Proportions & Scale Factors Quick Check
A proportion is an equation that states that two ratios are equal. It is expressed in the form:
$\frac{a}{b}=\frac{c}{d}$
A scale factor is a ratio comparing the sizes of two similar objects. It is used to find the ratio of corresponding lengths, areas, or volumes. It is expressed as a ratio, such as 1:2 or 3:1.
To solve a proportion, you can use cross multiplication. Cross multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio, and then setting the two products equal to each other:
$a \cdot d = b \cdot c$
To find a missing value in a proportion, you can use the concept of scale factors. If you know the ratio of corresponding lengths, areas, or volumes, you can use that ratio to find the missing value.
Overall, proportions and scale factors are used to compare and solve for unknown values in related objects or quantities.