Division of Fractions In this lesson we will be looking at the concept of division of fractions. This will include the division of complex fractions, improper fractions, fractions without whole numbers and fractions with whole Numbers or mixed numbers.

Division Symbols Remember that Math is a language. Therefore the symbols that we use have meaning. The following symbols all mean divide by or represent division. x y x x y y Hint: All of these division symbols are read as x divided by y. The variables x and y can represent any number.

Whole Numbers Whole numbers are the numbers beginning with zero and moving to the right. They do not include negative numbers. They are not fractions.

Fraction Fraction: The comparison of a part to a whole. ¼

Complex Fraction A fraction in which either the numerator, denominator, or both contain fractions. ½ Numerator 2 ½ ¾ Denominator ¾ 3

Improper Fraction A fraction in which the numerator is greater than the denominator Hint: 12/4 is equal to 3 wholes. The different ways to express fractions are representing the same amounts in different forms.

Mixed Numbers A mixed number is a whole number and a fraction expressed together. 1 whole 1/4 1 ¼ Hint: as an improper fraction this would be 5/4. 1/4

Story problem Maren ordered 4 bags of soil for her raised flower gardens. Each garden needs three- fourths (3/4) of a bag of soil. How many gardens can she fill completely with soil? Think Pair Share ¼ bag soil 1/3 of a garden A bag will complete one garden and a third of another. Can you express how many gardens 4 Bags will cover in terms of Gardens. Can you express how Much soil is left over in terms of bags.

Traditional approach 4 bags of soil divided by ¾ or the amount needed to complete one garden. Step 1: 4 ¾ = Step 2 4 X 4/3 = 16/3 Step 3 = 5 1/3 gardens.

Questions How do we divide by soil and end up answering in gardens using the traditional approach? Why do we invert and multiply in the standard algorith? Hint remember when we Think Pair Shared? What did that model reveal.

Further Questions Build a ratio table comparing garden to soil to show why the standard algorithm works. Use a number line to show why the standard algorithm works.

To get you started Ratio Table Garden 1 Soil 3/4

Number Line Model Lawns 0 3/4 1 Bags 1 1 1/3

Practice Problems Solve using the traditional method and one model Jenny is making brownies. It takes 2/3 of a bag of flour to make one batch of brownies. Jenny has 5 bags of flour. How many batches of brownies can she make?

Practice Problems continued Solve using the traditional method 3 ¼ = 5 4/3 = 2 3/8 = 6 5/6 = 1 2/3 5 6/3 =