Transcript Fractions
Fraction Facts • A fraction has a numerator and a denominator • A denominator can never be zero • You can multiply, divide, add and subtract fractions • A common factor is a number that both denominators are evenly divisible by • A common denominator is a number that both denominators share a factor with Denominator • The bottom number in a fraction is called a denominator, it represents the number of equal parts in a whole. • Example -In the picture shown below, there were four peices in one pizza. Four is the denominator because it is the number of parts to the whole. One piece was eaten, leaving three out of four pieces of the pizza. Numerator • The numerator is the top number in the fraction that represents the part of the whole being discussed • If the numerator is zero, the whole fraction is zero • If the numerator is larger than the denominator, the fraction is improper Improper Fractions • An improper fraction occurs when the numerator is larger than the denominator. Example above • Converting Mixed Fractions to Improper Fractions • To convert a mixed fraction to an improper fraction, follow these steps: • Convert 3 2/5 to an improper fraction. • Multiply the whole number by the denominator: • 3 × 5 = 15 • Add the numerator to that: • 15 + 2 = 17 • Then write that down above the denominator, like this: • 17/5 The four functions used • Multiplication • Division • Addition • Subtraction Multiplication • Multiply the numerators and put in the numerator of the result • Multiply the denominators and put in the denominator of the result Multiplication Practice Reducing • Also called simplifying • Divide by the Greatest Common Factor if possible to reduce a fraction to it’s lowest terms. • In the example on the bottom right, five is the Greatest Common Factor and is used to reduce the fraction. • What is a factor? Factors • A factor is a number that can be divided into another number without a remainder • 8’s factors are: • • • • 1 2 4 8 8/1 =8 8/2 = 4 8/4 = 2 8/8 = 1 • 3 is NOT a factor of 8, because it does not go into it evenly 8/3 = 2 with R=3 Common Factor • A common factor is a factor that two numbers have in common • For example, 6 is a factor of both 24 and 120 so it is a common factor of the two. • The Greatest Common Factor or (GCF) is the largest factor that the two numbers share. While 6 is a factor of both numbers, it is not the Greatest Common Factor because 24 is a larger common factor. Reduce the Fraction • Divide both the numerator and denominator by the Greatest Common Factor Practice Reducing Division • Just like multiplication with one more step • Invert the second fraction and multiply Division Practice Addition • To add two fractions, you must make sure they have a common denominator • After the fractions have a common denominator, the numerators are added together and the common denominator remains the same • After adding fractions they must be reduced Common Denominator • A common denominator is a number where both of the denominators share at least one factor that is not the number 1 • For example, if the denominators are 4 and 7, then a common denominator is 28. • 28 shares the factors 1, 2 and 4 with the number 4, and the factors 1 and 7 with the number 7. Addition - Let’s Try It together 1 1 + = 4 2 3 4 4 2 + = 16 8 1 2 6 17 13 25 12 16 8 + 2 3 = + 3 4 = 16 Addition Practice Subtraction Just like with adding fractions, in order to subtract fractions you must have a common denominator Review of common denominators on slides 17-19 Rather than adding numerators, you subtract them and then reduce. Subtraction - Let’s Try It Together 7 8 - 1 2 6 1 8 2 = 3 9 8 16 1 = 4 - 3 8 = 3 16 5 7 13 = 4 16 16 Subtraction Practice Reminders • Please don’t forget that I am here to help you! If you have any trouble understanding, please do not hesitate to contact me. Resources http://www.mathsisfun.com/fractions.html http://math.about.com/ http://www.math-aids.com/