Solving Proportions
Solving proportions means finding an unknown value in an equation that states two ratios are equal, like 3/4 = x/12. The standard method is cross multiplication: multiply the numerator of each fraction by the denominator of the other, then solve the resulting equation. Here, 3 x 12 = 4 x x, so 36 = 4x, and x = 9. This 7th grade skill from Saxon Math Course 2 is used in scale drawing, unit conversion, recipe scaling, and any real-world situation involving equivalent rates or ratios.
Key Concepts
Property Step 1: Find the cross products, which are equal. Step 2: Divide the known product by the known factor to find the missing term.
Examples Solve $\frac{6}{x} = \frac{3}{5}$: $3x = 30$, so $x=10$. Solve $\frac{n}{12} = \frac{2}{3}$: $3n = 24$, so $n=8$. Solve $\frac{5}{8} = \frac{10}{d}$: $5d = 80$, so $d=16$.
Explanation Finding a missing number is a treasure hunt. Cross multiplication gives you a map ($20n=360$), and division leads you straight to the treasure ($n=18$). X marks the spot!
Common Questions
How do you solve a proportion?
Cross-multiply: multiply each numerator by the opposite denominator. If 3/4 = x/12, then 3 x 12 = 4x, so 36 = 4x, giving x = 9.
What is cross multiplication?
Cross multiplication finds the products of the numerator of each fraction times the denominator of the other, then sets them equal. It is valid only when two fractions are set equal to each other (a proportion).
How is solving proportions used in scale drawings?
If a map has a scale of 1 inch = 50 miles, setting up 1/50 = 3/x and solving gives x = 150 miles for a 3-inch distance.
What grade learns to solve proportions?
Solving proportions is a central 7th grade math skill in Saxon Math Course 2, used throughout the course in percent, geometry, and rate problems.
Can you solve a proportion without cross multiplication?
Yes. You can also find the scale factor between the two ratios and multiply or divide. If 3/4 = x/12, notice 12 = 4 x 3, so x = 3 x 3 = 9. Both methods work.
What is a common mistake when solving proportions?
Cross-multiplying when the expression is not a proportion (not two equal fractions). Cross multiplication only applies when two fractions are set equal to each other.