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# Mixed Numbers Topic

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MIXED NUMBERS What Is a Mixed Number? • A mixed number has both a whole number and a fraction. If someone ate a whole cookie and a third of another, 1 1/3 would represent how many cookies were eaten. Other mixed numbers are: 4 2/3 3 1/7 1 6/9 7 4/5 • Mixed numbers can be added, subtracted, multiplied, and divided, but there are several steps in the operations. Each operation has its own set of steps. How to add, subtract, multiply and divide mixed numbers: • To add mixed numbers, the denominators of the fractions must be the same. o Begin by changing one or both denominators o Add the fractions and reduce to lowest terms, sometimes this means creating a mixed number. Improper fractions have a numerator larger than the denominator. Divide the numerator by the denominator to form a mixed number, for example, 12/7 = 1 5/7 21/5 = 4 1/5 13/10 = 1 3/10 3/2 = 1 ½ o Add the whole numbers; include any whole number resulting from adding the fractions. 5 2/3 + 3 5/9 → 5 6/9 + 3 5/9 6/9 + 5/9 = 11/9 → 1 2/9 5 + 3 + 1 2/9 = 9 2/9 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• To subtract mixed numbers, the denominators must be the same. o Begin by changing one or both denominators. o Subtract the fractions and reduce to lowest terms. o Subtract the whole numbers. 6 11/12 – 5 ¾ = 7 11/12 – 5 9/12 = 2 2/12 = 2 1/6 ______________________________ 3 6/7 – 1 2/3 = 3 18/21 – 1 14/21 = 2 4/21 • To multiply mixed numbers, both numbers must first be changed to improper fractions. o An improper fraction has a numerator larger than the denominator: 7/3, 8/5, 22/15 o To change a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator to the product. The product becomes the new numerator. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Examples: 5 ½ → 11/2 3 6/7 → 27/7 o Once the mixed numbers have been changed to improper fractions, multiply the numerators and the denominators. 5 ½ x 3 6/7 = 11/2 x 27/7 = 297/14 o Change the improper fraction to a mixed number by dividing 297/14 = 21 3/14 • To divide mixed numbers, use the same procedure as for multiplication, but invert the divisor before multiplying . © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 4 2/10 + 3 2/5 = ____________________________________________________________ 8 7/8 – 5 1/3 = ____________________________________________________________ 3 2/10 x 7 2/5 = ____________________________________________________________ 1 7/8 ÷ 2 1/3 = _____________________________________________________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.