Fractions Basics By Howard Rones

Numerator and Denominator Easy to remember! The Denominator is DOWN and the Numerator is NORTH.

Equivalent fractions represent the same fractional part of a whole. 1/2 2/4 4/8 Equivalent fractions represent the same fractional part of a whole.

Equivalent Fractions Look at these fraction bars. What fractions are equivalent to1/3? Here’s 1/3. 1 2 4 = = 3 6 12 Here’s 2/6. Here’s 4/12.

Equivalent Fractions Look at these fraction bars. What fractions are equivalent to ¾? Look at these fraction bars. What fractions are equivalent to ¾? Here’s 3/4. 3 6 9 = = 4 8 12 Here’s 6/8. Here’s 9/12.

Fractions Equivalent to 1 What fraction of the pizza is shaded? In each picture, one whole pizza is shaded. 4 8 =1 =1 4 8 6 =1 6 When the numerator and denominator are the same, the fraction is equal to 1.

Naming Equivalent Fractions Write three fractions that are equivalent to 2/3. 2 2 4 2 3 6 = = X X 3 2 6 3 3 9 one one In each case, we just multiplied by ONE so the new fraction must be equivalent to 2/3. 2 4 8 = X 3 4 12 one

Proper Fractions A proper fraction represents a part of a whole. The numerator must be smaller than the denominator. Examples: 4 3 1 5 11 9

Improper Fractions Improper fractions represent one whole or more than one whole. 4 is shaded blue. 4 4 is an improper fraction. 4

Improper Fractions 53 53 Each orange section is 1/3 of the rectangle. There are 5 sections shaded. is shaded 53 53 is improper.

Improper Fractions Improper fractions have numerators that are equal to or greater than the denominator. 6 23 9 5 11 9 …are all improper fractions.

Simplifying Fractions If the numerator and denominator have a COMMON FACTOR other than one, it can be simplified. Here, the 12 and the 15 have a COMMON FACTOR of 3. We can simplify by dividing the numerator and denominator by 3. 12 3 4 ÷ = 15 3 5 ÷

Simplifying Fractions Here, the 15 and the 25 have a COMMON FACTOR of 5. We can simplify by dividing the numerator and denominator by 5. 15 5 3 ÷ = 25 5 5 ÷

Simplifying Fractions Here, the 14 and the 49 have a COMMON FACTOR of 7. We can simplify by dividing the numerator and denominator by 7. 14 7 2 ÷ = 49 7 7 ÷

Simplifying Fractions We see the 40 and 60 both end in a zero. We can divide them both by 10. Then, we see the 4 and 6 are both even so we divide both by 2. Stop when the GCF is 1. 40 10 4 2 2 ÷ ÷ = = 60 10 6 2 3 ÷ ÷

Simplifying Fractions Here, the 12 and the 18 have COMMON FACTORS of 2, 3 and 6. 6 is the GREATEST common factor (GCF). If we divide by 6, we can simplify in one step. If we use the 2 or 3, it will take more steps. 12 6 2 ÷ = 18 6 3 ÷

Are these fractions equal? 5 10 ? 6 12 If two fractions are equal, their cross products are equal. 5 X 12 = 60 6 X 10 = 60 5 10 ? 6 12 60 = 60 The fractions are equal.

Are these fractions equal? 5 10 ? 7 11 If two fractions are equal, their cross products are equal. 5 X 11 = 55 7 X 10 = 70 5 10 ? 7 11 55 ≠ 70. The fractions are not equal.

More Equivalent Fractions Find the missing number in these equivalent fractions. 5 ? = 7 21 Think…7 X ? = 21. 7 X 3 = 21 so I’ll multiply the numerator and denominator by 3. 5 3 15 = X 7 3 21

More Equivalent Fractions Find the missing number in these equivalent fractions. 3 24 = 4 ? Think…3 X ? = 24. 3 X 8 = 24 so I’ll multiply the numerator and denominator by 8. 3 8 24 = X 4 8 32

More Equivalent Fractions Find the missing number in these equivalent fractions. 15 3 = 25 ? Think…15 ÷ ? = 3. 15 ÷ 5 = 3 so I’ll divide the numerator and denominator by 5. 15 5 3 = ÷ 25 5 5

Changing Improper Fractions to Mixed or Whole Numbers To change an improper fraction to a mixed number or whole number, think of it as a division problem. 5 = 5 ÷ 3 = 3 ) 5 3 1 2/3 3 ) 5 5 2 = 1 - 3 3 3 2

Changing Improper Fractions to Mixed or Whole Numbers To change an improper fraction to a mixed number or whole number, think of it as a division problem. 16 = 16 ÷ 4 = 4 ) 16 4 4 4 ) 16 16 = 4 - 16 4

Changing Mixed Numbers to Improper Fractions Here’s the “shortcut”. Follow the colors! 2 1 = 3 1 X 3 + 2 5 = 3 3

Changing Mixed Numbers to Improper Fractions Last one. Follow the colors! 4 3 = 5 3 X 5 + 4 19 = 5 5

Farewell Now that you know all the basics, you are ready to learn how to add, subtract and multiply fractions. We’ll leave division for your 6th grade teacher.