What is a Fraction? A fraction is a part or piece of something. The way we write fractions tells us the size of the piece we are referring to

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$October 0, 0 What is a Fraction? A fraction is a part or piece of something.$ $The numerator is the number on top in the fraction. It tells us how many leftover parts we have that will not make a full group.$

1 October 0, 0 What is a Fraction? A fraction is a part or piece of something. The way we write fractions tells us the size of the piece we are referring to ⅝ is the numerator is the denominator is the whole number The numerator is the number on top in the fraction. It tells us how many leftover parts we have that will not make a full group. The denominator is the number on the bottom in a fraction. It tells us how many pieces each group needs to be full. The whole number is how many full groups. This is what the fraction ⅝ looks like as a picture. or

2 October 0, 0 Improper Fractions and Mixed Numbers Fractions that tell about numbers that are greater than one can be written in two ways: Mixed Numbers: Include a whole number and a fraction ⅝ is a mixed number Improper Fractions: Have a numerator that is greater than the denominator (the top number is bigger than the bottom number) is an improper fraction ⅝ and are actually talking about the same number one whole block of eight, plus five more pieces or thirteen pieces in blocks of eight

3 Converting Between Mixed Numbers and Improper Fractions It is easy to change a mixed number to an improper fraction: If you look at the denominator, you know how many pieces your whole is broken into... October 0, 0 ⅝ the whole has eight pieces If the whole has eight pieces, and we have one whole, then we can replace the with more pieces added to the numerator. + Reducing Fractions To reduce a fraction to lowest terms, find the largest number that will divide evenly into both the numerator and the denominator. (Reducing the fraction will not change its value; the reduced fraction will be an equivalent.) Example: Reduce to lowest terms. The largest number that will divide evenly into both the numerator and the denominator is. (Greatest Common Factor) :,,, :,,,, 9, Thus, the fraction is the same as the fraction when reduced to lowest terms.

4 Common Denominators October 0, 0 Before we can add and subtract fractions, it is important to understand how to make fraction pairs with common denominators. Common denominators mean that two fractions have the same number on the bottom. The denominator tells us about how many pieces our whole has, so making common denominators allows us to easily compare fractions. 9 The first step in finding common denominators is to find the Least Common Multiple of the two fractions denominators 9: 9,,,,,,,... :,,,, 0,,,,... Now that we have found the LCM of the denominators, we need to make equivalent fractions with that number as the denominator 9: 9,,,,,,,... :,,,, 0,,,,... 9 To do this we need to decide what we did to each denominator to make the new denominator 9 X X Next we need to multiply our numerator by that same number to find your new numerator X X Then we put our new fractions together Review Worksheet

5 October 0, 0 Adding and Subtracting Fractions It is always easier to compare and perform operations on numbers when they are in the same form as each other To easily add and subtract fractions, make sure they have a common denominator Use pictures and diagrams to represent the math you are doing so you can make sure your answers are reasonable and understand exactly what you are doing Adding: If we have common denominators, the math is very simple +

6 October 0, 0 Subtracting: If we have common denominators the math is very simple _ can be reduced to to give the proper answer for this equation If the denominators are not the same, you must change them to equivalent fractions before adding or subtracting. + - Review Worksheet

7 October 0, 0 Multiplying Fractions by a Whole Number When multiplying fractions by a whole number remember: x means "groups of" So you can read x as groups of And x is the same as + + Therefore x Try These! x x x x worksheet - BLM. p. 9-0 #,,,

8 October 0, 0 Multiplying Fractions by Fractions When multiplying a fraction by a fraction remember x means of x is the same as of x Represent the Split each in half because it is of So of or x Another way to represent fraction multiplication is to make a grid. Start by drawing a grid which is by, since those are the denominators (the whole). Colour in blocks by blocks, since they are the numerators (the parts of the whole). The answer is since there are coloured in blocks out of a total 0. 0 We then reduce to lowest terms 0 0 When completing these questions, what do you notice? Try These! x x x x 0 p. - #,,, or, 9,

9 October 0, 0 Multiplying Fractions Greater Than When multiplying fractions greater than one you can use two methods. Method - Using improper fractions x x Start by converting any mixed numbers to improper fractions. Then multiply the numerators and the denominators. 9 Convert back to a mixed number and reduce to lowest terms. Method - Pulling apart the numbers. x x + x + x + x Pull the whole numbers and fractions apart and multiply them separately. Add together all the products of the multiplication. Don't forget to change to common denominators before adding. Convert to a mixed number and reduce to lowest terms. Multiplying Fractions Greater Than With Grids x 9

10 October 0, 0 Try These! + + BLM -.,. worksheet - multiplying with grids worksheet - grids methods of multiplying p. - # - Division of Fractions by Whole Numbers When dividing fractions by a whole number, you divide the numerator by the whole number and the denominator stays the same. 0 0

11 October 0, 0 BUT.... What if the numerator can't be divided by the whole? No Problem! We can invert and multiply. is the same as the fraction So is the same as To invert and multiply, first switch the numerator and denominator of the divisor. Then change to x. x Then reduce to lowest terms. Try These! 9 worksheet - BLM. p. #,,

12 October 0, 0 Dividing Fractions by Fractions To model fraction division we can use fraction strips: It takes of the So fraction strips to equal the length of the You can also divide straight across just like you do with multiplying fractions. What do these models represent? worksheet - BLM.

13 October 0, 0 But.... What if we can't easily divide across or use fraction strips to make a model? KFC! x 0 Try These! 9 0 worksheet - BLM.9 p. 9-0 #,,,,, or, 9,,, Order of Operations with Fractions Order of Operations applies when working with fractions. B E D M A S + - x

14 October 0, 0 Try These! + x + - worksheet - BLM.0 p #,, or,,

15 Attachments BLM..pdf BLM..pdf Multiplying with Grids.pdf Grid Methods Worksheet.pdf BLM..pdf BLM..pdf BLM.9.pdf BLM.0.pdf

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole // Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction