Solving Proportions
Solving Proportions is a core Grade 6-8 math skill where students find the unknown value in a proportion by using cross-multiplication or equivalent fractions. Proportions are used in real-world contexts including scaling, unit rates, similar figures, and percent problems.
Key Concepts
Property To find a missing number in a proportion, use a variable and find the multiplier between the terms. In the proportion $$\frac{2}{8} = \frac{6}{x}$$, you can solve for the unknown value, x.
Examples To solve $$\frac{24}{m} = \frac{8}{5}$$, notice that $8 \times 3 = 24$. Apply this to the denominator: $5 \times 3 = 15$, so $m=15$. To solve $$\frac{4}{5} = \frac{16}{y}$$, see that $4 \times 4 = 16$. Apply this to the denominator: $5 \times 4 = 20$, so $y=20$.
Explanation Put on your detective hat! When a number is missing from a proportion, find the relationship between the numbers you do know. If you see $2 \times 3 = 6$, you can apply that same secret rule to the other pair of numbers. It’s a simple trick to solve the mystery every time!
Common Questions
How do you solve a proportion?
Cross-multiply: if a/b = c/d, then ad = bc. Solve for the unknown variable by dividing both sides.
What is cross-multiplication?
Cross-multiplication is when you multiply the numerator of one fraction by the denominator of the other: a/b = c/d means a times d equals b times c.
What is an example of solving a proportion?
Solve 3/4 = x/12: cross-multiply to get 4x = 36, then divide by 4 to get x = 9.
Where are proportions used in real life?
Proportions are used in recipes, maps, scale drawings, unit conversions, and finding discounts or taxes.
What grade covers solving proportions?
Solving proportions is taught in Grade 6, 7, and 8 math.