Finding a Missing Number
Finding a missing number in a proportion uses cross-multiplication to create a simple equation, then division to solve for the unknown. For the proportion 20/n = 360, multiply the known cross-products and divide to find n. This Grade 7 math skill from Saxon Math, Course 2 teaches a systematic method for solving any proportion equation, which applies directly to scale drawings, unit rate conversions, similar figures in geometry, and countless real-world rate problems.
Key Concepts
Property First, find the total sum using the average and quantity. Then, subtract the sum of the known numbers from the total to find the missing number.
Examples The average of four numbers is 10. Three numbers are 5, 8, and 12. Total sum: $4 \times 10 = 40$. Fourth number: $40 (5+8+12) = 15$. The average of three exam scores is 90. Two scores are 85 and 95. Total needed: $3 \times 90 = 270$. Third score: $270 (85+95) = 90$.
Explanation This is like a math treasure hunt! You know the total value of all the items (the sum). You're told the value of all but one. To find the last one's value, just subtract what you already know from the grand total!
Common Questions
How do I find a missing number in a proportion?
Cross-multiply to set the products equal, then divide to isolate the variable. For 3/4 = 9/n, cross-multiply to get 3n = 36, then divide: n = 12.
What is cross-multiplication?
Cross-multiplication means multiplying the numerator of one fraction by the denominator of the other in a proportion. For a/b = c/d, cross-multiplying gives ad = bc.
Why does cross-multiplication work for proportions?
Cross-multiplication works because it clears the denominators from both sides of the equation simultaneously, leaving a simple multiplication equation to solve.
Can there be more than one unknown in a proportion?
A proportion has four terms and can only have one unknown for a unique solution. With two unknowns you would need additional information or a system of equations.
When do students learn to find missing numbers in proportions?
Finding missing proportion terms is a core Grade 7 skill. Saxon Math, Course 2 covers it in Chapter 5 with both abstract examples and real-world applications.
What are common errors when finding a missing number in a proportion?
A frequent error is multiplying in the same direction rather than across (same position in both fractions) instead of cross-multiplying. Always multiply the numerator of each fraction by the denominator of the other.
How does finding missing numbers in proportions apply to scale drawings?
If a map scale is 1 inch = 50 miles, finding the actual distance from a 3.5-inch map measurement uses the proportion 1/50 = 3.5/d, which you solve by cross-multiplication.