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Write 17,208,304 in words and VMCMXLV in Arabic figures.

Mathematics

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Answers

2 parts
6

38\frac{3}{8}

9

81 m281 \text{ m}^2

Step-by-step solution

31 steps

Okay, let's tackle these math problems.

Part 1· 3 steps

Numbers can be written in figures and in words. Write 17,208,304 in words.

  1. Break down the number by place value.

    The number is 17,208,304.

    • 17 is in the millions place.
    • 208 is in the thousands place.
    • 304 is in the hundreds, tens, and ones place.
  2. Write each part in words.

    • 17,000,000 is seventeen million.
    • 208,000 is two hundred eight thousand.
    • 304 is three hundred four.
  3. Combine the parts.

    The number in words is seventeen million, two hundred eight thousand, three hundred four.

    The answer is:

    • Seventeen million, two hundred eight thousand, three hundred four.

Part 2· 6 steps

Your uncle sent you some money through Western Union. The amount was written in Roman numbers as VMCMXLV. Write this amount in Arabic figures.

  1. Break down the Roman numeral into its components.

    V M C M X L V

  2. Convert each component to its Arabic value.

    • V = 5
    • M = 1000
    • C = 100
    • M = 1000
    • X = 10
    • L = 50
    • V = 5
  3. Apply the rules for Roman numerals (subtraction and addition).

    • VM: This is not a standard Roman numeral combination. It seems there might be a typo in the question, as 'V' (5) cannot precede 'M' (1000) in standard Roman numeral notation to indicate subtraction. If it were intended as a large number, it would typically be written with larger values first. Let's assume the 'V' at the beginning is a mistake and the number starts with MCMXLV, or that 'VM' is a non-standard representation for a very large number. Given the context of typical Roman numeral problems, it's more likely a standard number.

    Let's re-evaluate the Roman numeral string: VMCMXLV.
    If we interpret it strictly:
    V = 5
    M = 1000
    CM = 900 (C before M means 1000 - 100)
    XL = 40 (X before L means 50 - 10)
    V = 5

    If the 'V' at the beginning is a separate digit, it would be 5 + 1000 + 900 + 40 + 5 = 1950.
    However, Roman numerals are usually written in descending order of value, with subtractive pairs (like CM, XL) being exceptions. A 'V' at the very beginning followed by 'M' is highly unusual.

    Let's consider the possibility that the 'V' is part of a larger number, or that the question intended a different sequence.
    If it was MCMXLV, the value would be 1000+(1000−100)+(50−10)+5=1000+900+40+5=19451000 + (1000 - 100) + (50 - 10) + 5 = 1000 + 900 + 40 + 5 = 1945.

    Given the unusual "VM" at the start, and the common structure of Roman numerals, it's highly probable that the 'V' at the beginning is either a typo or meant to be part of a larger number that isn't standard.
    However, if we treat it as a sequence of individual Roman numerals and apply the rules:
    V = 5
    M = 1000
    CM = 900
    XL = 40
    V = 5

    If we assume the 'V' at the beginning is a separate value, and then the rest follows standard rules:
    5+1000+(1000−100)+(50−10)+5=5+1000+900+40+5=19505 + 1000 + (1000 - 100) + (50 - 10) + 5 = 5 + 1000 + 900 + 40 + 5 = 1950.

    However, the most common interpretation for a sequence like this, especially if it's a single number, would be to look for standard subtractive pairs.
    MCMXLV:
    M = 1000
    CM = 900 (1000 - 100)
    XL = 40 (50 - 10)
    V = 5
    Summing these: 1000+900+40+5=19451000 + 900 + 40 + 5 = 1945.

    The initial 'V' in "VMCMXLV" is problematic. If it's a typo and should be MCMXLV, the answer is 1945. If it's meant to be a very large number, it's not standard.
    Assuming the most common interpretation of such a sequence, and that the 'V' at the beginning is a mistake or part of a larger, non-standard notation, I will proceed with the standard interpretation of MCMXLV. If "VM" was intended to be a number, it's not standard.

    Let's assume the question meant MCMXLV.

  4. Identify the Roman numeral values.

    M = 1000
    C = 100
    X = 10
    L = 50
    V = 5

  5. Apply the rules for combining Roman numerals.

    • CM: C (100) before M (1000) means 1000−100=9001000 - 100 = 900.
    • XL: X (10) before L (50) means 50−10=4050 - 10 = 40.
  6. Sum the values.

    1000+900+40+5=19451000 + 900 + 40 + 5 = 1945.

    The answer is:

    • 1945

Part 3· 2 steps

The square root of 4 is 2. Find the square root of 196.

  1. Understand what a square root is.

    The square root of a number xx is a number yy such that y×y=xy \times y = x.

  2. Find the number that, when multiplied by itself, equals 196.

    We are looking for 196\sqrt{196}.
    We can test numbers:
    10×10=10010 \times 10 = 100
    12×12=14412 \times 12 = 144
    14×14=19614 \times 14 = 196

    The square root of 196 is 14.

    The answer is:

    • 14

Part 4· 2 steps

An examination started at 8:00am and lasted for 7 hours 30 minutes. When did it end?

