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Dividing Whole Numbers
When dividing numbers, we can think about them in the form of grouping or sharing. For example: 10 Γ· 2 = ? This question can be thought of as βHow many groups of 2 can you get from 10?β or βShare 10 between 2β.
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What about Γ· π π = ? Thinking: βHow many π can I get from 4?β 4 Γ· π π = 8 1 2 4 From the diagram you can see that 8 halves make 4.
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Try these: 3 Γ· π π = 5 Γ· π π = 7 Γ· π π = 2 Γ· π π = 6 halves 6 10 10 halves 21 21 thirds 8 8 quarters
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Identify the equivalent fraction using the same denominator.
Thinking/Reasoning 3 Γ· π π = 5 Γ· π π = 7 Γ· π π = 2 Γ· π π = 6 6 2 Γ· = Γ· = Γ· = 8 4 Γ· = 6 6 1 6 1 = 6 Γ· 1 ( The 6 and 1 are the numerators) 10 10 10 1 Identify the equivalent fraction using the same denominator. 21 21 21 1 8 8 8 1
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How would you use the diagrams to answer the question:
Dividing Fractions How would you use the diagrams to answer the question: π π Γ· π π = ? π π Γ· π π = 1 From the diagram you can see that ONE red shaded part FITS into the blue shaded part. Thinking: How many π π s can I get from π π ? 1 2 π π One π π Γ· π π = because 1 1 1 = 1
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How would you use the diagrams to answer the question: π π Γ· π π = ?
Another example: How would you use the diagrams to answer the question: π π Γ· π π = ? π π Γ· π π = π π From the diagram you can see that HALF the brown shaded part FITS into the yellow shaded part. Thinking: How many π π s can I get from π π ? Half 1 3 π π
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So, So far the denominators have been the same.
What will happen when the denominators are different? Thinking: How many π π s can I get from π π ? π π Γ· π π = π π Five sixths How would you use diagrams to answer this question? First find the equivalent fraction, using the common multiple as the denominator: π π = π ππ , π π = π ππ π π = π ππ π π = π ππ So, π ππ Γ· π ππ = π π
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Use diagrams/equivalence to answer these: 1) 3 4 Γ· 3 4 =
Independent activity Use diagrams/equivalence to answer these: 1) Γ· = 2) Γ· = 3) Γ· = 4) Γ· = 5) Γ· = 3 3 1 4 3 5 8 3 5 6 10 5 6
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Do you get the same answer using the diagrammatic method? Show how.
What is the rule for dividing fractions? 3 4 Γ· = 3 4 8 3 x Keep the first fraction (the dividend); 2. Change the Γ· to X; = 3 π₯ 8 4 π₯ 3 Turn the second fraction (the divisor) upside down (invert it). = 4. Apply rules of multiplying fractions. Do you get the same answer using the diagrammatic method? Show how. = 2
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Try these questions. (Answer using diagrams/written method)
Challenge 5: True or False Show your working to explain your choice of answer. Challenge 1: Challenge 2: Challenge 3: Challenge 4: 1 2 Γ· = 1 3 Γ· = 1 4 Γ· = 1 5 Γ· = 1 10 Γ· = 6) Where possible, simplify your answers. 2 5 Γ· = 4 12 Γ· = 3 4 Γ· = 4 5 Γ· = 9 11 Γ· = Where possible, simplify your answers. 3 Γ· = 6 Γ· 2 5 = 3 8 Γ· 5 = 2 5 Γ· 7= Where possible, simplify your answers. 1 6 Γ· = Γ· = Γ· 5 = Γ· = Γ· = Where possible, simplify your answers. 1 3 Γ· = 2 9 5 8 Γ· = 9 16 9 6 Γ· = Γ· 2 3 = 4 Γ· =
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All answers marked in red can be simplified.
Solutions Challenge 1: Challenge 2: Challenge 3: Challenge 4: Challenge 5: 2 5 Γ· = 6 10 4 12 Γ· = 3 4 Γ· = 4 5 Γ· = 9 11 Γ· = 3 Γ· = 12 6 Γ· 2 5 = 30 2 3 8 Γ· 5 = 3 40 2 5 Γ· 7= 2 35 1 6 Γ· = 5 48 Γ· = 60 6 Γ· 5 = Γ· = Γ· = 1 3 Γ· = False 5 8 Γ· = False 9 6 Γ· = True Γ· 2 3 = 4 True Γ· = False 1 2 Γ· = 7 10 1 3 Γ· = 5 6 1 4 Γ· = 6 8 1 5 Γ· = 9 30 1 10 Γ· = All answers marked in red can be simplified.
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Is this statement True or False? Why?
Plenary Is this statement True or False? Why? π π Γ· π π = π π Γ· π π
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