To determine which statement is not true, let's check each equation individually:
A) \( \frac{8}{10} = \frac{32}{40} \)
- Simplifying both sides:
- \( \frac{8}{10} = \frac{4}{5} \)
- \( \frac{32}{40} = \frac{4}{5} \)
Both sides are equal. This statement is true.
B) \( \frac{1}{3} = \frac{12}{36} \)
- Simplifying both sides:
- \( \frac{1}{3} \) remains \( \frac{1}{3} \)
- \( \frac{12}{36} = \frac{1}{3} \)
Both sides are equal. This statement is true.
C) \( \frac{24}{42} = \frac{28}{49} \)
- Simplifying both sides:
- \( \frac{24}{42} = \frac{4}{7} \)
- \( \frac{28}{49} = \frac{4}{7} \)
Both sides are equal. This statement is true.
D) \( \frac{13}{14} = \frac{169}{196} \)
- Simplifying both sides:
- \( \frac{13}{14} \) remains \( \frac{13}{14} \)
- \( \frac{169}{196} = \frac{13^2}{14^2} = \left(\frac{13}{14}\right)^2\)
\( \frac{13}{14} \) is not equal to \( \frac{169}{196} \) since \( \frac{13}{14} \) and \( \left(\frac{13}{14}\right)^2 \) are not equal.
So the statement that is not true is:
D) \( \frac{13}{14} = \frac{169}{196} \)