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Add the following: 1) 2 3/8 + 1 1/8; 2) 7 1/5 + 3 2/5. Multiply the following: 3) 2 x 1 1/8; 4) 3 x 3 1/5

Mathematics

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Step-by-step solution

16 steps

Add 12+38+13\frac{1}{2} + \frac{3}{8} + \frac{1}{3}.

  1. Find LCD of denominators 2, 8, 3.

    LCD=23×3=24\text{LCD} = 2^3 \times 3 = 24

  2. Convert 12\frac{1}{2}.

    12=1×122×12=1224\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}

  3. Convert 38\frac{3}{8}.

    38=3×38×3=924\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}

  4. Convert 13\frac{1}{3}.

    13=1×83×8=824\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}

  5. Add the fractions.

    1224+924+824=12+9+824=2924\frac{12}{24} + \frac{9}{24} + \frac{8}{24} = \frac{12 + 9 + 8}{24} = \frac{29}{24}

  6. 2924\frac{29}{24} is in simplest form (29 is prime).

    Final answer: 2924\boxed{\dfrac{29}{24}}

    Add 75+32\frac{7}{5} + \frac{3}{2}.

  7. Find LCD of denominators 5, 2.

    LCD=5×2=10\text{LCD} = 5 \times 2 = 10

  8. Convert 75\frac{7}{5}.

    75=7×25×2=1410\frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10}

  9. Convert 32\frac{3}{2}.

    32=3×52×5=1510\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}

  10. Add the fractions.

    1410+1510=14+1510=2910\frac{14}{10} + \frac{15}{10} = \frac{14 + 15}{10} = \frac{29}{10}

  11. 2910\frac{29}{10} is in simplest form.

    Final answer: 2910\boxed{\dfrac{29}{10}}

    Multiply 22×15\frac{2}{2} \times \frac{1}{5}.

  12. Multiply numerators and denominators.

    22×15=2×12×5=210\frac{2}{2} \times \frac{1}{5} = \frac{2 \times 1}{2 \times 5} = \frac{2}{10}

  13. Simplify 210\frac{2}{10}.

    2÷210÷2=15\frac{2 \div 2}{10 \div 2} = \frac{1}{5}

    Final answer: 15\boxed{\dfrac{1}{5}}

    Multiply 3×353 \times \frac{3}{5}.

  14. Write 3 as 31\frac{3}{1}.

    3×35=31×353 \times \frac{3}{5} = \frac{3}{1} \times \frac{3}{5}

  15. Multiply numerators and denominators.

    3×31×5=95\frac{3 \times 3}{1 \times 5} = \frac{9}{5}

  16. 95\frac{9}{5} is in simplest form.

    Final answer: 95\boxed{\dfrac{9}{5}}

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