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In this lesson, you will learn the principles of dividing mixed numbers by fractions and vice versa. By conceptualizing division in terms of equal groups, you can better understand the results. Discover how dividing a number doesn't always yield a smaller answer, and explore common misconceptions. Through practical examples, you'll analyze various problems, estimate quotients, and develop a mental strategy for division. This lesson equips you with insights for effectively handling fractions and mixed number divisions.
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What would happen if you divided a mixed number by a fraction? What would happen if you divided a fraction by a mixed number? I wonder… _ = ?
In this lesson you will learn how to divide mixed numbers and fractions by thinking about equal groups.
2 _ = 4 1 whole 1 whole _ 2 = 1 whole 1 whole 2 1 3 4 1 2 _ = 2
A common mistake is to think that dividing a number always leads to an answer that is smaller than the number being divided. _ 2 = 2 _ = 4 Dividend < Divisor Dividend > Divisor Quotient < 1 Quotient > 1
My answer should be more than 1. 1 _ = ? 2 1 whole 1 whole 1 whole This answer makes sense because it is more than 1. 1 whole 1 whole 1 set of 1 set of
My answer should be less than 1. 1 _ 2 = ? 1 whole 1 whole 1 whole 1 whole 1 whole 1 whole 1 whole This answer makes sense because it is less than 1. One set of 2…
My answer should be more than 1. 2 _ = ? 3 ? 1 whole 1 whole 1 whole 1 whole 1 whole 1 whole 1 whole 1 whole This answer makes sense because it is more than 1. of 1 set of 1 set of 1 set of
In this lesson you have learned how to divide mixed numbers and fractions by thinking about equal groups.
_ 1 = 1 whole 1 whole 1 whole 1 whole
Create a division problem using both a fraction and a mixed number that would result in a quotient of . • Create a division problem using both a fraction and a mixed number that would result in a quotient of 2.
Dividend > Divisor Dividend <Divisor Quotient < 1 Quotient > 1 • Analyze the following division problems. For each problem, estimate if the quotient will be less than 1 or greater than 1. _ 2= 1 _ = _ =
of what 1 _ = 2 number is 1 ? of 2 • The thought bubble above shows a different way to think about the problem. is 1. Think: of what number is 2 ? • Use this method of thinking to mentally calculate 2_ . • (Check by multiplying.)
2 _ = _ 1=
