2 Vocabulary Week 3Reciprocal – the fraction you get once you turn the fraction upside down, meaning the numerator becomes the denominator and the denominator becomes the numerator. Ex: 2/3 is the reciprocal of 3/2.Product – the answer to a multiplication problem.Improper Fraction – fraction where the numerator is larger than the denominator
4 Standard:MCC5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Objective:Students will learn about reciprocals and their importance in dividing fractions.Students will be able to convert a whole number and mixed number to a fraction to solve an equation where a fraction is divided by a whole number or a mixed number.
5 Reciprocals & Canceling Multiplying and Dividing Fractions
6 What is a reciprocal?The fraction you get once you turn the fraction upside down.
7 What pattern do you see here? 2/3 x 4/5 = 8/151/2 x 4/7 = 4/145/6 x 1/12 = 5/72What pattern do you see here?4/8 x 1/2 = 4/16 = 1/41/2 x 4/7 = 4/14 = 2/71/5 x 3/9 = 3/45 = 1/15
8 Reciprocal of a Fraction To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.Examples:FractionReciprocal3/85/61/319/7
9 Reciprocal of a Mixed Fraction To find the reciprocal of a Mixed Fraction, we must first convert it to an Improper Fraction, then turn it upside down.Example: What is the reciprocal of 2 1/3 ?Convert it to an improper fraction:2 1/3 = 2. Turn it upside down: The Answer is:
10 So what rule can we write? What pattern do you see?2/3 x 3/2 = 6/6 = 11/2 x 2/1 = 2/2 = 15/6 x 6/5 = 30/30 = 1So what rule can we write?
12 Canceling to Solve Fraction Multiplication Problems
13 Rules for Multiplying Fractions There are 3 simple steps to multiply fractions:1. Multiply the top numbers (the numerators).2. Multiply the bottom numbers (the denominators).3. Simplify the fraction if needed.Let’s add “canceling whenever possible’, where could we add this step in the list above?
15 Rules for Multiplying Fractions by Whole Numbers There are 4 simple steps to multiply fractions by whole numbers:1. First turn the whole number to a fraction by placing the whole number over 1. ex: 3 is 3/12. Multiply the top numbers (the numerators).3. Multiply the bottom numbers (the denominators).4. Simplify the fraction if needed.