Questions: -1/3 ? -5/8

Transcript text: $-\frac{1}{3} ?-\frac{5}{8}$

Solution

Solution Steps

Solution Approach

To solve the problem of comparing the fractions $-\frac{1}{3}$ and $-\frac{5}{8}$, we need to convert them to a common denominator and then compare the numerators. Alternatively, we can convert them to decimal form and compare the decimal values.

Step 1: Define the Fractions

We have two fractions to compare: \[ \text{fraction1} = -\frac{1}{3} \quad \text{and} \quad \text{fraction2} = -\frac{5}{8} \]

Step 2: Convert to a Common Denominator

To compare these fractions, we can convert them to a common denominator. The least common multiple of the denominators $3$ and $8$ is $24$. Thus, we convert each fraction: \[ -\frac{1}{3} = -\frac{8}{24} \quad \text{and} \quad -\frac{5}{8} = -\frac{15}{24} \]

Step 3: Compare the Numerators

Now we compare the numerators of the converted fractions: \[ -\frac{8}{24} \quad \text{and} \quad -\frac{15}{24} \] Since $-8 > -15$, we conclude that: \[ -\frac{1}{3} > -\frac{5}{8} \]

Final Answer

The comparison shows that $-\frac{1}{3}$ is greater than $-\frac{5}{8}$. Thus, the final answer is: \[ \boxed{-\frac{1}{3} > -\frac{5}{8}} \]

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