\(0.2:5 = 2:0.5\)
Goal: Check if the two ratios are equal. A ratio a : b equals c : d if (dfrac{a}{b} = dfrac{c}{d}) (and (b,d eq 0)).
Step 1 — Left side:
(0.2:5 = dfrac{0.2}{5})
(0.20 div 5 = 0.04)
Step 2 — Right side:
(2:0.5 = dfrac{2}{0.5})
To avoid decimals in the denominator, multiply top and bottom by 10:
(dfrac{2 imes 10}{0.5 imes 10} = dfrac{20}{5})
(20 div 5 = 4)
Step 3 — Compare values:
Left side = (0.04)
Right side = (4)
(0.04 eq 4)
Conclusion: The ratios are not equal, so the statement is false.