Mixed Number Conversions: Improper Fractions & Patterns
Discover how to convert mixed numbers to improper fractions, analyze patterns in the answers, and solve related challenges through engaging content and visual representations.
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Presentation Transcript
Sharing ideas from last lesson If you share baguettes between people, they each get of a baguette. Fill in the gaps to give an answer that is an improper fraction Show this by using diagrams below.
How else could we write C and D? This is as an improper fraction C is 4 3 (four thirds) This is as a mixed number C is 11 3 (one and one third)
How else could we write C and D? D is 5 This is as an improper fraction 3 (five thirds) D is 12 This is as a mixed number 3 (one and two thirds)
Summary A mixed number is the sum of an integer and a proper fraction. What are the integers and the proper fraction of each of the following mixed number fractions. 3 4 22 31 1 2 5 3 . 7
How would we write this mixed number as an improper fraction? 23 4 = 11 4 Let s use a representation to help 1 2 0 How many quarters in total? How would we write this?
How would we write this mixed number as an improper fraction? =10 31 3 3 Let s use a representation to help 0 1 3 2 How many thirds in total? How would we write this?
Your turn Write the following mixed numbers as improper fractions 1. 14 5 4. 13 7 5. 2. 14 24 7 5 6. 3. 15 34 7 5 7. 4. 16 44 7 5 What do you notice about the answers in each column? Can you explain why the patterns occur in this way?
On your whiteboards 10 1 6 Challenge: What about this one? 8 6 7 a? ? 9 3 5
Write these sums as mixed numbers: 1 8+5 8+7 8 5 8+7 8+11 8 6 8+7 8+11 8 Write similar sums that would have the answer 41 8
Now can we covert the other way, from an improper fraction to a mixed number? 8 3= 22 3 0 1 2 Where would 1 go? How do you know? What about 2? Why? How would we write this as a mixed number?
Now can we covert the other way, from an improper fraction to a mixed number? 12 5= 22 5 0 1 2 Where would 1 go? How do you know? What about 2? Why? How would we write this as a mixed number?
You try these: 28 5 25 12 11 3 17 9 1 2 18 53 212 33 9 5 Challenge where a > b ? ?
Challenge: 4 n 1. If is an improper fraction and n is a 3 positive whole number, what value could n be ? 1 2015 100 2. The value of the fraction is between which two positive whole numbers? 20 and 21
True or false? Give reasons for your answers 1. proper fractions. Improper fractions are always greater than T 2. denominator five. There are five proper fractions with the F 3. A fraction can be classified into three groups proper fractions, improper fractions and mixed number fractions. T
