Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting.

Fractions 02/12/112lntaylor ©

Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting more than two fractions Ipsative Choice Multiplying fractions Cross Cancellation Dividing fractions Simplify polynomials with fractions 1 2 3 4 5 6 7 8 9 02/12/112lntaylor ©

Learning Objectives LO 1 LO 2 Understand what a fraction represents Perform basic operations with fractions LO 3Simplify expressions and solve equations with fractions TOC 02/12/112lntaylor ©

Definitions Definition 1A fraction is a way of expressing part of a whole number TOC Definition 2 A fraction is also called a ratio and is part of the rational number set Definition 3 A fraction consists of a numerator (the top) which represents the pieces Definition 4A fraction consists of a denominator (the bottom) which represents how many pieces in the whole number 02/12/112lntaylor ©

Previous knowledge PK 1 PK 2 Basic Operations and Properties Combine Like Terms PK 3Exponent Rules TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Adding and subtracting fractions requires cross multiplication Multiplying fractions requires straight across multiplication Rule 3Dividing requires flipping a fraction and multiplying straight across Rule 4Learn to “get rid” of fractions by turning expressions into equations Basic Rules of Fractions TOC 02/12/112lntaylor ©

Adding Fractions 2 + 3 5 7 TOC 02/12/112lntaylor ©

Step 1 Step 2 Construct matrix with numerators on top and denominators on side Blank out boxes diagonally Step 3Multiply matrix Step 4Add the results; this becomes the numerator 2 + 3 57 + 15 + 14 = 29 5 x 7 = 35 23 57 Step 5Multiply left side numbers (denominators); this becomes the denominator 35 Step 6Reduce fraction if possible TOC 02/12/112lntaylor ©

Now you try 3 + 5 4 7 TOC 02/12/112lntaylor ©

Step 1 Step 2 Construct matrix with numerators on top and denominators on side Blank out boxes diagonally Step 3Multiply matrix Step 4Add the results; this becomes the numerator 3 + 5 47 + 20 + 21 = 41 4 x 7 = 28 35 47 Step 5Multiply left side numbers (denominators); this becomes the denominator 28 Step 6Reduce fraction if possible TOC 02/12/112lntaylor ©

Now you try 3 ─ 5 4 7 TOC 02/12/112lntaylor ©

Step 1 Step 2 Construct matrix with numerators on top and denominators on side Blank out boxes diagonally Step 3Multiply matrix Step 4Add the results; this becomes the numerator 3 ─ 5 47 - 20 + 21 = 1 4 x 7 = 28 3- 5 47 Step 5Multiply left side numbers (denominators); this becomes the denominator 28 Step 6Reduce fraction if possible TOC 02/12/112lntaylor ©

Adding/Subtracting more than 2 fractions 3 + 5 - 2 4 7 3 TOC 02/12/112lntaylor ©

Step 1 Step 2 Construct cascading matrix Blank out boxes diagonally Step 3Multiply matrix; you can only multiply by the box above! Step 4Add the results; this becomes the numerator 3 + 5 47 3 5 47 Step 5Multiply left side numbers (denominators); this becomes the denominator Step 6Reduce fraction if possible ─ 2 3 - 2 3 + 20- 8 + 21- 56 + 63+ 60 = 67 4 x 7 x 3 = 8484 TOC 02/12/112lntaylor ©

Now you try 3 + 5 - 1 4 7 6 TOC 02/12/112lntaylor ©

Step 1 Step 2 Construct cascading matrix Blank out boxes diagonally Step 3Multiply matrix; you can only multiply by the box above! Step 4Add the results; this becomes the numerator 3 + 5 47 3 5 47 Step 5Multiply left side numbers (denominators); this becomes the denominator Step 6Reduce fraction if possible ─ 1 6 - 1 6 + 20- 4 + 21- 28 + 126+ 120 = 218 4 x 7 x 6 = 168 168 = 109 84 TOC 02/12/112lntaylor ©

