Are 2/3 and 3/4 equal?
Understand the Problem
The question is asking whether the fractions 2/3 and 3/4 are equal to each other. To determine this, we can compare their values by finding a common denominator or converting them to decimals.
Answer
The fractions \( \frac{2}{3} \) and \( \frac{3}{4} \) are not equal, and \( \frac{2}{3} < \frac{3}{4} \).
Answer for screen readers
The fractions ( \frac{2}{3} ) and ( \frac{3}{4} ) are not equal, and ( \frac{2}{3} < \frac{3}{4} ).
Steps to Solve
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Finding a common denominator To compare the fractions, we first find a common denominator. The denominators of the fractions are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.
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Convert fractions to the common denominator Next, we convert each fraction to have the common denominator of 12.
For $ \frac{2}{3} $: $$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $$
For $ \frac{3}{4} $: $$ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $$
- Compare the converted fractions Now, we can compare the fractions $ \frac{8}{12} $ and $ \frac{9}{12} $. Since 8 is less than 9, we conclude that:
$$ \frac{2}{3} < \frac{3}{4} $$
The fractions ( \frac{2}{3} ) and ( \frac{3}{4} ) are not equal, and ( \frac{2}{3} < \frac{3}{4} ).
More Information
When comparing fractions, finding a common denominator helps you determine their relative sizes easily. This method can be used for any two fractions!
Tips
- One common mistake is assuming the fractions are equal without finding a common denominator. Always convert them before comparison.
- Another mistake is incorrectly calculating the equivalent fractions or common denominators. Double-check your multiplication and LCM.
