get all crazy with this “friend” Multiplying Fractions Let’s make fractions our friends! Now, let’s not get all crazy with this “friend” stuff, Mr. Russler. Chapter 9

Multiplying Fractions I have some great news when it comes to multiplying fractions… WE DON’T NEED COMMON DENOMINATORS! Are you sure? What’s that? Sweet! YES!

Multiplying Fractions When we multiply fractions, we can use the multiplication symbol: A raised dot: Or parenthesis: 𝟏 𝟑 x 𝟐 𝟓 𝟏 𝟑 ∙ 𝟐 𝟓 𝟏 𝟑 𝟐 𝟓

Multiplying Fractions Terms you need to know: numerator denominator Simplify – to reduce a fraction into its simplest form. Greatest Common Factor (GCF) – the greatest number that evenly divides both numerator and denominator. Reciprocal – the fraction you get when you exchange the numerator and denominator

Multiplying Fractions 𝟏 𝟑 ∙ 𝟐 𝟓 Let’s multiply the following: To multiply fractions → numerator x numerator denominator x denominator 𝟏 ∙ 𝟐 𝟑 ∙ 𝟓 = 𝟐 𝟏𝟓 *Then check to see if the answer can be simplified. 𝟐 𝟏𝟓 is reduced.

Multiplying Fractions 𝟑 𝟒 ×𝟓 Let’s try another one: Replace 5 with a fraction 𝟑 𝟒 × 𝟓 𝟏 3 Multiply numerators → Multiply denominators → 𝟑 ×𝟓 𝟒 ×𝟏 = 𝟏𝟓 𝟒 3 4 4) 15 = 3 𝟑 𝟒 12 3

Multiplying Fractions 𝟑 𝟖 ∙ 𝟐 𝟑 Let’s try another one: Multiply numerators → Multiply denominators → 𝟑 ∙ 𝟐 𝟖 ∙ 𝟑 = 𝟔 𝟐𝟒 𝟔 ÷ 𝟔 𝟐𝟒 ÷ 𝟔 = 𝟔 𝟐𝟒 The GCF of is 𝟔, so 𝟏 𝟒

RECIPROCALS = 𝟏 𝟐 𝟑 × 𝟑 𝟐 = 𝟔 𝟔 REMEMBER … RECIPROCAL MEANS FLIP Sometimes the product of two fractions is 1 These fractions are RECIPROCALS of each other Reciprocal – the fraction you get when you flip the numerator and denominator 𝟐 𝟑 × 𝟑 𝟐 = 𝟔 𝟔 = 𝟏 REMEMBER … RECIPROCAL MEANS FLIP

Find the reciprocal of each fraction RECIPROCALS Find the reciprocal of each fraction 𝟗 𝟏𝟎 𝟏𝟎 𝟗 𝟐 𝟓 𝟓 𝟐

Multiplying Fractions Your Turn! 𝟏. 𝟑 𝟕 ∙ 𝟏 𝟐 𝟐. 𝟒 𝟓 ∙ 𝟑 𝟒 Find the reciprocal of each fraction: 𝟑. 𝟑 𝟖 𝟒. 𝟒 𝟓 𝟓. 𝟑 𝟒 See how you did! 𝟏. 𝟑 𝟏𝟒 𝟐. 𝟑 𝟓 𝟑. 𝟖 𝟑 𝟒. 𝟓 𝟒 5. 𝟒 𝟑

9.2 Multiplication Shortcut Multiplying Fractions There is a shortcut!?! 9.2 Multiplication Shortcut

Multiplying Fractions Let me show you a simplifying method called cross-cancelling Reduce or cancel the “diagonals” before you multiply. Of course I can! 𝟑 𝟖 ∙ 𝟐 𝟑 = 𝟏 𝟒 ∙ 𝟏 𝟏 1 = 𝟏 𝟒 1 I think I get it! Can you show me another one? 4 1

Multiplying Fractions Let’s do a side-by-side. Standard method: Cross-cancel method: 𝟏𝟏 𝟏𝟐 ∙ 𝟏𝟒 𝟓𝟓 = 𝟏𝟓𝟒 𝟔𝟔𝟎 1 𝟏𝟏 𝟏𝟐 ∙ 𝟏𝟒 𝟓𝟓 7 = 𝟏 𝟔 ∙ 𝟕 𝟓 = 𝟕 𝟑𝟎 6 5 = 𝟕𝟕 𝟑𝟑𝟎 = 𝟕 𝟑𝟎 Cross-cancelling is fun, and it keeps the numbers way smaller!

Multiplying Fractions Cross-Cancelling Reduce or cancel the “diagonals” before you multiply. 1 𝟑 𝟒 ∙ 𝟒 𝟓 = 𝟑 𝟏 ∙ 𝟏 𝟓 = 𝟑 𝟓 1 2 6 𝟏𝟒 𝟐𝟓 ∙ 𝟑𝟎 𝟒𝟗 = 𝟐 𝟓 × 𝟔 𝟕 = 𝟏𝟐 𝟑𝟓 5 7

Multiplying Fractions Good luck! 𝟏. 𝟑 𝟖 ∙ 𝟖 𝟏𝟓 𝟐. 𝟏𝟒 𝟐𝟓 ∙ 𝟏𝟎 𝟐𝟏 3. 𝟑 𝟒 ∙ 𝟒 𝟓 See how you did! 1. 𝟏 𝟓 2. 𝟒 𝟏𝟓 𝟑. 𝟑 𝟓