Is 2 3/8 > 2 6/4?
Understand the Problem
The question is asking us to compare two mixed numbers, 2 3/8 and 2 6/4, and determine if the statement '2 3/8 is greater than 2 6/4' is true or false. This involves understanding how to compare fractions and mixed numbers.
Answer
False
Answer for screen readers
False
Steps to Solve
- Convert the mixed numbers to improper fractions
To compare the mixed numbers, convert them into improper fractions: $2 \frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}$
$2 \frac{6}{4} = \frac{(2 \times 4) + 6}{4} = \frac{8 + 6}{4} = \frac{14}{4}$
- Find a common denominator
To compare the fractions $\frac{19}{8}$ and $\frac{14}{4}$, we need a common denominator. The least common multiple of 8 and 4 is 8. So we convert $\frac{14}{4}$ to have a denominator of 8:
$\frac{14}{4} = \frac{14 \times 2}{4 \times 2} = \frac{28}{8}$
- Compare the fractions
Now we compare $\frac{19}{8}$ and $\frac{28}{8}$. Since they have the same denominator, we can compare their numerators:
$19 < 28$
Therefore, $\frac{19}{8} < \frac{28}{8}$
- Determine if the statement is true or false
Since $\frac{19}{8} < \frac{28}{8}$, this means $2 \frac{3}{8} < 2 \frac{6}{4}$. The statement "2 3/8 is greater than 2 6/4" is false.
False
More Information
The mixed number $2 \frac{6}{4}$ can also be simplified because $\frac{6}{4}$ is an improper fraction greater than 1. $2 \frac{6}{4} = 2 + \frac{6}{4} = 2 + 1 \frac{2}{4} = 3 \frac{2}{4} = 3 \frac{1}{2}$. $2 \frac{3}{8}$ is less than $3 \frac{1}{2}$.
Tips
A common mistake is not converting the mixed numbers to improper fractions or not finding a common denominator before comparing. Another mistake is to only compare the fractional parts of the mixed numbers, without considering the whole number parts, but that would not be applicable here as both whole numbers are the same in the original problem.
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