  1. Add the hours to the start time.

    Start time: 8:00 am
    Duration: 7 hours 30 minutes
    Add 7 hours to 8:00 am: 8:00 am+7 hours=3:00 pm8:00 \text{ am} + 7 \text{ hours} = 3:00 \text{ pm}.

  2. Add the minutes to the new time.

    Add 30 minutes to 3:00 pm: 3:00 pm+30 minutes=3:30 pm3:00 \text{ pm} + 30 \text{ minutes} = 3:30 \text{ pm}.

    The answer is:

    • 3:30 pm

Part 5· 4 steps

In a class of 59 pupils, there are 7 more boys than girls. How many boys are in that class?

  1. Set up equations based on the given information.

    Let BB be the number of boys and GG be the number of girls.
    Total pupils: B+G=59B + G = 59
    Boys are 7 more than girls: B=G+7B = G + 7

  2. Substitute the second equation into the first equation.

    (G+7)+G=59(G + 7) + G = 59
    2G+7=592G + 7 = 59

  3. Solve for GG.

    2G=59−72G = 59 - 7
    2G=522G = 52
    G=522G = \frac{52}{2}
    G=26G = 26

  4. Solve for BB using the value of GG.

    B=G+7B = G + 7
    B=26+7B = 26 + 7
    B=33B = 33

    The answer is:

    • 33 boys

Part 6

38\frac{3}{8}

Peter spent 14\frac{1}{4} of his money on biscuits and 12\frac{1}{2} of the rest on bananas. What fraction is left?

  1. Calculate the fraction spent on biscuits.

    Fraction spent on biscuits = 14\frac{1}{4}.

  2. Calculate the remaining fraction after buying biscuits.

    Remaining fraction = 1−14=44−14=341 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}.

  3. Calculate the fraction spent on bananas.

    Peter spent 12\frac{1}{2} of the rest on bananas.
    Fraction spent on bananas = 12×34=38\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}.

  4. Calculate the total fraction spent.

    Total fraction spent = Fraction on biscuits + Fraction on bananas
    Total fraction spent = 14+38\frac{1}{4} + \frac{3}{8}
    To add these, find a common denominator, which is 8.
    14=1×24×2=28\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
    Total fraction spent = 28+38=58\frac{2}{8} + \frac{3}{8} = \frac{5}{8}.

  5. Calculate the fraction of money left.

    Fraction left = 1−Total fraction spent1 - \text{Total fraction spent}
    Fraction left = 1−58=88−58=381 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{3}{8}.

    The answer is:

    • 38\boxed{\frac{3}{8}}

Part 7· 3 steps

If 21 students can weed a farm in 4 hours. How many students can weed the farm in 3123\frac{1}{2} hours?

  1. Understand the relationship between students and time.

    This is an inverse proportion problem: more students mean less time to complete the work.
    Let S1=21S_1 = 21 students, T1=4T_1 = 4 hours.
    Let S2S_2 be the unknown number of students, T2=312T_2 = 3\frac{1}{2} hours =3.5= 3.5 hours.

  2. Set up the inverse proportion equation.

    S1×T1=S2×T2S_1 \times T_1 = S_2 \times T_2

  3. Substitute the known values and solve for S2S_2.

    21×4=S2×3.521 \times 4 = S_2 \times 3.5
    84=3.5S284 = 3.5 S_2
    S2=843.5S_2 = \frac{84}{3.5}
    S2=84035S_2 = \frac{840}{35}
    S2=24S_2 = 24

    The answer is:

    • 24 students

Part 8· 3 steps

A man bought 80 eggs and discovered that 20 were bad. What percentage of the eggs was good?

  1. Calculate the number of good eggs.

    Total eggs = 80
    Bad eggs = 20
    Good eggs = Total eggs - Bad eggs = 80−20=6080 - 20 = 60.

  2. Calculate the fraction of good eggs.

    Fraction of good eggs = Number of good eggsTotal eggs=6080\frac{\text{Number of good eggs}}{\text{Total eggs}} = \frac{60}{80}.

  3. Convert the fraction to a percentage.

    Percentage of good eggs = 6080×100%\frac{60}{80} \times 100\%
    Percentage of good eggs = 68×100%\frac{6}{8} \times 100\%
    Percentage of good eggs = 34×100%\frac{3}{4} \times 100\%
    Percentage of good eggs = 0.75×100%0.75 \times 100\%
    Percentage of good eggs = 75%75\%.

    The answer is:

    • 75%

Part 9

81 m281 \text{ m}^2

The distance round a square plot is 36m. What is the area of the plot?

  1. Understand the properties of a square.

    A square has four equal sides. The distance around a square plot is its perimeter.
    Perimeter of a square = 4×side4 \times \text{side}.

  2. Calculate the length of one side of the square.

    Perimeter = 36 m
    4×side=36 m4 \times \text{side} = 36 \text{ m}
    side=364 m\text{side} = \frac{36}{4} \text{ m}
    side=9 m\text{side} = 9 \text{ m}.

  3. Calculate the area of the square plot.

    Area of a square = side×side\text{side} \times \text{side}
    Area = 9 m×9 m9 \text{ m} \times 9 \text{ m}
    Area = 81 m281 \text{ m}^2.

    The answer is:

    • 81 m2\boxed{81 \text{ m}^2}
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