 # 6.6a Solve problems that involve +, -, x, and / with fractions and mixed numbers, with and without regrouping.

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6.6a Solve problems that involve +, -, x, and / with fractions and mixed numbers, with and without regrouping

SOL 6.6a pg 30 STUDENTS ARE GIVEN A HANOUT FOR THIS WITH KEY WORDS, EXAMPLES, AND THE SOLVE CHART addition The act or process of combining numerical values, so as to find their sum sum An amount obtained as a result of adding numbers subtraction The arithmetic operation of finding the difference between two quantities or numbers difference An amount obtained as a result of subtracting numbers multiplication An arithmetic operation that is equivalent to repeated addition; the inverse of division; the product of two numbers is computed; "the multiplication of four by three gives twelve"; "four times three equals twelve". reciprocal Any two numbers whose product is 1. Example: ½ and 2 are reciprocals because ½ X 2 = 1 product An amount obtained as a result of multiplying numbers division The operation of determining how many times one quantity is contained in another; the inverse of multiplication. quotient An amount obtained as a result of dividing numbers numerator The expression written above the line in a fraction denominator The expression written below the line in a fraction that indicates the number of parts into which one whole is divided. improper fraction A fraction in which the numerator is larger than or equal to the denominator. The value of an improper fraction is greater than or equal to one. mixed number A numerical value that combines a whole number and a fraction simplest form A fraction is in simplest form when the greatest common factor of the numerator and denominator is 1. simplify To reduce the numerator and the denominator in a fraction to the smallest form possible. To divide the numerator and denominator by the GCF is simplifying a fraction. LCD The least common multiple of the denominators of two or more fractions. Example: 6 is the least common denominator of 2/3 and 1/6. estimate To make an approximate or rough calculation, often based on rounding Pg. 29 Improper Fractions the numerator part greater or equal to the denominator ex-17/2 or 5/5 How to make an improper to a mixed: DIVIDE the numerator by the denominator Practice- 1. 5/2 2. 14/8 3. 4/4 Mixed Fractions a whole number plus a fraction ex-2 ½ or 1 ¼. How to make a mixed an improper: Multiply the whole number by the denominator, then add on the numerator. This is your new numerator. The denominator stays the same! Practice- 1. 2 ¼ 2. 5 ¾ 3. 4 1/5 Remember to simplify whenever possible (GCF)!

Adding Fractionspg 32 Find the least common denominator (LCM) and make equivalent fractions 2/3 = 8 /12 + 3/4 = 9 /12 17/12 = 1 5/12 With mixed numbers you can change your mixed to improper then equivalents 3 ½ = 7/2 = 14 /4 + 2 ¾ = 11/4 = 11/4 25/4= 6 ¼ Or make equivalents and regroup 3 ½ = 2 /4 + 2 ¾ = 3 /4 5 5/4 = 6 ¼ Pg 31 Practice 1.4/5 + ¾ 2.3 ¾ + 2 ½ 3.7/12 + 5/6

Pg 33 Practice 1.5/8 – 5/12= 2. 2 7/8 - 5/6 = 3.10 – 4 ¾ = Subtracting Fractions pg 34 Find the least common denominator (LCM) and make equivalent fractions 2/3 = 8 /12 - 1/4 = 3 /12 5/12 With mixed numbers you can change your mixed to improper then equivalents 4 ½ = 9/2 = 18 /4 - 2 ¾ = 11/4 = 11/4 7/4 = 1 ¾ Or make equivalents and regroup 4 ½ = 4 2 /4 (borrow) 3 2/4 + 4/4= 3 6/4 -2 ¾ = 2 ¾ 2 ¾ - 1 ¾

Addition and Subtraction pg 36 Regrouping another way besides converting to impropers. Make equivalents and regroup 4 ½ = 4 2 /4 + 4/4 = 6/4 - 2 ¾ = 2 3 /4 1 ¾ 4 ½ = 4 2 /4 + 2 ¾ = 2 3 /4 5/4 7 1/4 Pg. 35 1.¾ + 1/3 = 2.2 3 /5 + 1/2 = 3.5 7/9 + 3 1/2 = 4. 6 – 5/7 = 5.1/8 + 1/6= 6.15 ½ - 3 2/3 = 7.12- 8 ½= 8.¾ + 1 ½ + 2 1/6 =

Pg 37 Practice 1.3/8 x 2/3= 2.1/3 x 5/6= 3.4/5 x 2/9= 4.9 1/3 x 2 2/3= 5.20 x 1 ½= 6.2/5 of 60= 7.18 ÷ 2 ½= 8.4 1/9 ÷ 6 2/3 9.¾ ÷ 2 = pg 38 Multiplying and Dividing Fractions 6.6a Multiplying * Any mixed or whole number must be made improper before multiplying 1. Multiply the numerator 2. Multiply the denominators Ex- ¾ x ½= 3/8 Ex- 2 ½ x 1 ¾ = 5/2 x 7/4= 35/8= 4 3/8 Ex- 3 x 5/6 = 3/1 x 5/6= 15/6 = 2 3/6= 2 ½ Ex- ½ OF 8 = ½ x 8= ½ x 8/1= 8/2= 4 Dividing 1.Flip (reciprocal) the second fraction and change the sign to multiplication. 2.Follow the steps for multiplication Ex ¾ ÷ ½ = ¾ x 2/1= 6/4= 1 ½ Ex 2 ¼ ÷ 5= 2 ¼ x 1/5 = 9/4 x 1/5= 9/20

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