Answer :
To classify the pair of ratios \(\frac{7}{8}\) and \(\frac{42}{48}\) as either proportional or not proportional, let's break down the steps needed to determine their relationship:
1. Identify the given ratios:
- Ratio 1: \(\frac{7}{8}\)
- Ratio 2: \(\frac{42}{48}\)
2. Simplify both ratios:
- For \(\frac{7}{8}\):
- The greatest common divisor (GCD) of 7 and 8 is 1.
- Simplified form: \(\frac{7}{8}\) (No change as the GCD is 1)
- For \(\frac{42}{48}\):
- The greatest common divisor (GCD) of 42 and 48 is 6.
- Simplified form: \(\frac{42 \div 6}{48 \div 6} = \frac{7}{8}\)
3. Compare the simplified forms:
- Simplified Ratio 1: \(\frac{7}{8}\)
- Simplified Ratio 2: \(\frac{7}{8}\)
4. Determine if the ratios are proportional:
- Since the simplified forms of both ratios are \(\frac{7}{8}\), they are equal.
- Therefore, the given ratios \(\frac{7}{8}\) and \(\frac{42}{48}\) are proportional.
Based on this analysis, the classification of the pair of ratios \(\frac{7}{8}\) and \(\frac{42}{48}\) should be marked as:
[tex]\[ \begin{array}{|c|c|c|} \hline & \text{Proportional} & \text{Not Proportional} \\ \hline \frac{7}{8} \text{ and } \frac{42}{48} & \text{1} & \text{0} \\ \hline \end{array} \][/tex]
So, they are Proportional.
1. Identify the given ratios:
- Ratio 1: \(\frac{7}{8}\)
- Ratio 2: \(\frac{42}{48}\)
2. Simplify both ratios:
- For \(\frac{7}{8}\):
- The greatest common divisor (GCD) of 7 and 8 is 1.
- Simplified form: \(\frac{7}{8}\) (No change as the GCD is 1)
- For \(\frac{42}{48}\):
- The greatest common divisor (GCD) of 42 and 48 is 6.
- Simplified form: \(\frac{42 \div 6}{48 \div 6} = \frac{7}{8}\)
3. Compare the simplified forms:
- Simplified Ratio 1: \(\frac{7}{8}\)
- Simplified Ratio 2: \(\frac{7}{8}\)
4. Determine if the ratios are proportional:
- Since the simplified forms of both ratios are \(\frac{7}{8}\), they are equal.
- Therefore, the given ratios \(\frac{7}{8}\) and \(\frac{42}{48}\) are proportional.
Based on this analysis, the classification of the pair of ratios \(\frac{7}{8}\) and \(\frac{42}{48}\) should be marked as:
[tex]\[ \begin{array}{|c|c|c|} \hline & \text{Proportional} & \text{Not Proportional} \\ \hline \frac{7}{8} \text{ and } \frac{42}{48} & \text{1} & \text{0} \\ \hline \end{array} \][/tex]
So, they are Proportional.
