Proportions
Proportions is a Grade 7 math skill from Yoshiwara Intermediate Algebra where two ratios are set equal to each other: a/b = c/d. Students solve proportions using cross-multiplication and apply them to scaling, unit conversion, and real-world problems.
Key Concepts
Property A proportion is a statement that two ratios are equal. For example, $\frac{a}{b} = \frac{c}{d}$.
If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$, as long as $b, d \neq 0$. This shortcut is known as cross multiplying.
Examples To solve the proportion $\frac{8}{3} = \frac{x}{9}$, we can cross multiply. This gives $8 \cdot 9 = 3 \cdot x$, so $72 = 3x$. Dividing by 3, we find $x=24$.
Common Questions
What is a proportion?
A proportion is an equation stating that two ratios are equal: a/b = c/d. It means a and b have the same relationship as c and d.
How do you solve a proportion using cross-multiplication?
Cross-multiply: a/b = c/d becomes ad = bc. Then solve for the unknown variable.
How do you solve x/4 = 3/6?
Cross-multiply: 6x = 12. Divide: x = 2.
Where are proportions used in real life?
Proportions are used in recipe scaling, map reading, similar triangles, currency conversion, and many other ratio-based applications.