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## Math 8

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**Math 8**Unit 3: Operations with Fractions**Unit 3: Operations with Fractions**What you’ll learn • Estimate the products and quotients of fractions and mixed numbers • Multiply a fraction by a whole number and by a fraction • Divide a fraction by a whole number and by a fraction • Multiply and divide mixed numbers • Use the order of operations with fractions**Unit 3: Operations with Fractions**Why it’s important: • Used with cooking for measuring • Used with shopping (sales ½ off) • Used with construction for measuring**Fraction Review**Review Fractions are used to show parts of a whole. Three parts out of four are coloured in. One part out of four is white.**Fraction Review**Review • The top is called the numerator. • The bottom is called the denominator. • The line is called the fraction bar. numerator fraction bar denominator**Fraction Review**Review Improper fractions have a numerator larger than the denominator. Mixed fractions are a combination of whole number and fraction. Improper fraction Mixed fraction**Fraction Review**Review Equivalent fractions – have the same value, they are multiples of each other.**Fraction Review**Review Find the smallest equivalent fraction. A. B. C. D.**Fraction Review**Review To add or subtract fractions they must have the same denominator. Use equivalent fractions to get the same denominator.**Fraction Review**Make equivalent fractions by doubling the quarter. The denominator must be the same for both fractions. Reduce the fraction to the smallest possible equivalent fraction.**Fraction Review**Make equivalent fractions by halving the two eighths. The denominator must be the same for both fractions. Reduce the fraction to the smallest possible equivalent fraction.**Unit 3: Operations with Fractions**3.1 Using Models To Multiply Fractions and Whole Numbers**3.1 Using Models To Multiply Fractions and Whole Numbers**• Focus: Use models to multiply a fraction by a whole number**3.1 Using Models To Multiply Fractions and Whole Numbers**• To add fraction you must have the same denominator. 3 8 1 4 = +**3.1 Using Models To Multiply Fractions and Whole Numbers**• We change the second fraction into eighths. 3 8 2 8 = +**3.1 Using Models To Multiply Fractions and Whole Numbers**• We add the numerators. 3 8 2 8 3+2 8 5 8 = = +**3.1 Using Models To Multiply Fractions and Whole Numbers**• Try:**3.1 Using Models To Multiply Fractions and Whole Numbers**Remember • Multiplication is accelerated addition • 2 + 2 + 2 = 6 • This can also be done as three groups of two 3 2 x 3 = 6 2**3.1 Using Models To Multiply Fractions and Whole Numbers**• Match the addition and multiplication • 3 + 3 + 3 + 3 • 5 + 5 • 2 + 2 + 2 + 2 + 2 • 1 + 1 + 1 • 4 x 3 • 1 x 3 • 2 x 5 • 5 x 2**3.1 Using Models To Multiply Fractions and Whole Numbers**• What is 3 times two thirds?**3.1 Using Models To Multiply Fractions and Whole Numbers**• What is 3 times two thirds?**3.1 Using Models To Multiply Fractions and Whole Numbers**• Write out the following multiplications as additions and draw a diagram.**3.1 Using Models To Multiply Fractions and Whole Numbers**• Homework**Unit 3: Operations with Fractions**3.2 Using Models to Multiply Fractions**3.2 Using Models to Multiply Fractions**• Focus: Use models to multiply fractions**Unit 3: Operations with Fractions**3.3 Multiplying Fractions**3.3 Multiplying Fractions**• Focus: Develop an algorithm to multiply fractions**3.3 Multiplying Fractions**• We have seen how to multiply fractions by whole numbers.**3.3 Multiplying Fractions**• Multiply the 5 by 18 Method 1 - reduce at end • Reduce by dividing the numerator and denominator by 6**3.3 Multiplying Fractions**• Reduce by dividing 18 and 6 by 6. You must do the same to a numerator and denominator. Method 2 - reduce at start 3 • Multiply the numerators, then the denominators. 1**3.3 Multiplying Fractions**• Example**3.3 Multiplying Fractions**• Example Split the coloured sections into two parts. 1 1 Keep one of the two parts.**3.3 Multiplying Fractions**• Example Divide 5 out of 10 in the numerator and out of 5 in the denominator. 2 3 Divide 2 out of 6 (or 2) in the numerator and out of 2 in the denominator. 1 1**Unit 3: Operations with Fractions**3.4 Multiplying Mixed Numbers**3.4 Multiplying Mixed Numbers**• Focus: Apply knowledge of multiplying fractions to multiply mixed numbers**3.4 Multiplying Mixed Numbers**To multiply mixed fractions, change the fraction into an improper fraction. Remember: Improper fraction Mixed fraction**3.4 Multiplying Mixed Numbers**• To change from mixed to improper: new numerator whole number x = denominator + numerator**3.4 Multiplying Mixed Numbers**• Convert to improper fractions:**3.4 Multiplying Mixed Numbers**• To convert to mixed fractions subtract the denominator from the numerator.