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Solve the following: 5(1)/(8) - 2(1)/(4) + (1)/(2).

Mathematics

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Answer

B

Step-by-step solution

16 steps

Part 6· 4 steps

  1. Convert mixed numbers to improper fractions.

    518=(5×8)+18=4185\frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{41}{8} 214=(2×4)+14=942\frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{9}{4}

  2. Rewrite the expression with a common denominator of 8.

    418−94+12=418−9×24×2+1×42×4\frac{41}{8} - \frac{9}{4} + \frac{1}{2} = \frac{41}{8} - \frac{9 \times 2}{4 \times 2} + \frac{1 \times 4}{2 \times 4} =418−188+48= \frac{41}{8} - \frac{18}{8} + \frac{4}{8}

  3. Perform the operations.

    =41−18+48=23+48=278= \frac{41 - 18 + 4}{8} = \frac{23 + 4}{8} = \frac{27}{8}

  4. Convert the improper fraction to a mixed number.

    278=338\frac{27}{8} = 3\frac{3}{8}

    The correct option is B.

    B. 338\boxed{\text{B. } 3\frac{3}{8}}

Part 7· 2 steps

  1. Set up the percentage equation.

    Let xx be the percentage.

    x% of 0.75=0.45x\% \text{ of } 0.75 = 0.45 x100×0.75=0.45\frac{x}{100} \times 0.75 = 0.45

  2. Solve for xx.

    x=0.450.75×100x = \frac{0.45}{0.75} \times 100 x=4575×100x = \frac{45}{75} \times 100 x=3×155×15×100x = \frac{3 \times 15}{5 \times 15} \times 100 x=35×100x = \frac{3}{5} \times 100 x=3×20x = 3 \times 20 x=60x = 60

    The correct option is A.

    A. 60%\boxed{\text{A. } 60\%}

Part 8· 3 steps

  1. Identify the hundreds digit and the digit to its right.

    The number is 87751. The hundreds digit is 7. The digit to its right (tens digit) is 5.

  2. Apply rounding rules.

    Since the digit to the right of the hundreds place (5) is 5 or greater, round up the hundreds digit. The 7 becomes 8. All digits to the right of the hundreds place become zero.

  3. Write the rounded number.

    87751 rounded to the nearest hundred is 87800.
    The correct option is B.

    B. 87800\boxed{\text{B. } 87800}

Part 9· 2 steps

  1. Interpret the phrase "increase of N240 by ratio 3:5".

    This phrase can be ambiguous. Given the options, we assume it means that the original amount (N240) and the increase itself are in the ratio 3:5.
    Let the increase be II.

    Original AmountIncrease=35\frac{\text{Original Amount}}{\text{Increase}} = \frac{3}{5} 240I=35\frac{240}{I} = \frac{3}{5}

  2. Solve for II.

    3I=240×53I = 240 \times 5 3I=12003I = 1200 I=12003I = \frac{1200}{3} I=400I = 400

    The increase is N400.
    The correct option is B.

    B. N400\boxed{\text{B. N400}}

Part 10· 3 steps

  1. Identify the principal, time, and rate.

    Principal (P) = N280
    Time (T) = 2122\frac{1}{2} years = 2.5 years
    Rate (R) = 3% per annum = 3100\frac{3}{100}

  2. Use the simple interest formula.

    Simple Interest (SI)=P×R×T100\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}

    (Here, R is the percentage value, so we divide by 100. Alternatively, use R as a decimal/fraction and omit the /100 in the formula).

    SI=280×3×2.5100\text{SI} = \frac{280 \times 3 \times 2.5}{100}

  3. Calculate the simple interest.

    SI=280×3×52100\text{SI} = \frac{280 \times 3 \times \frac{5}{2}}{100} SI=280×15200\text{SI} = \frac{280 \times 15}{200} SI=4200200\text{SI} = \frac{4200}{200} SI=21\text{SI} = 21

    The simple interest is N21.
    The correct option is C.

    C. N21\boxed{\text{C. N21}}

Part 11· 2 steps

  1. Convert the percentage to a fraction.

    A percentage means "per hundred". So, 3% means 3 out of 100.

    3%=31003\% = \frac{3}{100}

  2. Simplify the fraction to its lowest terms.

    The numbers 3 and 100 have no common factors other than 1. Therefore, the fraction 3100\frac{3}{100} is already in its lowest terms.
    The correct option is C.

    C. 3100\boxed{\text{C. } \frac{3}{100}}
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