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Perform the following operations: a) 589 + 759 b) 8589 - 4289 c) 325 * 569 d) 0.27 / 0.3 e) 2 3/8 / 7 1/2

Mathematics

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5 parts
c
184925
d
0.9
e

1960\frac{19}{60}

f

611156\frac{11}{15}

g
174

Step-by-step solution

19 steps

Part a· 1 step

589+759589 + 759

  1. Add the numbers.

    589+7591348\begin{align*} 589 \\ + 759 \\ \hline 1348 \end{align*}

    The sum is 1348.

Part b· 1 step

8589−42898589 - 4289

  1. Subtract the numbers.

    8589−42894300\begin{align*} 8589 \\ - 4289 \\ \hline 4300 \end{align*}

    The difference is 4300.

Part c184925

325×569325 \times 569

  1. Multiply 325 by 9.

    325×9=2925325 \times 9 = 2925

  2. Multiply 325 by 60.

    325×60=19500325 \times 60 = 19500

  3. Multiply 325 by 500.

    325×500=162500325 \times 500 = 162500

  4. Add the partial products.

    325×5692925(325×9)19500(325×60)162500(325×500)184925\begin{align*} 325 \\ \times 569 \\ \hline 2925 & (325 \times 9) \\ 19500 & (325 \times 60) \\ 162500 & (325 \times 500) \\ \hline 184925 \end{align*}

    The product is 184925\boxed{184925}.

Part d0.9

0.27÷0.30.27 \div 0.3

  1. Convert the division to an equivalent form with a whole number divisor by multiplying both numbers by 10.

    0.27÷0.3=(0.27×10)÷(0.3×10)=2.7÷30.27 \div 0.3 = (0.27 \times 10) \div (0.3 \times 10) = 2.7 \div 3

  2. Perform the division.

    2.7÷3=0.92.7 \div 3 = 0.9

    The quotient is 0.9\boxed{0.9}.

Part e

1960\frac{19}{60}

238÷7122\frac{3}{8} \div 7\frac{1}{2}

  1. Convert the mixed numbers to improper fractions.

    238=(2×8)+38=16+38=1982\frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8} 712=(7×2)+12=14+12=1527\frac{1}{2} = \frac{(7 \times 2) + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}

  2. Rewrite the division as multiplication by the reciprocal of the second fraction.

    198÷152=198×215\frac{19}{8} \div \frac{15}{2} = \frac{19}{8} \times \frac{2}{15}

  3. Multiply the fractions.

    198×215=19×28×15=38120\frac{19}{8} \times \frac{2}{15} = \frac{19 \times 2}{8 \times 15} = \frac{38}{120}

  4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.

    38120=38÷2120÷2=1960\frac{38}{120} = \frac{38 \div 2}{120 \div 2} = \frac{19}{60}

    The result is 1960\boxed{\frac{19}{60}}.

Part f

611156\frac{11}{15}

213+4252\frac{1}{3} + 4\frac{2}{5}

  1. Convert the mixed numbers to improper fractions.

    213=(2×3)+13=6+13=732\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} 425=(4×5)+25=20+25=2254\frac{2}{5} = \frac{(4 \times 5) + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5}

  2. Find a common denominator for the fractions.

    The least common multiple of 3 and 5 is 15.

    73=7×53×5=3515\frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} 225=22×35×3=6615\frac{22}{5} = \frac{22 \times 3}{5 \times 3} = \frac{66}{15}

  3. Add the fractions.

    3515+6615=35+6615=10115\frac{35}{15} + \frac{66}{15} = \frac{35 + 66}{15} = \frac{101}{15}

  4. Convert the improper fraction back to a mixed number.

    101÷15=6 with a remainder of 11101 \div 15 = 6 \text{ with a remainder of } 11

    So, 10115=61115\frac{101}{15} = 6\frac{11}{15}.
    The sum is 61115\boxed{6\frac{11}{15}}.

Part g174

4002÷234002 \div 23

  1. Perform long division.

    Divide 40 by 23. 23×1=2323 \times 1 = 23.

    123)4002‾−23↓17\begin{array}{r} 1 \\ 23\overline{)4002} \\ -23\downarrow \\ \hline 17 \end{array}

  2. Bring down the next digit (0).

    Divide 170 by 23. 23×7=16123 \times 7 = 161.

    1723)4002‾−23↓170−161↓9\begin{array}{r} 17 \\ 23\overline{)4002} \\ -23\downarrow \\ \hline 170 \\ -161\downarrow \\ \hline 9 \end{array}

  3. Bring down the next digit (2).

    Divide 92 by 23. 23×4=9223 \times 4 = 92.

    17423)4002‾−23↓170−161↓92−920\begin{array}{r} 174 \\ 23\overline{)4002} \\ -23\downarrow \\ \hline 170 \\ -161\downarrow \\ \hline 92 \\ -92 \\ \hline 0 \end{array}

    The quotient is 174\boxed{174}.

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