Ratio

01/11/2025

A ratio is a mathematical comparison of two numbers, often written as a fraction or using a colon (e.g., \(3:2\) or \(\frac{3}{2}\)). Ratios show the relationship between quantities, such as the ratio of apples to oranges or the ratio of red to black balls in a box. They can be simplified to their lowest terms and are used to solve problems in many fields. How to write a ratio Use a colon: Write the two numbers with a colon in between, such as \(8:6\).  Use the word “to”: Write the numbers with the word “to” in between, as in “eight to six”.  Use a fraction: Write one number over the other to show the relationship, such as \(\frac{8}{14}\).  How to write a ratio Use a colon: Write the two numbers with a colon in between, such as \(8:6\).  Use the word “to”: Write the numbers with the word “to” in between, as in “eight to six”.  Use a fraction: Write one number over the other to show the relationship, such as \(\frac{8}{14}\). 

Proportion (mathematics)

22/10/2025

From Wikipedia, the free encyclopedia

A proportion is a mathematical statement expressing equality of two ratios.[1][2]

a:b=c:d{\displaystyle a:b=c:d}

a and d are called extremes, b and c are called means.

Proportion can be written as ab=cd{\displaystyle {\frac {a}{b}}={\frac {c}{d}}}, where ratios are expressed as fractions.

Such a proportion is known as geometrical proportion,[3] not to be confused with arithmetical proportion and harmonic proportion.

  • Fundamental rule of proportion. This rule is sometimes called Means‐Extremes Property.[4] If the ratios are expressed as fractions, then the same rule can be phrased in terms of the equality of “cross-products”[2] and is called Cross‐Products Property.[4]

If  ab=cd

{\displaystyle \ {\frac {a}{b}}={\frac {c}{d}}}

, then  ad=bc

{\displaystyle \ ad=bc}
  • If  ab=cd{\displaystyle \ {\frac {a}{b}}={\frac {c}{d}}}, then  ba=dc{\displaystyle \ {\frac {b}{a}}={\frac {d}{c}}}
  • If  ab=cd{\displaystyle \ {\frac {a}{b}}={\frac {c}{d}}}, then

 ac=bd

{\displaystyle \ {\frac {a}{c}}={\frac {b}{d}}}

, db=ca

{\displaystyle \ {\frac {d}{b}}={\frac {c}{a}}}

.

  • If  ab=cd{\displaystyle \ {\frac {a}{b}}={\frac {c}{d}}}, then

 a+bb=c+dd

{\displaystyle \ {\dfrac {a+b}{b}}={\dfrac {c+d}{d}}}

, a−bb=c−dd

{\displaystyle \ {\dfrac {a-b}{b}}={\dfrac {c-d}{d}}}

.

  • If  ab=cd{\displaystyle \ {\frac {a}{b}}={\frac {c}{d}}}, then

 a+cb+d=ab=cd

{\displaystyle \ {\dfrac {a+c}{b+d}}={\frac {a}{b}}={\frac {c}{d}}}

, a−cb−d=ab=cd

{\displaystyle \ {\dfrac {a-c}{b-d}}={\frac {a}{b}}={\frac {c}{d}}}

.