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6.6 (most often as word problems) a) multiply and divide fractions and mixed numbers; and (cannot use calculator) b) estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions (can use calculator) Info: Key Words Operation Question: Solve: (show your work) Final Answer: SOL 6.6a Pg. NO Calculator 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. Whole number is quotient, remainder is new numerator and denominator stays the same. 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! (see 6.4 fpr vocabulary) pg Key Words for Word ProblemsSubtraction- a-b Difference, fewer, more, left, less, minus, need to, remains, subtract, words ending “er” (comparing words) Addition- a + b add, altogether, both, in all, sum, total Multiplication- a(b ) a x b a•b OF, every, at this rate, times, multiplied by a*b Division- a/b a÷b a b per, split, divide, out of, each, ratio of Pg Adding Fractions (no regrouping) pg Practice 1. 4/9 + 1/3 Make equivalent fractions and then add 2/3 = 8 /12 + 3/4 = 9 /12 17/12 = 2. 3 ¼ 1 5/12 +2½ Mixed - Make equivalents and add 3. 7/12 + 1/6 3 ½ = 2 /4 + 2 ¼ = 1 /4 5 3/4 Subtracting Fractions Pg pg Practice 1. 5/8 – 5/12= Find the least common denominator (LCM) and make equivalent fractions 2/3 = 8 /12 - 1/4 2. 2 7/8- 5/6= = 3 /12 5/12 Mixed-Make equivalents and subtract 3. 10 – 4 ¾ = 4 ¾ = - 2 ½ = 2 ¾ 2/4 1/4 Pg. 1. ¾ + 2. 2 3 /5 + 3. 5 4. 7/9 Addition and Subtraction pg Regrouping = 1/3 1/2 = Make equivalents and regroup + 3 1/2 = 6 – 5/7= 4 ½ = 2 /4 + -2 ¾ = 3 /4 1¾ 4/4 = 6/4 5. 1/8 + 1/6= 4 ½ = + 2 ¾ = 6. 15 ½ - 3 2/3= 3 /4 5/4= 1 ¼ 7. 12- 8 ½= 8. ¾ + 1 ½ + 2 2 /4 1/6 = 7 1/4 pg Pg 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= Multiplying and Dividing Fractions 6.6 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 5. 20 x 1 ½= 6. 2/5 of 60= 7. 18 ÷ 2 ½= 8. 4 1/9 ÷ 6 2/3 9. ¾ ÷ 2= Dividing 1. Flip (reciprocal) the second fraction and change the sign to multiplication. 2. Follow the steps for multiplication 3. KEEP CHANGE FLIIP!!! Ex ¾ ÷ ½= ¾ x 2/1= 5/4= 1 ¼ Ex 2 ¼ ÷ 5= 9/2 ÷ 5/1 = 9/2 x 1/5= 9/10 Practice Estimate and add the fractions 1. 5 4/7 3 ½ + 4 1/3 _____________ 2. ½ 1 2/3 ¾ 2 2/5 + 1/3 ______________ Estimating fractions pg Round to the nearest whole number. If halfway mark, round up. 2 ¼ is closer to 2 than 3. 3 ¾ is closer to 4 than 3 Drawing pictures can help- 3 3/5 3 4 The bar is closer to 4 than 3 3 3/5 3 4 The number line is closer to 4 than 3