6. Higher Order Thinking Diego compared the differences for \( \frac{10}{10}-\frac{1}{10} \) and \( \frac{100}{100}-\frac{10}{100} \). He said the differences both equal \( \frac{9}{10} \). Is Diego correct? Explain.

Let's evaluate the two expressions step by step to determine if Diego's claim is correct. 1. **Calculate the first expression:** \[ \frac{10}{10} - \frac{1}{10} \] - First, we simplify \( \frac{10}{10} \): \[ \frac{10}{10} = 1 \] - Now, we can rewrite the expression: \[ 1 - \frac{1}{10} \] - To perform the subtraction, we convert \( 1 \) into a fraction with a denominator of \( 10 \): \[ 1 = \frac{10}{10} \] - Now we can subtract: \[ \frac{10}{10} - \frac{1}{10} = \frac{10 - 1}{10} = \frac{9}{10} \] 2. **Calculate the second expression:** \[ \frac{100}{100} - \frac{10}{100} \] - First, we simplify \( \frac{100}{100} \): \[ \frac{100}{100} = 1 \] - Now, we can rewrite the expression: \[ 1 - \frac{10}{100} \] - To perform the subtraction, we convert \( 1 \) into a fraction with a denominator of \( 100 \): \[ 1 = \frac{100}{100} \] - Now we can subtract: \[ \frac{100}{100} - \frac{10}{100} = \frac{100 - 10}{100} = \frac{90}{100} \] - We can simplify \( \frac{90}{100} \): \[ \frac{90}{100} = \frac{9}{10} \] 3. **Conclusion:** - The first expression evaluates to \( \frac{9}{10} \). - The second expression also evaluates to \( \frac{9}{10} \). Since both differences equal \( \frac{9}{10} \), Diego is correct in stating that the differences are equal.