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There are 91 oranges in a basket. If 2/7 of the oranges are bad, how many are good? If P - 3/8 = 5/8, find P. Express 15 cm as a decimal of 1 km. If 9.8 X 1.89 = 18.522, find 98 X 189.

Mathematics

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  1. Calculate the number of bad oranges.

    Total oranges = 91.
    Fraction of bad oranges = 27\frac{2}{7}.
    Number of bad oranges =27×91= \frac{2}{7} \times 91.

    27×91=2×917=2×13=26\frac{2}{7} \times 91 = 2 \times \frac{91}{7} = 2 \times 13 = 26

    There are 26 bad oranges.

  2. Calculate the number of good oranges.

    Number of good oranges = Total oranges - Number of bad oranges.

    91−26=6591 - 26 = 65

    There are 65 good oranges.

  3. Compare with the given options.

    The calculated number of good oranges is 65, which corresponds to option C.

    The final answer is C. 65\boxed{\text{C. 65}}.


  4. Isolate PP in the equation.

    The given equation is P−38=58P - \frac{3}{8} = \frac{5}{8}.
    To find PP, add 38\frac{3}{8} to both sides of the equation.

    P=58+38P = \frac{5}{8} + \frac{3}{8}
  5. Add the fractions.

    Since the fractions have the same denominator, add the numerators.

    P=5+38=88P = \frac{5+3}{8} = \frac{8}{8}
  6. Simplify the result.

    P=1P = 1
  7. Compare with the given options.

    The calculated value of PP is 1, which corresponds to option C.

    The final answer is C. 1\boxed{\text{C. 1}}.


  8. Convert 1 km to cm.

    We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m}.
    We also know that 1 m=100 cm1 \text{ m} = 100 \text{ cm}.
    Therefore, 1 km=1000 m×100 cm/m=100,000 cm1 \text{ km} = 1000 \text{ m} \times 100 \text{ cm/m} = 100,000 \text{ cm}.

  9. Express 15 cm as a decimal of 1 km.

    This means we need to find the value of 15 cm1 km\frac{15 \text{ cm}}{1 \text{ km}} in decimal form.

    15 cm100,000 cm=15100,000\frac{15 \text{ cm}}{100,000 \text{ cm}} = \frac{15}{100,000}
  10. Convert the fraction to a decimal.

    15100,000=0.00015\frac{15}{100,000} = 0.00015
  11. Compare with the given options.

    The calculated value is 0.00015, which corresponds to option D.

    The final answer is D. 0.00015\boxed{\text{D. 0.00015}}.


  12. Analyze the relationship between the given multiplication and the required multiplication.

    We are given 9.8×1.89=18.5229.8 \times 1.89 = 18.522.
    We need to find 98×18998 \times 189.

  13. Express 98 and 189 in terms of 9.8 and 1.89.

    98=9.8×1098 = 9.8 \times 10 189=1.89×100189 = 1.89 \times 100
  14. Substitute these expressions into the required multiplication.

    98×189=(9.8×10)×(1.89×100)98 \times 189 = (9.8 \times 10) \times (1.89 \times 100)

    Rearrange the terms:

    98×189=(9.8×1.89)×(10×100)98 \times 189 = (9.8 \times 1.89) \times (10 \times 100)
  15. Use the given information to calculate the product.

    We know 9.8×1.89=18.5229.8 \times 1.89 = 18.522.
    We also know 10×100=100010 \times 100 = 1000.

    98×189=18.522×100098 \times 189 = 18.522 \times 1000
  16. Perform the final multiplication.

    Multiplying by 1000 shifts the decimal point three places to the right.

    18.522×1000=1852218.522 \times 1000 = 18522

    The final answer is 18522\boxed{\text{18522}}.

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