DIVIDING FRACTIONS!

Divide a whole number by a unit fraction

2 WAYS! METHOD #1 of dividing fractions: Create equivalent fractions and create a common denominator for both fractions. Using the newly created equivalent fractions, divide across LET’s WATCH! using-the-common-denominator using-the-common-denominator number number nonunit-fraction nonunit-fraction

Let’s Practice! 2 divided by 1/4: 2/1 divided by 1/4: Common denominator: 4 8/4 divided by 1/4 = 8

Two numbers are reciprocals if their product is 1. A reciprocal of a number (fraction) is when you “flip” the fraction’s numerator and denominator. EXAMPLE: 3/4 The reciprocal is: 4/3

Let’s Watch and Practice! dividing-by-a-number-gives-the-same-result-as- multiplying-by-its-reciprocal dividing-by-a-number-gives-the-same-result-as- multiplying-by-its-reciprocal reciprocals-by-thinking-about-inverse-relationship- between-multiplication-and-division reciprocals-by-thinking-about-inverse-relationship- between-multiplication-and-division fractions-problems-using-reciprocals fractions-problems-using-reciprocals fractions-using-the-reciprocal fractions-using-the-reciprocal

Look at the relationship between the fractions and. If you switch the numerator and denominator of a fraction, you will find its reciprocal. Dividing by a number is the same as multiplying by its reciprocal. 3 4 __ ÷ 4 = 624 = __

Additional Example 1A: Finding Reciprocals Find the reciprocal. 1 9 __ 1 9 = 1 Think: of what number is 1? 1 9 __ = 1 of is __ 9 1 The reciprocal of is __

Additional Example 1B: Finding Reciprocals Find the reciprocal. 2 3 __ 2 3 = 1 Think: of what number is 1? 2 3 __ = = __ of is __ 3 2 The reciprocal of is. 2 3 __ 3 2

__ = 1 Write 3 as. 1 5 __ 5 16 __ 16 5 __ = = 1 80 __ of is __ 5 16 __ The reciprocal of is __ 5 16 __ 16 5 __ Additional Example 1C: Finding Reciprocals Find the reciprocal. 3

Check It Out: Example 1A Find the reciprocal. 1 4 __ 1 4 = 1 Think: of what number is 1? 1 4 __ = 1 of is __ 4 1 The reciprocal of is __

Check It Out: Example 1B Find the reciprocal. 4 5 __ 4 5 = 1 Think: of what number is 1? 4 5 __ = = 1 20 __ of is __ 5 4 The reciprocal of is. 4 5 __ 5 4

1 8 Check It Out: Example 1C Find the reciprocal. 4

Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. ÷ __ 8 7 ÷ 7 = Rewrite as multiplication using the reciprocal of 7,. 1 7 __ Multiply by the reciprocal. 8 7 __ ____ = The answer is in simplest form. = 8 49 __

When you divide by a proper fraction, the quotient will be greater than the dividend. For example, since there are 8 halves in 4, 4  ½ = 8. Caution!

DO NOW

A juice container contains 2/4 quart of juice. Niasia pours 1/3 quart of the juice into a cup. How much juice is left in the container? There are 334 students in LV MOORE. If 2/5 of the students are girls, how many are boys? (do not leave it as 3/5 are boys – find the actual #) The recipe for cookies requires 4/5 cup of sugar. If Jonah wants to make 1/3 of the total recipe, how much sugar does he need for the adjusted recipe?

REVIEW! Write an equivalent fraction for: 7/8 Compare fractions! = 2/3 7/8 5/6 7/18 4/9 + 5/6 1 5/ /3 Calculate the perimeter of a triangle with 3 sides measuring: 5/6, 7/8, 1 ¾ 5/11 * 2/3 6 ½ divided by 6/7

Relationship between multiplication and division (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3 How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers ÷ 5 6 __ 5 6 ÷ = Rewrite as multiplication using the reciprocal of,. 3 2 __ Simplify before multiplying. 5 6 __ ____ = You can write the answer as a mixed number. = 5 4 __ Multiply. = __

Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ __ Write the mixed numbers as improper fractions. 2 = and 1 = __ Rewrite as multiplication ______ = You can write the answer as a mixed number. = __ 1 12 __ Simplify before multiplying. = __ 2 ÷ 1 = ÷ 3 4 __ 1 12 __ 11 4 __ __ 11 4 __ 1 12 __ 11 4 __ __ Multiply. =

Check It Out: Example 2A Divide. Write each answer in simplest form. ÷ __ 2 3 ÷ 3 = Rewrite as multiplication using the reciprocal of 3,. 1 3 __ Multiply by the reciprocal. 2 3 __ ____ = The answer is in simplest form. = 2 9 __

Check It Out: Example 2B ÷ 7 10 __ 7 10 __ ÷ = Rewrite as multiplication using the reciprocal of,. 5 1 __ Simplify before multiplying __ ____ = You can write the answer as a mixed number. = 7 2 __ Multiply. = __

Check It Out: Example 2C 3 ÷ __ Write the mixed numbers as improper fractions. 3 = and 1 = __ Rewrite as multiplication ______ = You can write the answer as a mixed number. = __ Simplify before multiplying. = __ 3 ÷ 1 = ÷ 2 3 __ __ 10 9 __ 11 3 __ __ 9 10 __ Multiply. =

DO NOW Find the reciprocal Divide. Write each answer in simplest form. 3. ÷ ÷ 2 5. Rhonda put 2 pounds of pecans into a -pound bag. How many bags did Rhonda fill? 1 11 __ 8 13 __ __ 13 8 __ 1 35 __ , or 1 11 bags

1. Identify the reciprocal of. A. –15 C. B. D. 15 Lesson Quiz for Student Response Systems

2. Identify the reciprocal of. A. 15 C. B. 7 D. Lesson Quiz for Student Response Systems

3. Divide and identify the answer in the simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

4. Divide and identify the answer in the simplest form. A. C. B. D. Lesson Quiz for Student Response Systems

Dividing Fractions Math Journaling – Explain in words what it means to divide a whole number by a fraction and 2 fractions. How do you use multiplication to divide any number by a fraction?