Sixer Guide to:

1. Sixer Guide to: Equivalent Fractions

2. You have exactly 30 seconds to do the following: Open you math Keytab to a new page Write today’s date on the left with you name on the right Underline today’s title which will be “Equivalent fractions”.

3. Equivalent fractions A fraction can have many different appearances, these are called equivalent fractions In the following picture we have ½ of a cake because the whole cake is divided into two equal parts and we have only one of those parts. But if we cut the cake into smaller equal pieces, we can see that = Or we can cut the original cake into 6 equal pieces,

4. = = Equivalent fractions A fraction can have many different appearances, these are called equivalent fractions Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same. Therefore, If you don’t like this, we can cut the original cake into 8 equal pieces,

5. = = = Equivalent fractions A fraction can have many different appearances, they are called equivalent fractions Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same. Wow, that’s confusing! Therefore, We can generalize this to whenever n is not 0 =

6. Equivalent Fractions One Whole 1

7. Equivalent Fractions Cut them in half

8. Equivalent Fractions Shown is one half 1 2 How many pieces we want How many pieces it’s cut into

9. Equivalent Fractions Shown is one half 1 2 NUMERATOR DENOMINATOR

10. Equivalent Fractions I cut my shape again I still show 1 2

11. Equivalent Fractions But I also show 2 4

12. Equivalent Fractions One half is EQUIVALENT TO 2 quarters 1 2 2 4

13. Equivalent Fractions 1 2 2 4 This symbol looks like an equals sign with a third line. It is the mathematical sign for EQUIVALENT TO - which means “is worth the same as”.

14. Equivalent Fractions We can use equivalent fraction to make our numbers easier to handle. Smaller numbers are SIMPLE 160 200 16 20 4 5 ÷ 10 ÷ 4 ÷ 10 ÷ 4

15. Equivalent Fractions Look for numbers that both the NUMERATOR and the DENOMINATOR can be divided by. We want numbers bigger than 1. 15 45 60 80 We call these COMMON FACTORS

16. Equivalent Fractions These numbers have 3 as a common factor. This means they can both be shared by 3. 15 45 ÷ 3 ÷ 3 60 80 ÷ 10 A common factor here is 10 ÷ 10

17. Equivalent Fractions 15 45 5 15 ÷ 3 ÷ 3 60 80 6 8 ÷ 10 ÷ 10

18. Equivalent Fractions 15 45 5 15 ÷ 3 ÷ 5 ÷ 3 ÷ 5 60 80 6 8 ÷ 10 ÷ 2 ÷ 10 ÷ 2

19. Equivalent Fractions 15 45 5 15 1 3 ÷ 3 ÷ 5 ÷ 3 ÷ 5 60 80 6 8 3 4 ÷ 10 ÷ 2 ÷ 10 ÷ 2

20. Equivalent Fractions If the top number is a 1, we know we can stop. 15 45 1 3 If the top and bottom number are not DIVISIBLE by the same number, we stop. 60 80 3 4

21. Equivalent Fractions They have no FACTORS in common other than 1 15 45 1 3 60 80 3 4 They have no FACTORS in common other than 1

22. You now have exactly 30 seconds to do the following: Open you math text to page 164

23. How do we know that two fractions are the same? More examples: is not reduced because 10 can divide into both 110 and 260. is reduced. is reduced To find out whether two fraction are equal, we need to reduce them to their lowest terms.

24. equal? reduce reduce reduce How do we know that two fractions are the same? Examples: Are and Now we know that these two fractions are actually the same!

25. reduce reduce reduce How do we know that two fractions are the same? Another example: Are and equal? This shows that these two fractions are not the same!