Give two equivalent fractions for \(\frac { 6} { 8} \).

Step 1:

Simplify \(\frac { 6} { 8} \): 
Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2: 
\(\frac { 6 \div 2} { 8 \div 2} = \frac { 3} { 4} \).

Step 2:

Find an equivalent fraction by multiplying both the numerator and the denominator by the same number, for example, 2: 
\(\frac { 6 \times 2} { 8 \times 2} = \frac { 12} { 16} \).

Step 3:

So, \(\frac { 3} { 4} \) and \(\frac { 12} { 16} \) are equivalent to \(\frac { 6} { 8} \).

Supplemental Knowledge:

Equivalent fractions are different fractions that represent the same value or proportion of the whole. To find equivalent fractions, you can either multiply or divide both the numerator and the denominator by the same non-zero number.

Theory in Practice:

Understanding equivalent fractions can be very useful in everyday life:

- Cooking: When adjusting recipes, knowing that \(\frac { 1} { 2} \) cup is equivalent to \(\frac { 2} { 4} \) or \(\frac { 4} { 8} \) cups helps in scaling ingredients accurately. 
- Shopping: When comparing prices, recognizing that a discount of \(\frac { 50} { 100} \) is equivalent to \(\frac { 1} { 2} \) helps you understand savings better. 
- Construction: When measuring lengths, knowing that \(\frac { 3} { 4} \) inch is equivalent to \(\frac { 6} { 8} \) inch ensures precision in cutting materials.

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