Understanding Division of Fractions 6. NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions,

Objectives/ Learning Statements I can Interpret and compute quotients of fractions I can fluently solve word problems using the quotients of fractions. I can fluently solve problems involving division of fractions by fractions I can fluently solve and model problems dividing fractions by whole numbers and whole numbers by fractions.

Words you should Know Dividend Divisor Quotient Factor Multiple Reciprocal multiplicative inverses visual fraction model Unit fraction Simplify to lowest terms Partitive Model Measurement Model Mixed Number Improper Fraction Remainder Expression Equation Area = Length X Width Area ÷ Length = Width Area ÷ Width = Length

What is Division? Dividend ÷ Divisor = Quotient Division can be defined as “ A part or whole being shared equally”. Notice that the Dividend always comes first in the equation and refers to what is being shared. Also, notice that the second part of the equation directly behind the division symbol is called the Divisor. Depending on the type of question , you are answering the divisor can describe 2 different things based on 2 different models called Partitive and Measurement . The answer to a division problem what’s called a quotient . The Quotient or answer to a division number sentence can also describe 2 different things based on the Partitive and Measurement model. It is important to know what each part of a division equation represents and to place each part in the correct order when setting up an equation to get the correct quotient. Quick tips to remember Quotient × Divisor= Dividend Quotient ÷ Dividend = Divisor Quotient ÷ Divisor= Dividend Try applying it using some real world whole numbers.! What operation can we use to check our Division? Multiplication

Partitive Model Partitive Model’s Divisor The divisor describes how many ( people, rooms, groups, etc. ) are sharing something. Example 6 ÷2 = 3 The divisor 2 could possibly be describing 6 books shared equally by 2 people, or 2 classrooms or, or 2 groups of students. Partitive Model’s Quotient The quotient describes How much of the whole or part being shared (Dividend) each group or person will receive. So if 6 books are shared equally by 2 groups, then each group will receive 3 books.

Measurement Model Measure Model’s Divisor Measure Model’s Quotient . Divisor often describes the size of each piece that will be equally shared. Example 6 ÷ 1 3 = 18 The divisor 1 3 could possibly describing a 6 foot log being equally cut into smaller logs that are each 𝟏 𝟑 of a foot. Quotient describes “how many groups can be made out of what is being shared?” So, if a 6 foot log Is equally chopped into smaller logs that 1/3 of a feet each. 18 smaller logs can be made from the 6 foot log . 1/3 is a unit fraction because it has a numerator of 1.

The Division symbol ÷/ 𝑛 𝑑 The division symbol can be used to represent a fraction. The fraction symbol can be used to represent a division expression. More Examples 3 friends share 5 candy bars. 5 ÷3= 5 3 * The candy bars are being shared ( Dividend) so must come first in the expression. So each friend will receive 5 3 or 1 2 3 pieces of the candy bar. Example The Expression 5 ÷2 can be written as 5 2 Remember the operation of Division is not Commutative, therefore, order matters. So, the Expression 2÷𝟓 can be expressed as 𝟐 𝟓 .

Below are some Common Misconceptions and Errors related to division Below are some Common Misconceptions and Errors related to division . ( OH NOO!!) What would you tell someone to fix them. SKILLS for 6.NS.1 ( SEE KHANACADEMY “ 6.ns.1.” FOR Practice and support after teacher modeling ) Divide whole numbers by fractions Divide fractions Dividing Fraction Word Problems Understanding Dividing Fractions by fractions 1.) order doesn’t matter when setting up an equation for dividing 2.) All division problems are the same. 3.) Fractions have nothing to do with division.

Note- taking Steps Examples