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Ratio Manipulation

Lesson · Beginner

Algebra: Expressions & Identities

ab=cd\frac{a}{b}=\frac{c}{d}
a+bb=c+dd\frac{a+b}{b}=\frac{c+d}{d}
aa+b=cc+d\frac{a}{a+b}=\frac{c}{c+d}
ab−a=cd−c\frac{a}{b-a}=\frac{c}{d-c}
a−ba+b=c−dc+d\frac{a-b}{a+b}=\frac{c-d}{c+d}
a1b1=a2b2=⋯=anbn=k⟹λ1a1+λ2a2+⋯+λnanλ1b1+λ2b2+⋯+λnbn=k\frac{a_1}{b_1}=\frac{a_2}{b_2}=\cdots=\frac{a_n}{b_n}=k \quad\Longrightarrow\quad \frac{\lambda_1a_1+\lambda_2a_2+\cdots+\lambda_na_n} {\lambda_1b_1+\lambda_2b_2+\cdots+\lambda_nb_n}=k
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