Proportions
Proportions defines a proportion as an equation stating that two ratios are equal (a/b = c/d) and introduces cross-multiplication as the method to solve for unknowns: if a/b = c/d, then ad = bc. Covered in Yoshiwara Elementary Algebra Chapter 3: Graphs of Linear Equations, this tool helps Grade 6 students solve real-world scaling, unit conversion, and similarity problems efficiently. Cross-multiplication eliminates fractions and simplifies the equation to a straightforward linear or arithmetic computation.
Key Concepts
Property A proportion is a statement that two ratios are equal. We can clear the fractions from a proportion by cross multiplying.
If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$.
Examples To solve $\frac{x}{10} = \frac{3}{5}$, we cross multiply to get $5x = 10(3)$. This gives $5x=30$, so $x=6$.
Common Questions
What is a proportion in math?
A proportion is a statement that two ratios are equal: a/b = c/d. It means the relationship between a and b is the same as the relationship between c and d.
How do you solve a proportion using cross-multiplication?
Multiply the numerator of each fraction by the denominator of the other: ad = bc. Then solve for the unknown variable.
What is cross-multiplication?
Cross-multiplication means multiplying diagonally across an equation of two fractions: if a/b = c/d, then a × d = b × c. It clears both denominators at once.
Where are proportions covered in Yoshiwara Elementary Algebra?
Proportions are in Chapter 3: Graphs of Linear Equations of Yoshiwara Elementary Algebra.
When do you use proportions in real life?
Proportions are used for scale drawings, recipes, unit conversion, map reading, and any situation where two equivalent ratios describe a relationship.