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Which is the smallest six-digit number that can be formed using the digits 6, 2, 0, 4, 1, 7? A mountain is 4289 m high. Which digit has the highest value in the height of the mountain? Margaret collec

Mathematics

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Answer

C

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Here are the solutions to the problems:

1. Which is the smallest six-digit number that can be formed using the digits 6, 2, 0, 4, 1, 7?

  1. Arrange the given digits in ascending order

    0, 1, 2, 4, 6, 7.

  2. To form the smallest six-digit number, the first digit cannot be zero.

    Place the smallest non-zero digit (1) first, followed by zero, then the remaining digits in ascending order.
    The number is 102467.
    The correct option is C.

    C. 102467\boxed{\text{C. } 102467}

    2. A mountain is 4289 m high. Which digit has the highest value in the height of the mountain?

  3. Identify the place value of each digit in 4289.

    • The digit 4 is in the thousands place, so its value is 4×1000=40004 \times 1000 = 4000.
    • The digit 2 is in the hundreds place, so its value is 2×100=2002 \times 100 = 200.
    • The digit 8 is in the tens place, so its value is 8×10=808 \times 10 = 80.
    • The digit 9 is in the ones place, so its value is 9×1=99 \times 1 = 9.

  4. Compare the values.

    The highest value is 4000, which corresponds to the digit 4.
    The correct option is A.

    A. 4\boxed{\text{A. } 4}

    3. Margaret collected 74289 eggs from her farm. By how many times is the value of digit 4 more than the value of digit 8 in the number of eggs collected?

  5. Determine the value of digit 4 in 74289.

    The digit 4 is in the thousands place, so its value is 4×1000=40004 \times 1000 = 4000.

  6. Determine the value of digit 8 in 74289.

    The digit 8 is in the tens place, so its value is 8×10=808 \times 10 = 80.

  7. Find the difference between the values.

    Difference =4000−80=3920= 4000 - 80 = 3920.
    The correct option is D.

    D. 3920\boxed{\text{D. } 3920}

    4. A 14 seater bus was used to transport 132 people to a rally. How many trips did the bus make to transport all the people?

  8. Divide the total number of people by the bus capacity.

    13214=9 with a remainder of 6\frac{132}{14} = 9 \text{ with a remainder of } 6

  9. The bus makes 9 full trips, transporting 9×14=1269 \times 14 = 126 people.

    There are 132−126=6132 - 126 = 6 people remaining.

  10. To transport the remaining 6 people, one more trip is needed.

    Total trips =9+1=10= 9 + 1 = 10 trips.
    The correct option is C.

    C. 10\boxed{\text{C. } 10}

    5. Zuri bought 3563\frac{5}{6} kg rice and 1341\frac{3}{4} kg of beans. How many kilograms did she buy altogether?

  11. Convert the mixed fractions to improper fractions.

    356=(3×6)+56=18+56=2363\frac{5}{6} = \frac{(3 \times 6) + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} 134=(1×4)+34=4+34=741\frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}

  12. Find a common denominator for 6 and 4, which is 12.

    Convert the fractions.

    236=23×26×2=4612\frac{23}{6} = \frac{23 \times 2}{6 \times 2} = \frac{46}{12} 74=7×34×3=2112\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}

  13. Add the fractions.

    4612+2112=46+2112=6712\frac{46}{12} + \frac{21}{12} = \frac{46 + 21}{12} = \frac{67}{12}

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

    6712=5 with a remainder of 7=5712 kg\frac{67}{12} = 5 \text{ with a remainder of } 7 = 5\frac{7}{12} \text{ kg}

    The correct option is A.

    A. 5712 kg\boxed{\text{A. } 5\frac{7}{12} \text{ kg}}

    6. Grade 6 learners were asked by their Mathematics teacher to work out the reciprocal of (112)2(1\frac{1}{2})^2. What answer did they get?

  15. Convert the mixed number to an improper fraction.

    112=(1×2)+12=321\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}

  16. Square the fraction.

    (32)2=3222=94\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2} = \frac{9}{4}

  17. Find the reciprocal of 94\frac{9}{4}.

    The reciprocal of a fraction ab\frac{a}{b} is ba\frac{b}{a}.
    The reciprocal of 94\frac{9}{4} is 49\frac{4}{9}.
    The correct option is D.

    D. 49\boxed{\text{D. } \frac{4}{9}}

    **7. Andrew walked a distance of 3 km 80

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