Starter Simplify these fractions 12 16 56 91 121 132 44 55 57 76

Starter Simplify these fractions 3 4 8 13 11 12 4 5 3 4

Mixed Numbers and Improper Fractions Thursday, 22 November 2018 Mixed Numbers and Improper Fractions Objectives : To convert a mixed number to an improper fraction To convert an improper fraction into a mixed number

Mixed Numbers and Improper Fractions Here is 1 and 2 3 . If we count the thirds here we have 5 thirds. So 1 2 3 = 5 3 5 3 is called an improper fraction. This is a posh way of saying that the numerator is greater than the denominator.

Mixed Numbers and Improper Fractions Here is 2 and 3 5 . How many fifths do we have? 13. So 2 3 5 = 13 5

2 3 5 2 3 5 = 2×5 +3 5 = 13 5 Mixed Numbers and Improper Fractions Let’s find a way to do this without drawing out the bars every time. 2 3 5 If we’re counting in fifths, one whole is five fifths, so two wholes must be ten fifths. 2 3 5 = 2×5 +3 5 = 13 5

Mixed Numbers and Improper Fractions Ex1: Whole class. What is the animal hiding behind the fractions? Convert the mixed fraction find out! 1 3 4 3 1 2 7 4 7 1 4 7 2 1 6 2 4 5 2 1 2 1 6 7 1 1 3 1 1 7 1 5 6 2 2 3 3 1 5 3 1 4 3 6 7 Note: this is a revealer. Ask for answers. When a child names a box and gives you the correct answer, click on the box. 2 3 7 1 3 5 2 5 7 3 2 5 1 2 7

Mixed Numbers and Improper Fractions Ex2. Convert these mixed numbers into improper fractions. 2 1 7 2 2 5 1 1 2 3 3 4 1 2 3 2 1 3 1 4 7 1 4 5 1 1 5 2 6 7 3 1 6 1 3 5 2 5 7 3 2 3 3 5 6 2 1 2 1 1 6 3 1 3 2 2 3 3 3 7 BrainBox Extension: 𝑥 𝑦 10

Mixed Numbers and Improper Fractions Ex2. Convert these mixed numbers into improper fractions. 15 7 12 5 3 2 15 4 5 3 7 3 11 7 9 5 6 5 20 7 19 6 8 5 19 7 11 3 23 6 5 2 7 6 10 3 8 3 24 7 BrainBox Extension: 10𝑥+𝑦 10

17 5 =3 2 5 Mixed Numbers and Improper Fractions How about we work the other way? 17 5 =3 2 5 What is 17 5 as a mixed number? We can again use diagrams. Here’s 5 fifths. Here’s another 5 fifths. Now we have 10 fifths. This is the same as 2 wholes. Here’s another 5 fifths. Now we have 15 fifths. This is the same as 3 wholes. We have 15 fifths. We need to add 2 more to make 17.

17 5 17 5 =(17÷5) 𝑟 5 =3 2 5 Mixed Numbers and Improper Fractions Let’s find a way to do this without drawing out the bars every time. 17 5 If we’re counting in fifths, a whole is 5 fifths. So to find out how many wholes we have, we divide by 5. In this case 17 divided by 5 is 3. 17 doesn’t divide nicely by 5, though. We have a remainder of 2. We have 2 fifths left over. 17 5 =(17÷5) 𝑟 5 =3 2 5

A B C D Mixed Numbers and Improper Fractions 𝟓 𝟒 𝟏𝟗 𝟔 𝟐𝟔 𝟓 𝟐𝟑 𝟑 𝟐𝟎 𝟕 Let’s try some questions. The best way to learn is by doing! Convert these to mixed numbers and find the odd one out. A B C D 𝟓 𝟒 𝟏𝟗 𝟔 𝟐𝟔 𝟓 𝟐𝟑 𝟑 𝟐𝟎 𝟕 𝟒 𝟑 𝟗 𝟓 𝟏𝟎 𝟕 𝟕 𝟑 𝟏𝟕 𝟒 𝟏𝟓 𝟕 𝟏𝟗 𝟗 𝟏𝟏 𝟑 𝟐𝟖 𝟓 𝟒𝟏 𝟔 𝟖𝟖 𝟗

A B C D Mixed Numbers and Improper Fractions 1 𝟏 𝟒 𝟑 𝟏 𝟔 𝟓 𝟏 𝟓 𝟕 𝟐 𝟑 Let’s try some questions. The best way to learn is by doing! Convert these to mixed numbers and find the odd one out. A B C D 1 𝟏 𝟒 𝟑 𝟏 𝟔 𝟓 𝟏 𝟓 𝟕 𝟐 𝟑 A. All the others start with a prime number 2 6 7 1 1 3 1 4 5 1 3 7 A. All the others start with 1 2 1 3 4 1 4 2 1 7 2 1 9 B. All the others have two wholes 3 2 3 5 3 5 6 5 6 9 7 9 C. All the others have an odd number of wholes

Equivalent Fractions 5 QUICK QUESTIONS CHECK Now it’s time to check your learning. You’ll see five questions. They all have a 30 second timer. How many can you get right?

3 1 2 Convert to an improper fraction Equivalent Fractions Timer Question 1 Convert to an improper fraction 3 1 2 Timer

7 5 7 Convert to an improper fraction Equivalent Fractions Timer Question 2 Convert to an improper fraction 7 5 7 Timer

Equivalent Fractions Question 3 Convert to a mixed number 11 2 Timer

Equivalent Fractions Question 4 Convert to a mixed number 32 9 Timer

Equivalent Fractions Question 5 Which is bigger 20 7 𝑜𝑟 3 1 3 Timer

Equivalent Fractions Your answers: 7 2 54 7 5 1 2 3 5 9 3 1 3

Problem Solving Some pizzas Damon cuts his pizzas into eights. He eats 2 whole pizzas and 3 slices Brett cuts his pizzas into fifths. He eats 12 slices. Who ate more? Justify it.

Problem Solving 2 3 8 𝑜𝑟 12 5 19 8 𝑜𝑟 12 5 95 40 𝑜𝑟 96 40 Some pizzas Damon cuts his pizzas into eights. He eats 2 whole pizzas and 3 slices Brett cuts his pizzas into fifths. He eats 12 slices. 2 3 8 𝑜𝑟 12 5 19 8 𝑜𝑟 12 5 95 40 𝑜𝑟 96 40