Equivalent Ratios
1. The problem involves understanding equivalences among percentages, fractions, and decimals shown as nodes on four graphs.
2. For the top-left graph: 50%, 1/2, 1:2, and 0.5 are all equivalent since:
$$50\% = \frac{50}{100} = \frac{1}{2} = 0.5$$
The ratio 1:2 also represents half because 1 part out of 2 total parts equals $\frac{1}{2}$.
3. For the top-right graph: 40%, 2/5, 2:5, and 0.4 are equivalent:
$$40\% = \frac{40}{100} = \frac{2}{5} = 0.4$$
The ratio 2:5 corresponds to $\frac{2}{5}$ which equals 0.4.
4. For the bottom-left graph: 1/4 and 1:4 are given; 1/4 as a decimal is 0.25 (not labeled), and 1:4 as a ratio equals $\frac{1}{4}$.
5. For the bottom-right graph: 13/25 and 0.52 are given and equivalent:
$$\frac{13}{25} = 0.52$$
Since $\frac{13}{25} = \frac{13 \times 4}{25 \times 4} = \frac{52}{100} = 0.52$.
Summary: Each graph connects equivalent representations of the same quantity in different forms (percent, fraction, ratio, decimal).
Final conclusion: The links confirm equivalences:
- 50%, 1/2, 1:2, 0.5
- 40%, 2/5, 2:5, 0.4
- 1/4, 1:4 (with decimal 0.25 implied)
- 13/25, 0.52
All values in each graph represent the same numeric value.