 Greatest Common Factor: The largest integers that divides without remainders into a set of integers.  Equivalent Fractions: Fractions which have the same value even though they may look different.  Simplest Form: Reduced down as far as it will go.  Least Common Denominator: The lowest common denominator or LCD is the LCM of the denominators.  Mixed Number: A number consisting of an integer and a proper fraction.  Improper Fraction: A fraction in which the numerator is greater than the denominator.  Reciprocal: A fraction multiplied by it’s opposite.  U.S. Customary System: The units of measurement for length. ( 3/2, 2/3 )  Capacity: A measurement of how much a container will hold.

Examples of Adding Fractions Example 1: 2/8 + 5/8 = 2+5/8 = 7/8 Example 2: 2/9 + 6/9 = 2+5/9 = 7/9 Rules: When adding fractions make sure you always have the same denominator. Also, make sure that when you are done solving the problem you reduce.

Examples of Subtracting Fractions Example 1: 7/8 - 3/8 = 7-3/8 = 4/8 = ½ Example 2: 5/7 – 2/7 = 3/7 Rules: When subtracting fractions make sure you always have the same denominator. Also, make sure that when you are done solving the problem that you reduce.

Examples of adding mixed numbers Example 1: 7 1/ /3 = 18 2/3 Example 2: 8 2/ /6 = 14 6/6 = 15 Rules: When you add mixed numbers make sure that your denominator is the same then you can add the fractions. When you are done, make sure you reduce as far as possible. If you have an improper fraction then add the whole number to the numerator. If it goes over the denominator amount round to the next whole number.

Examples of Subtracting Mixed numbers Example 1: 5 7/6 – 4 7/6 = 1 Example 2: 6 1/6 – 3 2/3 = 6 1/6- 3 4/6 = 5 7/6 – 3 4/6 = 2 3/6 = 2 ½ Rules: When subtracting mixed numbers, make sure you always have the same denominator. If you run into not being able to subtract, subtract a whole number then add that to your fraction. Also, when you are done reduce the fraction as far as it will go.

Examples of Multiplying Fractions and Mixed numbers Example 1: 1/3 x ½ = 1x1/ 3x2 = 1/6 Example 2: ½ x 2/4 = 1x2/ 2x4 = 2/8 = ¼ Rules: When you are multiplying fractions you Do Not have to have the same denominator. All you have to do is multiply across. Make sure when you are done you reduce down as far as it will go.

Examples of Multiplying Mixed Numbers Example 1: 5 ¼ x 4 2/3 = 21/4 x 14/3 = 24 ½ Example 2: 2 ½ x 2 ¼ = 5/2 x 9/4 = 45/8 = 5 5/8 Rules: While multiplying mixed numbers, make sure that you Do Not have a whole number, take the denominator and multiply the whole number by the denominator. Then multiply the improper fraction. Then at the end, reduce your number as far as it will go.

Examples of Dividing Fractions Example 1: 5/9 ÷ 2/3 = 5/9 x 3/2 = 5/6 Example 2: ½ ÷ ¼ = ½ x 4/1 =4/2 = 2 Rules: When you are dividing fractions make sure you Skip the first fraction, Change the division sign to a multiplication sign, Flip the last fraction. At the end, make sure you reduce the fraction till as far as it will go.

Examples of Dividing mixed Numbers Example 1: 8 3/4 ÷ 2 5/8 = 35/4 ÷ 21/8 = 35/4 x 8/21 = 5/1 x 2/3 = 10/3 = 3 1/3 Example 2: 21 ÷ 3 ½ = 21 ÷ 7/2 = 21/1 x 2/7 = 3/1 x 2/1 = 6 Rules: When Dividing Mixed Numbers, multiply the denominator to the whole number. Then, Skip the first improper fraction, Change the division sign to a multiplication sign, Flip the last improper fraction, and then multiply. Make sure you reduce as far as it will go down.

Examples of Measuring in Customary Units Rules: The rules for measuring in customary units are looking for the different lines when using a ruler and round the measurement to the nearest customary unit.

Examples of Converting Customary Units Example 1: 63 ft. x 1/3 ft. = 21 ft. x I yd./3 = 21 Rules: Some Rules for converting customary units: Simplify the problem where you can. This means reduce if possible. Write whole numbers over 1 to make them into fractions. For metric conversions, remember that you are using a base of ten so all you have to do is move your decimal.

How Fractions are used in real life  Cooking Measurements, to measure ingredients.  Building Architecture, to measure the wood.  Restaurants, to measure portions.  Sports have half time, to give the players a rest.  Sewing, to figure out the amount of material needed.  Experiments in science, to give precise measures.  Scrap booking, measure sizes of the mattes.  Sales, to reduce the price down.  Paint Measurements, how much paint is needed.  Using serving size while you are eating, diet control.

Examples of Fraction Operations through Writing