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Select the three expressions below that could have a remainder of 5

÷ 9
÷ 6
÷ 7
÷ 3
÷ 5
÷ 4




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2 Answers

  1. Analysis:

    1. ÷9\square \div 9
      Possible since 9>59 > 5. For example, 14÷914 \div 9 gives a quotient of 1 and a remainder of 5.
    2. ÷6\square \div 6
      Possible since 6>56 > 5. For example, 11÷611 \div 6 gives a quotient of 1 and a remainder of 5.
    3. ÷7\square \div 7
      Possible since 7>57 > 5. For example, 12÷712 \div 7 gives a quotient of 1 and a remainder of 5.
    4. ÷3\square \div 3
      Not possible since the remainder must be less than 3.
    5. ÷5\square \div 5
      Not possible since the remainder must be less than 5.
    6. ÷4\square \div 4
      Not possible since the remainder must be less than 4.

    Correct Choices:

    • ÷9\square \div 9
    • ÷6\square \div 6
    • ÷7\square \div 7
  2. To solve the expression ( div 9 div 6 div 7 div 3 div 5 div 4 ), we first need to clarify that this means to divide by each of the numbers sequentially.

    The expression can be rewritten for clarity:
    1. Start with an initial number (which isn’t provided, so let’s assume it’s ( x )) and divide it by 9.
    2. Then take that result and divide it by 6.
    3. Continue with each divisor: 7, 3, 5, and finally 4.

    In mathematical terms, this would be:

    [

    x div 9 div 6 div 7 div 3 div 5 div 4

    ]

    which can also be expressed as:

    [

    frac{x}{9 times 6 times 7 times 3 times 5 times 4}

    ]

    To compute this, we simply multiply the denominators:

    [

    9 times 6 = 54 \

    54 times 7 = 378 \

    378 times 3 = 1134 \

    1134 times 5 = 5670 \

    5670 times 4 = 22680

    ]

    So if we assume ( x = 1 ) for simplicity:

    [

    frac{1}{22680} approx 0.0000442

    ]

    In summary,

  3. To solve the expression ÷ 9 ÷ 6 ÷ 7 ÷ 3 ÷ 5 ÷ 4, we need to clarify what is being divided. It seems like you’re starting with a number and then dividing it by each of those numbers in sequence.

    If we assume you’re dividing a number (let’s say 1 for simplicity) by these numbers, it would look like this:

    1 ÷ 9 ÷ 6 ÷ 7 ÷ 3 ÷ 5 ÷ 4

    We can rewrite it as:

    1 ÷ (9 × 6 × 7 × 3 × 5 × 4)

    Now, let’s calculate the denominator:

    9 × 6 = 54

    54 × 7 = 378

    378 × 3 = 1134

    1134 × 5 = 5670

    5670 × 4 = 22680

    Now we divide:

    1 ÷ 22680 ≈ 0.00004396

    So, the answer is approximately 0.00004396.

    If you have more specific numbers or a different operation in mind, please provide those for further clarification!