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Division with Unit Fractions & Whole Numbers
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What you will learn from this videoWhat you will learn
- How to divide a whole number by a unit fraction.
- How to divide a unit fraction by a whole number.
- That this knowledge can help us make slime, musical instruments & make sure everyone gets their fair share of pie!
- Discussion Questions
Before Video
How can you use what you know about multiplication to find 32 ÷ 8?ANSWERThink what number I can multiply by 8 to get 32, and then use the multiplication fact to find the answer. 8 × 4 = 32, so 32 ÷ 8 = 4.
ANSWERInside a square, I drew 3 rows and colored one of the rows green to represent [ggfrac]1/3[ggfrac] . I drew 5 columns and colored three of the columns blue to represent [ggfrac]3/5[/ggfrac]. The answer is represented by the part of the square where the colors overlap. The answer is [ggfrac]3/15[/ggfrac].
[ggfrac]3/32[/ggfrac] of the back yard.
Ravi is not correct. He multiplied both the numerator and denominator of [ggfrac]2/3[/ggfrac] by 5. He should have just multiplied the numerator by 5, so the answer is [ggfrac]10/3[/ggfrac].
You can draw a circle to represent 1 and divide it in half. Each part represents [ggfrac]1/2[/ggfrac]. So you have two [ggfrac]1/2[/ggfrac]s. You keep drawing halves until you have five [ggfrac]1/2[/ggfrac]s. You find that [ggfrac]1/2[/ggfrac] × 5 = [ggfrac]5/2[/ggfrac] , so [ggfrac]2/5[/ggfrac] is the wrong answer.
After Video
You need [ggfrac]1/2[/ggfrac] cup of milk to make your favorite cake. You have 3 cups of milk. Describe a model that represents this situation and can help you find how many cakes you can make. ANSWERYou need to solve the equation 3 ÷ [ggfrac]1/2[/ggfrac] = ? Draw 3 circles to represent the 3 cups of milk. Each circle is divided in half and each half represents the [ggfrac]1/2[/ggfrac] cup of milk you need for each cake. You can count to find the number of half cups of milk you have. You have 6 half cups of milk. You can make 6 cakes.
I need to find the answer to 2 ÷ [ggfrac]1/4[/ggfrac] = ? First, I convert the division problem into a multiplication problem: 2 × 4. 2 × 4 = 8. I can make 8 birdhouses with the 2-yard-long wood board.
ANSWER[ggfrac]1/3[/ggfrac] ÷ 2 = [ggfrac]1/6[/ggfrac] . Each small piece is [ggfrac]1/6[/ggfrac] of the pie.
[ggfrac]1/6[/ggfrac] yard.
Delroy is not correct. To find the answer, you need to solve the equation 8 ÷ [ggfrac]1/4[/ggfrac] = ? To divide 8 by [ggfrac]1/4[/ggfrac], you change the division equation into the multiplication equation 8 × 4 = ? 8 × 4 = 32, so there are 32 one-fourth pieces.
- Vocabulary
- Division DEFINE
Finding how many equal groups or how many in each group.
Whole number –The counting numbers: 0, 1, 2, 3, 4, ... - Fraction DEFINE
A symbol that describes parts of a whole that is divided into equal parts. For example, [ggfrac]1/3[/ggfrac] or [ggfrac]2/3[/ggfrac].
- Unit fraction DEFINE
A fraction with a numerator of 1. For example, [ggfrac]1/5[/ggfrac] , [ggfrac]1/2[/ggfrac] or [ggfrac]1/10[/ggfrac]
- Equation DEFINE
A mathematical statement that uses an equal sign to show that two expressions are equal. For example, 3 × 4 = 12 or 16 ÷ 2 = 4 × 2.
- Partition DEFINE
Splitting into parts. For example, a circle can be partitioned into fourths.
- Multiplication DEFINE
Combining groups of equal size. You can think of multiplication as repeated addition.
- Opposite operations DEFINE
An operation that undoes another operation. Division and multiplication are opposite operations.
- Division DEFINE
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide
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Level 1
A pattern shows a triangle, rectangle, and pentagon. What is the next shape in the pattern? Explain.
Level 2
What are the next two numbers in the pattern? Explain how you know. 3, 6, 10, 20, 24, 48, 52, ____, ____
Level 3
Adam starts a pattern in sidewalk chalk. He tells Brianne that she can fill in the next number in the pattern using the rule “double plus 1.” What number should Brianne write? 1, 3, 7, 15, ____. Brianne starts another pattern with a new rule. She tells Adam he can fill in the next number, but there’s a challenge! Her rule is a little bit like the one he used, but it’s definitely not the same. What number should Adam write? What is Brianne's rule? 1, 6, 26, 106, ____.