Multiplying and Dividing Fractions 2

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1 Unit : Linear Equations Name Directions: Solve. Multiplying and Dividing Fractions 7

2 Appendix B: Answer Keys Transparency/Guided Practice Book Answers 4

3 Unit : Linear Equations Name Directions: Calculate. Multiplying and Dividing Fractions

4 Appendix B: Answer Keys Guided Practice Book Answers (cont.) 68

5 4 How to Divide Fractions Facts to Know The key to dividing with fractions is understanding reciprocals. A reciprocal is two numbers that have the product of. Here are some examples: Samples and are reciprocals because x 6 or 6 4 and are reciprocals because 4 x 4 or Knowing what a reciprocal is will be your key to understanding how to divide with fractions. Dividing Fractions by Fractions Dividing a number by gives the same answer as multiplying by. For example, 6 just as 6 x. The answers are the same. The reciprocal of is. Turning a fraction upside down is called inverting. To divide by a fraction, invert the fraction you are dividing by and then multiply. Sample: Let s say you re building a kite, and you have a piece of string 4 yard long. Into how many yard pieces can you snip the string? 8 The problem looks like this: Step Invert the fraction you are dividing by. 8 inverted is ? Step Multiply across x 8 4 Step Reduce or change an improper fraction to a mixed or whole number, if possible. 4 pieces of string The fraction to invert is always the fraction to the right of the division sign. 7.

6 4 How to Divide Fractions Facts to Know (cont.) Canceling in Dividing Fractions Sometimes you can cancel in division. Invert before you cancel and multiply after you cancel. Sample:? 6 Step Invert and change to multiplication. x 6 6 Step is a factor of and 6. Cancel and divide the numerator and denominator by. x 6 Step Multiply. x 6 Dividing a Fraction by a Whole Number When dividing a fraction by a whole number, first change the whole number to a fraction with a denominator of. Sample: Suppose a recipe calls for dividing pound of butter into four equal parts. Hint: You must divide by 4. Step Change the whole number, 4, to a fraction. 4 4 Step Invert the divisor. 4 inverted is 4 Step Multiply. x 4 8 pound of butter. Dividing a Whole Number by a Fraction Sometimes the whole number is not the number you are dividing byit is the number being divided. Sample: Divide 4 pounds of candy into bags holding pound each. Hint: You must divide 4 by. Step Change the whole number to a fraction. 4 4 Step Step Invert the divisor. (Invert the number to the right of the division sign.) inverted is Multiply. 4 4 x 8 or 8 bags Dividing and Mixed Numbers Before dividing, change any mixed numbers to improper fractions. Sample: 4? Step Change the mixed number to an improper fraction. 4 4 Step Invert and multiply. 4 x

7 4 Practice Dividing Fractions Directions: Divide the fractions below

8 4 Practice Dividing Fractions Directions: Divide the fractions, whole numbers, or mixed numbers. Reduce when possible

9 How to Multiply Fractions Facts to Know All fractions can be multiplied by multiplying the numerators and then multiplying the denominators. You don t need common denominators to multiply. Sample: Andrew can jog a mile in of an hour. Lauren can run the same distance in that time. 4 How long would it take Lauren to run a mile? To find out, you need to multiply by. 4 Step Multiply the numerators. x Step Multiply the denominators. x x 4 8 Step Write the answer as a fraction. x 4 4 x 8 Sometimes the answer to a multiplication problem can be reduced. Sample: 4 x 6? Step Step Multiply the fractions. Write the fraction in simplest form by dividing the numerator and denominator by the greatest common factor, which in this case is. 4 x Multiplying Three Fractions Now and then you will have to multiply three fractions together. Sample: x x? Step Step Step Multiply the numerators of the first two fractions. Then multiply that answer by the numerator of the third fraction. Multiply the denominators of the first two fractions. Then multiply that answer by the denominator of the third fraction. Write fraction in simplest form, if possible. The fraction 4 is reduced as far as it can be. x x x x 4.

10 How to Multiply Fractions Facts to Know (cont.) Canceling as a Shortcut Sometimes the fractions in a multiplication problem can be canceled. Canceling is a shortcut to reducing. To cancel find a number that divides evenly into both the numerator and denominator of the problem. Sample: 4 x 7 4? Step Find a number that will divide evenly. The number will divide evenly into and 4. Step Cancel and 4 by. 4 8 Step Multiply across by the new numbers. Step 4 Reduce if possible, but by canceling you already did some of the work of reducing. 4 x Multiplying Fractions and Whole Numbers When multiplying a fraction by a whole number, turn the whole number into a fraction with a denominator of. Sample: Andrew plans to sprint of a mile each day for four days in a row as part of his regular workout. How many miles will this total? You will need to multiply by 4. Step Write 4 as an improper fraction with a denominator of. 4 4 Step Step Change the improper fraction to a whole or mixed number. x 4 Multiplying Mixed Numbers When multiplying mixed numbers, it is usually helpful to change the mixed number to an improper fraction. Sample: x 4? Multiply across. Step Change both mixed numbers to improper fractions. ( x ) + 7 Step Step Multiply across the new numbers. Change the improper fraction to a whole or mixed number. 4 (4 x ) + 7 x 4 4

11 Practice Multiplying Fractions Directions: Multiply the fractions. Remember to write the answer in simplest form when possible.. x 4. 9 x 4. 0 x 9 6 x 4. x 7. 8 x 4. 4 x 7 x. 8 x 4. 8 x 7 9. x 4 4. x 6 7. x x x 4. x 6. x 4 x x 6. x 4 7. x x 8. x 0 7. x x x x x x 7 8 x 4 0. x x 0. x 0 x x 7 0. x. 9 0 x 4 x x 0. x 4. 6 x 4 x.

12 Practice Multiplying Fractions Directions: Multiply the fractions and whole numbers. Use canceling whenever you can.. 4 x. 7 x x 4. 8 x. 4 x 6. 0 x 0. 8 x 4. 7 x. 6 x x 7. x. 4 x 4. 6 x 8. x 4. x x Directions: Multiply the mixed numbers. Use canceling whenever you can x. 4 7 x 9. 6 x 6 7 x 8. 7 x 0. 9 x x 4 x x 9. 9 x x 7 x x x x x 7 6

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Pre-Algebra Notes Unit Five: Rational Numbers and Equations

Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the