Equations with Fractions and Decimals — SAT Math Explained
Linear equations where the coefficients or constants are fractions or decimals, requiring additional steps to solve cleanly.
The Core Idea
Fractions and decimals are not obstacles — they follow the same rules. The key strategy is often to eliminate them early by multiplying through by the LCD (Least Common Denominator) or by a power of 10.
Key Vocabulary
The smallest number that all denominators in an equation divide into evenly
Multiplying every term on both sides by the LCD to eliminate all denominators
Multiplying every term by a power of 10 (10, 100, 1000) to turn decimals into integers
A fraction where the numerator is larger than the denominator (e.g., 7/3)
Step-by-Step: How to Approach Equations with Fractions and Decimals
Identify all fractions or decimals in the equation
For fractions: find the LCD of all denominators
Multiply every single term on both sides by the LCD
Simplify — fractions should be eliminated
Solve the resulting whole-number equation normally
Check by substituting back into the original fractional equation
Pro Tips
For decimals with tenths only, multiply by 10. For hundredths, multiply by 100, etc.
Always multiply EVERY term — don't skip constants
After clearing fractions, double-check by re-examining the original equation
Common Errors to Avoid
Multiplying only the fraction terms but forgetting the constant terms
Finding the wrong LCD by not fully factoring denominators
Making sign errors when multiplying negatives
How This Connects to Other Topics
Critical for solving rational equations later and for working with real-world measurements that involve non-integer values
Practice: Equations with Fractions and Decimals
5 SAT-style questions. Select your answer and get an instant explanation.
Solve for x: x/3 = 7
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