High School

Solve the following problems:

1. \( \frac{8}{9} \div 6 = \)
2. \( 1 \div \frac{7}{10} = \)
3. \( 18 \div \frac{6}{9} = \)
4. \( 5 \div \frac{15}{18} = \)
5. \( 6 \div \frac{12}{15} = \)
6. \( 2 + \frac{4}{5} = \)
7. \( \frac{3}{14} \div 2 = \)
8. \( \frac{16}{20} \div 6 = \)
9. \( \frac{3}{8} \div 12 = \)
10. \( 9 \div \frac{27}{30} = \)
11. \( 5 + \frac{2}{3} = \)
12. \( 10 \div \frac{4}{5} = \)
13. \( 24 \div \frac{6}{7} = \)
14. \( \frac{9}{17} \div 1 = \)
15. \( \frac{16}{20} \div 3 = \)

Answer :

Here's how you can solve the following division and addition problems involving fractions:

  1. [tex]\frac{8}{9} \div 6[/tex]

    • To divide by a whole number, you multiply by its reciprocal.
    • Reciprocal of 6 is [tex]\frac{1}{6}[/tex].
    • [tex]\frac{8}{9} \times \frac{1}{6} = \frac{8 \times 1}{9 \times 6} = \frac{8}{54} = \frac{4}{27}[/tex] after simplifying.

  2. [tex]1 \div \frac{7}{10}[/tex]

    • Dividing by a fraction is the same as multiplying by its reciprocal.
    • Reciprocal of [tex]\frac{7}{10}[/tex] is [tex]\frac{10}{7}[/tex].
    • [tex]1 \times \frac{10}{7} = \frac{10}{7}[/tex].

  3. [tex]18 \div \frac{6}{9}[/tex]

    • Reciprocal of [tex]\frac{6}{9}[/tex] is [tex]\frac{9}{6}[/tex] or [tex]\frac{3}{2}[/tex] after simplifying.
    • [tex]18 \times \frac{3}{2} = \frac{54}{2} = 27[/tex].

  4. [tex]5 \div \frac{15}{18}[/tex]

    • Reciprocal of [tex]\frac{15}{18}[/tex] is [tex]\frac{18}{15}[/tex] or [tex]\frac{6}{5}[/tex] after simplifying.
    • [tex]5 \times \frac{6}{5} = 6[/tex].

  5. [tex]6 \div \frac{12}{15}[/tex]

    • Reciprocal of [tex]\frac{12}{15}[/tex] is [tex]\frac{15}{12}[/tex] or [tex]\frac{5}{4}[/tex] after simplifying.
    • [tex]6 \times \frac{5}{4} = \frac{30}{4} = 7.5[/tex].

  6. [tex]2 + \frac{4}{5}[/tex]

    • This is simply adding a whole number to a fraction.
    • [tex]2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}[/tex] or [tex]2.8[/tex].

  7. [tex]\frac{3}{14} \div 2[/tex]

    • Reciprocal of 2 is [tex]\frac{1}{2}[/tex].
    • [tex]\frac{3}{14} \times \frac{1}{2} = \frac{3}{28}[/tex].

  8. [tex]\frac{16}{20} \div 6[/tex]

    • Reciprocal of 6 is [tex]\frac{1}{6}[/tex].
    • [tex]\frac{16}{20} \times \frac{1}{6} = \frac{16}{120} = \frac{2}{15}[/tex] after simplifying.

  9. [tex]\frac{3}{8} \div 12[/tex]

    • Reciprocal of 12 is [tex]\frac{1}{12}[/tex].
    • [tex]\frac{3}{8} \times \frac{1}{12} = \frac{3}{96} = \frac{1}{32}[/tex] after simplifying.

  10. [tex]9 \div \frac{27}{30}[/tex]

    • Reciprocal of [tex]\frac{27}{30}[/tex] is [tex]\frac{30}{27}[/tex] or [tex]\frac{10}{9}[/tex] after simplifying.
    • [tex]9 \times \frac{10}{9} = 10[/tex].

  11. [tex]5 + \frac{2}{3}[/tex]

    • [tex]5 + \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{17}{3}[/tex] or [tex]5.67[/tex] when simplified.

  12. [tex]10 \div \frac{4}{5}[/tex]

    • Reciprocal of [tex]\frac{4}{5}[/tex] is [tex]\frac{5}{4}[/tex].
    • [tex]10 \times \frac{5}{4} = \frac{50}{4} = 12.5[/tex].

  13. [tex]24 \div \frac{6}{7}[/tex]

    • Reciprocal of [tex]\frac{6}{7}[/tex] is [tex]\frac{7}{6}[/tex].
    • [tex]24 \times \frac{7}{6} = \frac{168}{6} = 28[/tex].

  14. [tex]\frac{9}{17} \div 1[/tex]

    • Any number divided by 1 is itself.
    • So, [tex]\frac{9}{17}[/tex].

  15. [tex]\frac{16}{20} \div 3[/tex]

    • Reciprocal of 3 is [tex]\frac{1}{3}[/tex].
    • [tex]\frac{16}{20} \times \frac{1}{3} = \frac{16}{60} = \frac{4}{15}[/tex] after simplifying.

I hope this step-by-step explanation helps you understand how to solve these problems!

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