Fractions

Parts of a Fraction Numerator- the parts of the whole that is present/shaded 5 10 Denominator- the total number of parts in the whole 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10

*This means that all of the total parts are present* Whole numbers When your numerator and your denominator are equal 8 *This means that all of the total parts are present* 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

This means we have more than one whole of a fraction present. Improper Fractions When you have a bigger number in the numerator than in the denominator 9 2 This means we have more than one whole of a fraction present. 1/2 2/2 3/2 4/2 5/2 6/2 7/2 8/2 9/10 10/2

Mixed Numbers This is when you have a “mixture” of a whole number and a fraction for one value “This means that you have gone one whole ( 2/2) plus another one half more on your number line” 1 1 2 1/2 2/2 3/2 4/2 1 1 ½ 2 2 ½ 0 ½ 2/2 3/2 4/2 5/2

Equivalent Fractions This is when you have two or more fractions that represent the same/equal value. 1 2 2 4 *I check this by doing the “Butterfly Method”* 1/2 2/2 1/4 2/4 3/4 4/4

Equivalent Fractions Butterfly Method is when you use an X-like pattern to multiply the numerator of one fraction to the denominator of the other. If they both equal the same product, they are equivalent. 4 4 1 2 2 4

Comparing Fractions The butterfly method can also be used to compare which fraction is larger than the other 8 15 2 3 5 4

How can I convert fractions to have common denominators? When adding, subtracting, or comparing fractions, you need to have common denominators. Common denominators (also called “like denominators”) are fractions that have the same digit as their denominators. (The same number of parts in each whole) I would choose 6 to be my like denominator because 6 is divisible by 3 1 + 2 + 4 6 3 6 I need to change two thirds into a fraction that has the same denominator as one sixth and four sixths. 1/6 2/6 3/6 4/6 5/6 6/6 1/3 2/3 3/3 1/6 2/6 3/6 4/6 5/6 6/6 +

How can Convert Fractions to have common denominators? Determine the relationship between the denominator and the common denominator Then perform the same relationship to convert the numerator (I would choose 6 as my common denominator because 6 is divisible by 3 and is already the denominator of the other two fractions) 2 x2 = 4 3 x 2 = 6 *REMEMBER-Whatever you do to the bottom, you do to the top!!!

How can I convert fractions to have common denominators? Once your fractions are converted to their new equivalent forms (that share the same denominators), you can now add them. 1 + 4 + 4 = 9 6 6 6 6 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6 9/6 10/6 11/6 12/6 1/6 2/6 3/6 4/6 5/6 6/6 1/6 2/6 3/6 4/6 5/6 6/6 1/6 2/6 3/6 4/6 5/6 6/6

How can I convert improper fractions to mixed numbers? When we have an improper fraction, we are saying that we have more than one whole. Therefore, we can simplify it to be a mixed number. 9 6 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6 9/6

How can I convert improper fractions to mixed numbers? 1 + 4 + 4 = 9 6 6 6 6 We can look at picture or a number line and see that after adding all of the parts up, one whole is present plus three sixth more. 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6 9/6 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6 9/6 + + = 1 1 1/6 1 2/6 1 3/6 0 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6 9/6

How can I convert improper fractions to a mixed number? Sometimes you have to convert more than one of the fraction’s denominators To do this, determine a common multiple among the denominators. 1 + 2 2 3 I am going to chose the common denominator of 6 because it is a multiple of both 2 and three. 1 x3 3 3 + 4 = 7 2 X3 6 6 6 6 2 x2 4 3 X2 6 1/2 2/2 1/3 2/3 3/3

How can I convert improper fractions to mixed numbers? You can also use the equation we have been discussing in class: divide the numerator by the denominator. If you have a remainder, place it as a numerator with the divisor as its denominator *Top in Bottom out!!! 1 3/6 6 9 -6 3 9 6

How can I change a mixed number to an improper fraction? Multiply the denominator by the whole number Add that product to the numerator Denominator under the sum (2 + 1) + 1 ½ 3 2 X (2 x 1) 2

How do I simplify/reduce to the simplest form? When you reduce/simplify you are converting a fraction with a larger number of parts and reduce it to a more simple form that has a less number of parts. To do this, we need to determine a number that both the numerator and the denominator can be divided by evenly. (a number both are divisible by) You will know you have the simplest form when you can not reduce again to get a smaller equivalent fraction When you simplify a fraction, the value is not changed. The only thing that changes is the number of parts that are in your fraction. 4 ÷2 2 2 ÷2 1 12 ÷2 6 6 ÷2 3 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 12/12 1/6 2/6 3/6 4/6 5/6 6/6 1/3 2/3 3/3

Don’t see something you need? Please, email me so that I can create an additional slide or two for reference! Hope this helps!