 Then write the result on top of the denominator. 14 3

Are Improper Fractions Bad ? No For everyday use, people understand mixed fractions better. It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages“ improper fractions are used easier in mathematical formulas

Comparing and Ordering Mixed Numbers and Fractions

Explore Drake rode his bike for three-fourths of a mile and Josh rode his bike for one-fourth of a mile. Which boy rode his bike farther? Draw a diagram to demonstrate the comparison Explain why the fractions are easily compared

Solution These fractions have like denominators, so we can compare the numerators Since three is greater than one, three-fourths is greater than one-fourth. Therefore, Drake rode his bike farther.

Try This

Explore 2 Josephine ate three-fourths of a pie and Penelope ate two-thirds of a pie. If both pies are the same size, then which girl ate more pie? Draw a diagram to demonstrate the comparison Explain why the fractions are not as easily compared

Solution 2 These fractions have different denominators. We need to change these fractions to equivalent fractions with a common denominator in order to compare.

LCD The least common denominator (LCD) of two or more denominators is the smallest whole number that is divisible by each of the denominators

Explore 3 Compare 14/9 and 5/3

Solution 3 Find a common denominator The LCM of 9 and 3 is 9 Convert each fraction to an equivalent fraction with a denominator of 9

REview https://www.brainpop.com/math/numbersando perations/reducingfractions/ https://www.brainpop.com/math/numbersando perations/mixednumbers/

Quiz