# 交叉相乘

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

(当bd都不等于时)，可以交叉相乘来得到：[1]

${\displaystyle ad=bc\qquad }$${\displaystyle \qquad a={\frac {bc}{d}}.}$

## 过程

${\displaystyle {\frac {a}{b}}\nwarrow {\frac {c}{d}}\quad {\frac {a}{b}}\nearrow {\frac {c}{d}}.}$

${\displaystyle {\frac {a}{b}}={\frac {c}{d}}}$ (bd都不等于)

${\displaystyle ad=bc}$

${\displaystyle a={\frac {bc}{d}}}$

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

${\displaystyle {\frac {ad}{bd}}={\frac {cb}{db}}.}$

${\displaystyle ad=cb.}$

## 使用方法

${\displaystyle {\frac {x}{b}}={\frac {c}{d}}}$

${\displaystyle x={\frac {bc}{d}}.}$

${\displaystyle {\frac {x}{7\ \mathrm {hours} }}={\frac {90\ \mathrm {miles} }{3\ \mathrm {hours} }}.}$

${\displaystyle x={\frac {90\ \mathrm {miles} \times 7\ \mathrm {hours} }{3\ \mathrm {hours} }}.}$

${\displaystyle x=210\ \mathrm {miles} }$

${\displaystyle a={\frac {x}{d}}}$

b部分视为1，也可以视为下列方程来用交叉相乘来解决

${\displaystyle {\frac {a}{1}}={\frac {x}{d}}.}$