Is there another method? TOC 02/12/112lntaylor ©

Rooftop Method 3 + 5 - 1 4 7 6 TOC 02/12/112lntaylor ©

Step 1 Step 2 Build a rooftop Add the results; this is your numerator Step 3Multiply the denominators; this is your denominator Step 4 3 + 5 47 Reduce fraction if possible ─ 1 6 3 x 7 x 6 = 126 + 126 4 x 5 x 6 = 120 + 120 4 x 7 (-1) = - 28 - 28 218 4 x 7 x 6 = 168 168 = 109 84 TOC 02/12/112lntaylor ©

Now you try! 3 + 5 + 1 5 7 3 TOC 02/12/112lntaylor ©

Step 1 Step 2 Build a rooftop Add the results; this is your numerator Step 3Multiply the denominators; this is your denominator Step 4 3 + 5 57 Reduce fraction if possible + 1 3 3 x 7 x 3 = 63 + 63 5 x 5 x 3 = 75 + 75 5 x 7 x 1 = 35 35 173 5 x 7 x 3 = 105 105 TOC 02/12/112lntaylor ©

Ipsative Choice Decide which method you will master Matrix or Rooftop? TOC 02/12/112lntaylor ©

Define Decide Ipsative choice means “forced choices” Either choice works – matrix or rooftop method MasterDo all problems the same way until you have mastered the method Ipsative Choice TOC 02/12/112lntaylor ©

Multiplying Fractions TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Multiply numerators; this becomes the new numerator Multiply denominators; this becomes the new denominator Rule 3Reduce fraction if possible 2 3 5 7 2(5)(5)= 10 3 721 TOC 02/12/112lntaylor ©

Now you try! 3 4 4 3 TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Multiply numerators; this becomes the new numerator Multiply denominators; this becomes the new denominator Rule 3Reduce fraction if possible 3 4 3 4 3(3)(3)= 9 4 416 TOC 02/12/112lntaylor ©

Cross Cancellation 7 4 6 3 TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Numerators can be moved anytime YOU want Reduce fraction Rule 3Multiply straight across 3 4 7 6 3(7)(7) (4) 6 1 2 1 x 7 = 7 2 x 4 = 8 Rule 4Reduce fraction if possible TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Numerators can be moved anytime YOU want Reduce fraction Rule 3Multiply straight across 3 4 5 9 3(5)(5) (4) 9 1 3 1 x 5 = 5 3 x 4 = 12 Rule 4Reduce fraction if possible TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Write top fraction Flip bottom fraction Rule 3Check for cross cancellation; you can here but we will skip it 3 4 9 5 Rule 4Multiply straight across ─ 3 4 9 5 3 x 5 = 15 4 x 9 = 36 Rule 5Reduce fraction if possible 5 12 TOC 02/12/112lntaylor ©

Rule 1 Rule 2 Write top fraction Flip bottom fraction Rule 3Check for cross cancellation; none here 3 5 4 7 Rule 4Multiply straight across ─ 3 5 4 7 3 x 7 = 21 5 x 4 = 40 Rule 5Reduce fraction if possible 21 40 TOC 02/12/112lntaylor ©

Step 4 Step 5 Combine like terms if necessary Divide by the y coefficient Step 6Simplify if possible Step 7You can erase the “= y ” if you want Step 2 Step 1 Turn the expression into an equation by introducing “ = y” Every term gets a denominator Step 3 Multiply every term’s numerator with every other denominator (Roof top method) 2x² 3 + 4x– 10x 1 5 =y (5)(1) 2x²+ 4x (3)(1) – 10x (3)(5)(1)(3)(5) = y 10x²+ 12x– 150x= 15y 10x² – 138x = 15y 10x² – 138x = y 15 x (10x – 138) 15 TOC 02/12/112lntaylor ©

Step 4 Step 5 Combine like terms if necessary Divide by the y coefficient Step 6Simplify if possible Step 7You can erase the “= y ” if you want Step 2 Step 1 Turn the expression into an equation by introducing “ = y” Every term gets a denominator Step 3 Multiply every term’s numerator with every other denominator (Roof top method) 2x² 7 + 3x– 10x 1 5 =y (5)(1) 2x²+ 3x (7)(1) – 10x (7)(5)(1)(7)(5) = y 10x²+ 21x– 350x= 35y 10x² – 329x = 35y 10x² – 329x = y 35 x (10x – 329) 35 TOC 02/12/112lntaylor ©

Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting.

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Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting.

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Presentation on theme: "Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting."— Presentation transcript:

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