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Solve the following problems: a) 3 rac710 - 1 rac89 b) 2 rac210 + 1 rac67

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2 parts
a

173901\frac{73}{90}

b

42354\frac{2}{35}

Step-by-step solution

11 steps

Part a· 5 steps

3710−1893\frac{7}{10} - 1\frac{8}{9}

  1. Convert mixed numbers to improper fractions.

    3710=3×10+710=37103\frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{37}{10} 189=1×9+89=1791\frac{8}{9} = \frac{1 \times 9 + 8}{9} = \frac{17}{9}

  2. Find the Least Common Multiple (LCM) of the denominators 10 and 9.

    The LCM of 10 and 9 is 90.

  3. Convert fractions to equivalent fractions with a denominator of 90.

    3710=37×910×9=33390\frac{37}{10} = \frac{37 \times 9}{10 \times 9} = \frac{333}{90} 179=17×109×10=17090\frac{17}{9} = \frac{17 \times 10}{9 \times 10} = \frac{170}{90}

  4. Perform the subtraction.

    33390−17090=333−17090=16390\frac{333}{90} - \frac{170}{90} = \frac{333 - 170}{90} = \frac{163}{90}

  5. Convert the improper fraction to a mixed number.

    16390=17390\frac{163}{90} = 1\frac{73}{90}

    The simplified answer is 17390\boxed{1\frac{73}{90}}.

Part b

42354\frac{2}{35}

2210+1672\frac{2}{10} + 1\frac{6}{7}

  1. Convert mixed numbers to improper fractions.

    2210=2×10+210=22102\frac{2}{10} = \frac{2 \times 10 + 2}{10} = \frac{22}{10} 167=1×7+67=1371\frac{6}{7} = \frac{1 \times 7 + 6}{7} = \frac{13}{7}

  2. Find the LCM of the denominators 10 and 7.

    The LCM of 10 and 7 is 70.

  3. Convert fractions to equivalent fractions with a denominator of 70.

    2210=22×710×7=15470\frac{22}{10} = \frac{22 \times 7}{10 \times 7} = \frac{154}{70} 137=13×107×10=13070\frac{13}{7} = \frac{13 \times 10}{7 \times 10} = \frac{130}{70}

  4. Perform the addition.

    15470+13070=154+13070=28470\frac{154}{70} + \frac{130}{70} = \frac{154 + 130}{70} = \frac{284}{70}

  5. Simplify the improper fraction.

    Divide both numerator and denominator by their HCF, which is 2.

    284÷270÷2=14235\frac{284 \div 2}{70 \div 2} = \frac{142}{35}

    Convert to a mixed number:

    14235=4235\frac{142}{35} = 4\frac{2}{35}

    The simplified answer is 4235\boxed{4\frac{2}{35}}.

Part c· 1 step

834−656+128\frac{3}{4} - 6\frac{5}{6} + \frac{1}{2}

  1. Convert mixed numbers to improper fractions.

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