Subjects quantitative reasoning

Equivalent Ratios

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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.