How do you determine if two fractions are equivalent and simplify them?
Understand the Problem
The question is asking for help with understanding how to identify equivalent fractions and how to simplify them by dividing both the numerator and denominator by the same number.
Answer
The fractions \( \frac{16}{8} \) and \( \frac{8}{4} \) are equivalent.
Answer for screen readers
The fractions ( \frac{16}{8} ) and ( \frac{8}{4} ) are equivalent.
Steps to Solve
-
Identifying the Fraction We start with the fraction ( \frac{16}{8} ). To analyze it, we need to identify the numerator (16) and the denominator (8).
-
Simplifying the Fraction To simplify the fraction, we divide both the numerator and denominator by the greatest common divisor (GCD).
The GCD of 16 and 8 is 8. We divide both by 8:
[ \frac{16 \div 8}{8 \div 8} = \frac{2}{1} ]
- Identifying Equivalent Fractions Now, we can check if ( \frac{2}{1} ) is equivalent to ( \frac{8}{4} ). We simplify ( \frac{8}{4} ) just like before:
[ \frac{8 \div 4}{4 \div 4} = \frac{2}{1} ]
Since both simplified fractions are equal, we confirm that they are equivalent.
- Conclusion Thus, ( \frac{16}{8} ) and ( \frac{8}{4} ) are equivalent fractions.
The fractions ( \frac{16}{8} ) and ( \frac{8}{4} ) are equivalent.
More Information
Equivalent fractions are fractions that represent the same value even though they have different numerators and denominators. Simplifying fractions helps us identify these equivalences.
Tips
- Failing to find the greatest common divisor (GCD) can lead to incorrect simplifications.
- Dividing only one part of the fraction (numerator or denominator) instead of both can lead to incorrect results.
AI-generated content may contain errors. Please verify critical information
