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# Fractions

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1. Fractions A Review of the Basics

2. But First…We Remind You of… • Factors and Multiples

3. What are Factors • Numbers that multiply together to make our “given” number Greatest Common Factor (GCF) • The greatest common factor is the largest factor that two numbers share.

4. Example 12 42 1 x 12 1 x 42 Factors of 12: 1, 2, 3, 4, 6,12 2 x 21 2 x 6 3 x 14 3 x 4 4 x ?? 4 x 3 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 5 x ?? 6 x 7 7 x 6 Common Factors: 1, 2, 3, 6 Greatest Common Factor: 6

5. What is the GCF of 18 and 27? 18 27 Factors of 18: 1, 2, 3, 6, 9, 18 1 x 18 1 x 27 2 x ? 2 x 9 3 x 9 3 x 6 Factors of 27: 1, 3, 9, 27 4 x ? 5 x ? 4 x ? 6 x ? 5 x ? 7 x ? Common Factors: 1, 3, 9 8 x ? 6 x 3 9 x 3 GCF: 9

6. What is the GCF of 48 and 60? Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 48 60 1 x 48 1 x 60 2 x 30 2 x 24 3 x 20 3 x 16 4 x 15 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 4 x 12 5 x 12 6 x 8 6 x 10 Common Factors: 1, 2, 3, 4, 6, 12 GCF: 12

7. What are Multiples • A multiple is formed by multiplying a given number by the counting numbers. Ex. “x” by 1, 2, 3, 4, 5, 6 etc. Least Common Multiple (LCM) • the smallest number that is common between two lists of multiples.

8. EXAMPLE: Find the LCM of 12 and 18 • The multiples of 12: • 12 x 1 = 12 • 12 x 2 =24 • 12 x 3 = 36 • 12 x 4 = 48 • 12 x 5 =60 • The multiples of 18: • 18 x 1 = 18 • 18 x 2 = 36 • 18 x 3 = 54 • 18 x 4 = 72 • 18 x 5 = 90

9. 12, 24, 36, 48, 60 18, 36, 54, 72, 90 The first number you see in both lists is 36. The least common multiple of 12 and 18 is 36.

10. Example 2: Find the LCM of 9 and 10 9, 18, 27, 36, 45, 54, 63, 72 81, 90, 99 10, 20, 30, 40, 50, 60, 70, 80 90, 100, 110 If you don’t see a common multiple, make each list go further. The LCM of 9 and 10 is 90

11. Example 3:Find the LCM of 4 and 12 4, 8, 12, 16 12, 24, 36 Answer: 12

12. Example 4:Find the LCM of 6 and 20 6, 12, 18, 24, 30, 36 42, 48, 54, 60 20, 40, 60, 80, 100, 120 Answer: 60

13. What are Fractions? • Parts of a whole. • Numbers between two whole numbers Example

14. Parts of a Fraction Numerator: The PART how many of the whole we have Denominator: The WHOLE  how many pieces the whole has been broken into.

15. Mixed Numbers and Improper Fractions

16. Proper Fraction • a numerator that is less than its denominator. • Value is between 0 and 1 • Ex.

17. Improper Fraction • Numerator that is more than or equal to its denominator. • Value is greater than 1 or less than -1. • Ex.

18. Mixed Number • shows the sum of a whole number and a proper fraction. • Ex.

19. Writing Mixed Numbers as Improper Fractions • Multiply denominator by whole number. • Add the product and the numerator. • The resulting sum = numerator of the improper fraction. • The denominator stays the same.

20. Example 4 2 14 3 3

21. Writing Improper Fractions as Mixed Numbers • divide the denominator into the numerator. • quotient = whole number • remainder = numerator of the fraction. • divisor = denominator of the fraction.

22. Example 2 whole number 13 5 13 5 10 3 numerator denominator 3 2 5

23. Equivalent Fractions Fractions that are the same amount, but with different numerators and denominators. 2 4 = 8 4

24. Creating Equivalent Fractions • Multiply the numerator and denominator by the same number. We can choose any number to multiply by. Let’s multiply by 2. 3 x 2 6 So, 3/5 is equivalent to 6/10. = x 2 10 5

25. If you have larger numbers, divide the numerator and denominator by the same number. ÷ 7 Divide by a common factor. Is the same as Factors of 28 1 28 2 14 4 7 Factors of 35 1 35 5 7 ÷ 7

26. Fractions in Simplest Form Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1. Examples of fractions that are in simplest form: 4 2 3 8 5 11

27. Writing Fractions in Simplest Form. • Find the greatest common factor (GCF) of the numerator and denominator. • Divide both numbers by the GCF.

28. Example: 5 20 ÷ 4 = Simplest Form 7 ÷ 4 28 20: 1, 2, 4, 5, 10, 20 20 28 28: 1, 2, 4, 7, 14, 28 1 x 20 2 x 10 4 x 5 1 x 28 2 x 14 4 x 7 Common Factors: 1, 2, 4 GCF: 4 We will divide by 4.

29. Comparing and Ordering Fractions

30. Strategy • Must make denominators the same. • Compare the numerators.

31. Writing Equivalent Fractions Easy way • Find a common denominator is to multiply the two original denominators. 5 3 > 4 6 6 x 4 = 24 20 > 18 x 4 x 6 18 20 24 24

32. Another way • Find the LCM of both denominators. 7 5 < 9, 18, 27, 36, 45 9 12 12, 24, 36, 48, 60 20 < 21 x 3 x 4 20 21 36 36

33. Ordering Fractions • Find the LCM of the denominators. • Use the LCM to write equivalent fractions. • Put the fractions in order using the numerators.

34. Example - Order from Least to Greatest: 3 2 1 5 8 4 x 8 x 5 x 10 15 16 10 40 40 40 8, 16, 24, 32, 40, 48 1/4 < 3/8 < 2/5 5, 10, 15, 20, 25, 30, 35, 40 4, 8, 12, 16, 20, 24, 28, 32, 36, 40