Chapter 3 Fractions

The Meaning Of a Fraction Fraction = Part of a Whole 3 4 = Numerator Top Number? Bottom Number? = Denominator Pages 67 – 68

What do they mean? Numerator = number of objects that are being looked at Denominator = number of total equal parts that make up the Whole Note: the fraction bar means to divide the numerator by the denominator Pages 67 – 68

Easy Way To Remember! 3 4 Numerator = North What you have Divided by Whole Amount Denominator = Down Pages 67 – 68

Equivalent Fractions There are many ways to write the same fraction. These are fractions that have different numbers but are the same value. 1 2 2 4 3 6 4 8 26 52 Page 69

Reducing Fractions Are the numerator and denominator both even? Divide by 2 Add the digits of the numerator separate from the digits of the denominator. Do they add up to a number that is divisible by 3? Divide by 3. Do the numerator and the denominator end in a 0 or 5? Divide by 5 Page 70

Reducing Fractions You just have to try 7, 11, and 13. A fraction in it’s lowest terms cannot be reduced. Page 70

Converting Mixed Numbers to Improper Fractions 2 3 9 ? 9 = Multiply the 9 and the 2. Then add the 3 to find the new numerator. Page 71

Renaming Improper Fractions Divide the numerator by the denominator to find the whole part. Any reminder is the fractional part. Page 72

Writing Fractions as Decimals To convert a fraction to a decimal, divide the numerator by the denominator. Follow directions about where and when to round. Pages 73 – 74

Writing Decimals as Fractions The denominator of the fraction will have as many zeros as there are decimal places in the original decimal number. Don’t forget to reduce Page 75

Multiplying Fractions Multiply the numerator by the numerator and the denominator by the denominator Then reduce Pages 76 – 77

Multiplying Fractions by Whole Numbers Any whole number can be written as a fraction by inserting a 1 in the denominator. Then multiply as you would any other fractions Page 78

Multiplying Mixed Numbers Change the mixed number to an improper fraction. Then multiply. Before you multiply a mixed number by a whole number, convert the mixed number to an improper fraction. Pages 79 – 80

Reciprocals Write each number as a fraction. Then reverse the positions of the numerator and the denominator. Page 81

Dividing Fractions First, change the divisor (or the second fraction) to its reciprocal. Then multiply. Pages 82 – 83

Dividing Mixed Numbers First change both numbers to fractions. Next, change the divisor to its reciprocal. Then multiply fractions. Page 84

Solving Equations Using Multiplication and Division To solve a variable equation you must isolate the variable. To do this move all numbers to the other side by performing the opposite operation that is being done to both sides. Pages 85 – 86

Finding Common Denominators List the multiples of the larger number until you find a multiple of the smaller number Then calculate the numerators Page 88

Comparing Fractions If the numerators are all the same As the denominator gets bigger the fraction gets smaller Page 89

Comparing Fractions Fractions that have the same denominator compare the numerator If they don’t have the same denominator or numerator change the fractions so they have common denominator. Page 89

Adding Fractions To add fractions with like denominators, add the numerators. The denominator stays the same. When adding fractions with different denominators, first find a common denominator. The least common denominator (LCD) is the smallest number that can be evenly be made by each denominator Pages 90 – 91

Subtracting Fractions To subtract one fraction from another, you must have like denominators. When denominators are alike, you subtract one numerator from another. Page 92

Adding Mixed Numbers Rewrite the fractions with a common denominator. Add the whole numbers. Then add the fractions. Then convert the sum to a proper mixed number or a whole number Pages 93 – 95

Subtracting Mixed Numbers When subtracting mixed numbers, subtract the fraction from the fraction and the whole number from the whole number. Be sure that the fractions have a common denominator. Be careful to line up whole number under the whole number and fraction under fraction. You can borrow 1 from a whole number and convert it into a fraction with equal numerator and denominator Pages 97 – 99