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Change each of these mixed numbers with improper fractions to whole or mixed numbers. Reduce your answers to lowest terms if necessary.

Mathematics

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Here are the solutions to the problems:

Part 1

Read and fill in the blanks.

(9) The numerator is more than the denominator. B: The fraction is more than 1.
(10) The fraction is equal to 1. A: The numerator is equal to the denominator.
(11) The fraction is less than 1. A: The numerator is less than the denominator.
(12) The fraction is more than 1. B: The numerator is more than the denominator.

Part 2· 6 steps

Change each of these mixed numbers with improper fractions to whole or mixed numbers. Reduce your answers to lowest terms if necessary.

  1. Convert the mixed number to an improper fraction.

    215=(2×5)+15=10+15=1152\frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}

    The fraction is already in lowest terms.
    (13) 115\boxed{\frac{11}{5}}

  2. Convert the mixed number to an improper fraction.

    496=(4×6)+96=24+96=3364\frac{9}{6} = \frac{(4 \times 6) + 9}{6} = \frac{24 + 9}{6} = \frac{33}{6}

  3. Reduce the improper fraction to lowest terms by dividing the numerator and denominator by their greatest common divisor, which is 3.

    336=33÷36÷3=112\frac{33}{6} = \frac{33 \div 3}{6 \div 3} = \frac{11}{2}

    (14) 112\boxed{\frac{11}{2}}

  4. Convert the improper fraction to a mixed number by dividing the numerator by the denominator.

    20÷8=2 with a remainder of 420 \div 8 = 2 \text{ with a remainder of } 4

    So, 208=248\frac{20}{8} = 2\frac{4}{8}.

  5. Reduce the fractional part to lowest terms by dividing the numerator and denominator by their greatest common divisor, which is 4.

    248=24÷48÷4=2122\frac{4}{8} = 2\frac{4 \div 4}{8 \div 4} = 2\frac{1}{2}

    (15) 212\boxed{2\frac{1}{2}}

  6. Convert the improper fraction to a whole or mixed number by dividing the numerator by the denominator.

    15÷5=3 with a remainder of 015 \div 5 = 3 \text{ with a remainder of } 0

    So, 155=3\frac{15}{5} = 3.
    (16) 3\boxed{3}

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