# Properties of Ratio

• The order of the terms in a ratio is very important.
• Ratio between two quantities should be in the most simplified form.
• Ratio is a comparison of two or more quantities of the same kind only.
• If the ratio of two quantities can be expressed as a ratio of two integers, the quantities are said to be commensurable; otherwise, they are said to be incommensurable.
• Continued ratio is the relation between the magnitudes of three or more quantities of the same kind. The continued ratio of three similar quantities a, b, c is written as a:b:c.
• Whenever a ratio a:b is given between two magnitudes, we always express the actual magnitudes as ka and kb,where k is a constant.
• If a:b and c:d are two ratios, then ac:bd is their compound ratio.
• a2:b2 is the duplicate ratio of a:b.
• a3:b3 is the triplicate ratio of a:b.
• is the sub-duplicate ratio of a:b.
• is the sub-triplicate ratio of a:b.
• If a given number N has to be divided into two parts A and B which are in the ratio a:b, then
• If a given number N has to be divided into three parts A, B and C which are in the ratio of a:b:c; then,

# Properties of Proportion

• If , then  (Invertendo)
• If , then  (Alternendo)
• If , then  (Componendo)
• If , then  (Dividendo)
• If , then  (Componendo and Dividendo)