20 g : 100 g = 1 metre : 500 cm
Goal: Check if the two ratios are the same:
We know:
(1 ext{ metre} = 100 ext{ cm})
So the right ratio becomes:
(100 ext{ cm} : 500 ext{ cm})
Left ratio (grams):
(20 : 100)
Divide both numbers by (20):
(dfrac{20}{20} : dfrac{100}{20} = 1 : 5)
Right ratio (centimetres):
(100 : 500)
Divide both numbers by (100):
(dfrac{100}{100} : dfrac{500}{100} = 1 : 5)
Both ratios become:
(1 : 5)
Since they are the same, the statement is true.
Compare (20 : 100) and (100 : 500):
(20 imes 500 = 10000)
(100 imes 100 = 10000)
Both products are equal, so the ratios are equivalent.