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Evaluate the statement 20 − (12) ÷ 3 = 6. Solve for the missing number in - 12 / 3 = 6, - (12 / 3) = 6, 18 + + 12 = 98, and 15 + + 12 = 95.

Mathematics

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6 steps
  1. Evaluate the statement 20−(12)÷3=620 - (12) \div 3 = 6.

    First, perform the division:

    12÷3=412 \div 3 = 4

    Substitute this back into the statement:

    20−4=620 - 4 = 6 16=616 = 6

    This statement is false.

  2. Solve for the missing number in □−12÷3=6\square - 12 \div 3 = 6.

    Let the missing number be xx.

    x−12÷3=6x - 12 \div 3 = 6

    Perform the division first:

    x−4=6x - 4 = 6

    Add 4 to both sides of the equation:

    x=6+4x = 6 + 4 x=10x = 10

    The missing number is 10\boxed{10}.
    The student's work used 30, which is incorrect because 30−4=26≠630 - 4 = 26 \neq 6.

  3. Solve for the missing number in □−(12÷3)=6\square - (12 \div 3) = 6.

    Let the missing number be yy.

    y−(12÷3)=6y - (12 \div 3) = 6

    Perform the operation inside the parentheses first:

    y−4=6y - 4 = 6

    Add 4 to both sides of the equation:

    y=6+4y = 6 + 4 y=10y = 10

    The missing number is 10\boxed{10}.
    The student's work used 30, which is incorrect because 30−4=26≠630 - 4 = 26 \neq 6.

  4. Solve for the missing number in 18+□+12=9818 + \square + 12 = 98.

    Let the missing number be zz.

    18+z+12=9818 + z + 12 = 98

    Combine the constant terms on the left side:

    30+z=9830 + z = 98

    Subtract 30 from both sides of the equation:

    z=98−30z = 98 - 30 z=68z = 68

    The missing number is 68\boxed{68}.
    The student's work correctly found 68.

  5. Solve for the missing number in 15+□+12=9515 + \square + 12 = 95.

    Let the missing number be ww.

    15+w+12=9515 + w + 12 = 95

    Combine the constant terms on the left side:

    27+w=9527 + w = 95

    Subtract 27 from both sides of the equation:

    w=95−27w = 95 - 27 w=68w = 68

    The missing number is 68\boxed{68}.
    The student's work correctly found 68.

  6. Solve for the missing number in 18+□+12=9818 + \square + 12 = 98.

    Let the missing number be vv.

    18+v+12=9818 + v + 12 = 98

    Combine the constant terms on the left side:

    30+v=9830 + v = 98

    Subtract 30 from both sides of the equation:

    v=98−30v = 98 - 30 v=68v = 68

    The missing number is 68\boxed{68}.
    The student's work used 65, which is incorrect because 18+65+12=95≠9818 + 65 + 12 = 95 \neq 98.

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