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Define equivalent fractions and simplifying fractions. Simplify 6/12, 8/16, and 10/20.

Mathematics

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Section A: Definitions

  1. An equivalent fraction is a fraction that has a different numerator and denominator but represents the same value as another fraction. For example, 12\frac{1}{2} and 24\frac{2}{4} are equivalent fractions.

  2. Simplifying a fraction means reducing it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). The simplified fraction has no common factors other than 1 in its numerator and denominator.

Section E: Simplifying Fractions

  1. To simplify 612\frac{6}{12}:

  1. Find the greatest common divisor (GCD) of 6 and 12.

    The GCD of 6 and 12 is 6.

  2. Divide both the numerator and the denominator by their GCD.

    $$
\frac{6 \div 6}{12 \div 6} = \frac{1}{2}
$$
The simplified fraction is $\boxed{\frac{1}{2}}$.

    2. To simplify 816\frac{8}{16}:

  3. Find the greatest common divisor (GCD) of 8 and 16.

    The GCD of 8 and 16 is 8.

  4. Divide both the numerator and the denominator by their GCD.

    $$
\frac{8 \div 8}{16 \div 8} = \frac{1}{2}
$$
The simplified fraction is $\boxed{\frac{1}{2}}$.

    3. To simplify 1020\frac{10}{20}:

  5. Find the greatest common divisor (GCD) of 10 and 20.

    The GCD of 10 and 20 is 10.

  6. Divide both the numerator and the denominator by their GCD.

    $$
\frac{10 \div 10}{20 \div 10} = \frac{1}{2}
$$
The simplified fraction is $\boxed{\frac{1}{2}}$.
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