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Challenge! I have tens, ones and tenths. My digits are next-door numbers and they add up to 9. What number am I?

Mathematics

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Here are the solutions to the problems:

Look at the calculations. Write each answer on the grid.

  1. Perform each calculation.

    • For 31÷1031 \div 10: Dividing by 10 moves the decimal point one place to the left. 31÷10=3.131 \div 10 = 3.1
    • For 0.1×100.1 \times 10: Multiplying by 10 moves the decimal point one place to the right. 0.1×10=10.1 \times 10 = 1
    • For 24÷1024 \div 10: Dividing by 10 moves the decimal point one place to the left. 24÷10=2.424 \div 10 = 2.4
    • For 7.4×107.4 \times 10: Multiplying by 10 moves the decimal point one place to the right. 7.4×10=747.4 \times 10 = 74
    • For 6÷106 \div 10: Dividing by 10 moves the decimal point one place to the left. 6÷10=0.66 \div 10 = 0.6
  2. Place the digits of each result into the correct columns (100s, 10s, 1s, 0.1s) in the grid.

    Calculation100s10s1s0.1s
    31÷10=3.131 \div 10 = 3.10031
    0.1×10=10.1 \times 10 = 10010
    24÷10=2.424 \div 10 = 2.40024
    7.4×10=747.4 \times 10 = 740740
    6÷10=0.66 \div 10 = 0.60006

    9 Challenge! I have tens, ones and tenths. My digits are next-door numbers and they add up to 9. What number am I?

  3. Identify the properties of the digits.

    The number has three digits: a tens digit (TT), a ones digit (OO), and a tenths digit (tt).
    The digits are "next-door numbers," meaning they are consecutive integers (e.g., 1, 2, 3 or 5, 4, 3).
    The sum of the digits is 9: T+O+t=9T + O + t = 9.

  4. Find the set of three consecutive integers that sum to 9.

    Let the middle digit be xx. The three consecutive digits can be represented as x−1x-1, xx, and x+1x+1.
    Their sum is (x−1)+x+(x+1)=3x(x-1) + x + (x+1) = 3x.
    Set the sum equal to 9:

    3x=93x = 9 x=93x = \frac{9}{3} x=3x = 3

    So, the three digits are x−1=2x-1 = 2, x=3x = 3, and x+1=4x+1 = 4. The digits are 2, 3, and 4.

  5. Arrange the digits (2, 3, 4) into a number $T O . t$ such that they are "next-door numbers."

    There are two possible arrangements where the digits are consecutive in order:

    • Option 1 (Ascending order): Tens digit = 2, Ones digit = 3, Tenths digit = 4. This forms the number 23.4. Check: 2+3+4=92+3+4=9. The digits 2, 3, 4 are next-door numbers.
    • Option 2 (Descending order): Tens digit = 4, Ones digit = 3, Tenths digit = 2. This forms the number 43.2. Check: 4+3+2=94+3+2=9. The digits 4, 3, 2 are next-door numbers.

    Since the question asks "What number am I?" (singular), and in primary school mathematics, consecutive numbers are often presented in ascending order by default, we will provide the ascending option.

    The number is 23.4\boxed{23.4}.

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