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Lesson 4.3 Special Quotients
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Set the Purpose You have learned that multiplication and division have an inverse relationship. Today, you are going to use multiplication facts to understand some special division rules.
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Connect You have learned that in math, sharing equally is one meaning of division. Think of a situation where you might need to share 4 objects equally among 4 people.
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Example Sharing 4 snacks with 4 friends
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Word Problem Four friends want to share 4 books. How many books would each friend get? What number sentence could you use to show this?
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Word Problem What if there were 4 books and 1 person? Draw a picture to show how many books 1 person would get. What number sentence could you use to show this? What two multiplication sentences are related to these two division sentences?
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Wrong! What is wrong with this number sentence? 1 ÷ 4 = 4
What does that number sentence mean?
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Special Quotients How can you divide with 1 and 0?
A sandwich is cut into 8 pieces. How many people can have 1 piece each? 1group of 8
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Continued…. Dividing by 1
1 x 8 = 8 So, 8 ÷ 1 = Rule: Any number divided by 1 is itself.
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Practice! 9 ÷ 1 = 12 ÷ 1 = 1,200 ÷ 1 =
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1 as a quotient To find 8 ÷ 8, think 8 times what number equal 8?
8 x 1 = 8 So, 8 ÷ 8 = Rule: Any number (except 0) divided by itself is 1.
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Practice! 7 ÷ 7 = 21 ÷ 21 = 3,000 ÷ 3,000 =
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Dividing 0 by a number To find 0 ÷ 8, think 8 times what number equals 0? 8 x 0 = 0 So, 0 ÷ 8 = Rule: 0 divided by any number (except 0) is 0.
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Practice! 0 ÷ 5 = 0 ÷ 20 = 0 ÷ 100 =
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Dividing by 0 = NO!! To find 8 ÷ 0, think 0 times what number equals 8? You CAN’T! There is NO such number! Rule: You cannot divide by 0. * You cannot divide 8 of something into zero groups.
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Practice! Explain if it’s > , < , or = 8 ÷ 8 4 ÷ 4 3 ÷ 3 0 ÷ 6
8 ÷ ÷ 4 3 ÷ ÷ 6 0 ÷ ÷ 7
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Extra Practice
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Extra Practice
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Remember! 0 and 1 Any number (except 0) divided by itself is equal to 1. Any number divided by 1 is that number. Zero divided by any number (except 0) is zero. Zero cannot be a divisor.
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