To determine which symbol correctly compares the mixed numbers [tex]\( 6 \frac{3}{8} \)[/tex] and [tex]\( 6 \frac{15}{24} \)[/tex], we will follow these detailed steps:
### Step 1: Convert the Mixed Numbers to Improper Fractions
A mixed number consists of a whole number and a fraction. We'll start by converting each mixed number into a decimal form.
#### Converting [tex]\( 6 \frac{3}{8} \)[/tex]:
- The whole number is 6.
- The fractional part is [tex]\( \frac{3}{8} \)[/tex].
- Convert [tex]\( \frac{3}{8} \)[/tex] to a decimal: [tex]\( \frac{3}{8} = 0.375 \)[/tex].
- Combine the whole number and the decimal: [tex]\( 6 \frac{3}{8} = 6 + 0.375 = 6.375 \)[/tex].
#### Converting [tex]\( 6 \frac{15}{24} \)[/tex]:
- The whole number is 6.
- The fractional part is [tex]\( \frac{15}{24} \)[/tex].
- First, simplify [tex]\( \frac{15}{24} \)[/tex] if possible: [tex]\( \frac{15}{24} = \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \)[/tex] (note this step for clarity, although [tex]\( \frac{15}{24} \)[/tex] is already usable as a fraction).
- Convert [tex]\( \frac{15}{24} \)[/tex] or [tex]\( \frac{5}{8} \)[/tex] to a decimal: [tex]\( \frac{5}{8} = 0.625 \)[/tex].
- Combine the whole number and the decimal: [tex]\( 6 \frac{15}{24} = 6 + 0.625 = 6.625 \)[/tex].
### Step 2: Compare the Decimal Equivalents
Now, compare the decimal values obtained from each mixed number:
- [tex]\( 6.375 \)[/tex] for [tex]\( 6 \frac{3}{8} \)[/tex]
- [tex]\( 6.625 \)[/tex] for [tex]\( 6 \frac{15}{24} \)[/tex]
### Step 3: Determine the Correct Symbol
- Compare [tex]\( 6.375 \)[/tex] and [tex]\( 6.625 \)[/tex]:
- Since [tex]\( 6.375 < 6.625 \)[/tex], the correct symbol is [tex]\( < \)[/tex].
### Conclusion
The correct symbol to compare [tex]\( 6 \frac{3}{8} \)[/tex] and [tex]\( 6 \frac{15}{24} \)[/tex] is [tex]\( < \)[/tex].
Therefore, the answer is:
D. [tex]\( < \)[/tex]
