Hamilton's Math To Build On - copyright 1993

Measuring Fractions & Decimals:
Memory Aid

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About Math To Build On || Preface || Contents || Glossary
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Doubling a Measuring Fraction

    To double a fraction, you normally multiply it by 2, then reduce the answer to the lowest denominator.

      Example:

    A quicker way is to divide the denominator by 2.

      Example:

    Of course, this works only with fractions that have an even number for the denominator, but our measuring fractions are all based on even numbers. (Examples: 1/2, 1/4, 1/8, and 1/16.)

Halving a Measuring Fraction

    To divide a fraction in half, you were told in school to invert and multiply. The shortcut is just to multiply the denominator by 2.

    To find half of these fractions, multiply the denominator by 2.

      Examples:


Halving Mixed Numbers

    You can separate mixed numbers into two categories:

    (1) Mixed Numbers with an Even Whole Number

      32 7/8 is a mixed number with an even whole number (32).

      In this case, divide the whole number by 2: 32/2 = 16
      Use the shortcut for dividing a fraction: 7/8x2 = 7/16
      Add them back together: 16 7/16

      Half of 32 7/8 is 16 7/16

    (2) Mixed Numbers with an Odd Whole Number

      11 3/8 is a mixed number with an odd whole number (11).

      Divide the whole number by 2: 11/2 = 5.5 (drop the decimal to make the whole number 5).
      Add the numerator to the denominator: 3 + 8 = 11 (11 is the new numerator).
      Double the denominator: 8 x 2 = 16 (16 is the new denominator).
      When you put the two together, the fraction is 11/16.

      Your final answer is 5 11/16


Rough Conversions

    Here's a trick for making a rough conversion of decimals of a foot to inches and fractions of an inch.

    Each 0.01' is roughly equal to 1/8". There are ninety-six 1/8" in a foot and one hundred 0.01' in a foot.

    These facts come in handy with grading when a surveyor says that you need to take off another 0.15'. A fast head calculation tells you that fifteen 1/8" equals 15/8 or 1 7/8".

    You can add an extra 0.01' for every three inches to correct for the missing 0.04'.

    The degree to which these tricks are effective depends on the degree of accuracy you need in your measurement.

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