Fractions and Operations — SAT Math Guide

Q: What You Need to Know

• **Adding/subtracting fractions**: Find common denominators first • **Multiplying fractions**: Multiply numerators together, denominators together • **Dividing fractions**: Multiply by the reciprocal (flip the second fraction) • **Mixed numbers**: Convert to improper fractions before operating • **

Fractions and operations SAT questions test your ability to add, subtract, multiply, and divide fractions accurately. You'll work with proper fractions, improper fractions, and mixed numbers in real-world contexts. These problems appear 2-3 times across the Problem Solving and Data Analysis domain on the Digital SAT. Don't worry — with the right techniques, you'll handle these confidently!

What You Need to Know

Adding/subtracting fractions: Find common denominators first

Multiplying fractions: Multiply numerators together, denominators together

Dividing fractions: Multiply by the reciprocal (flip the second fraction)

Mixed numbers: Convert to improper fractions before operating

Simplifying: Always reduce to lowest terms

Cross-multiplication: Useful for solving proportions and equations

📐 KEY FORMULA: a/b ÷ c/d = a/b × d/c

💡 PRO TIP: When adding fractions with different denominators, multiply by the LCD (least common denominator) to avoid huge numbers.

How to Solve Fractions and Operations on the SAT

Example Question 1 — Medium Difficulty

A recipe calls for 2¼ cups of flour. If Maria wants to make ⅔ of the recipe, how many cups of flour will she need?

A) 1½ cups

B) 1⅓ cups

C) 1⅙ cups

D) 2⅙ cups

Solution:

Step 1: Convert mixed number to improper fraction: 2¼ = 9/4

Step 2: Multiply by ⅔: (9/4) × (2/3) = 18/12

Step 3: Simplify: 18/12 = 3/2 = 1½

✅Answer: A — Maria needs 1½ cups of flour for ⅔ of the recipe.

Example Question 2 — Hard Difficulty

If x + ⅓ = ¾ - ⅙, what is the value of x?

A) ¼

B) ⅓

C) 7/12

D) 5/12

Solution:

Step 1: Solve the right side first: ¾ - ⅙ = 9/12 - 2/12 = 7/12

Step 2: Substitute: x + ⅓ = 7/12

Step 3: Subtract ⅓ from both sides: x = 7/12 - 4/12 = 3/12 = ¼

✅Answer: A — The value of x is ¼.

Common SAT Math Mistakes to Avoid

❌Mistake: Adding denominators when multiplying fractions

✅Fix: Only multiply numerator × numerator and denominator × denominator

❌Mistake: Forgetting to flip the second fraction when dividing

✅Fix: Remember "keep, change, flip" — keep first fraction, change ÷ to ×, flip second fraction

❌Mistake: Not finding common denominators when adding/subtracting

✅Fix: Always convert to equivalent fractions with the same denominator first

❌Mistake: Leaving answers in improper fraction form

✅Fix: Convert improper fractions back to mixed numbers when the SAT math section expects it

Practice Question — Try It Yourself

A construction worker uses ⅝ of a bag of cement in the morning and ¼ of the same bag in the afternoon. What fraction of the bag remains unused?

A) ⅛

B) 3/8

C) ½

D) ⅞

Show Answer

Answer: A — First find total used: ⅝ + ¼ = ⅝ + 2/8 = 7/8. Remaining: 1 - 7/8 = ⅛

Key Takeaways for the SAT

Convert mixed numbers to improper fractions before performing operations

Use cross-multiplication to solve fraction equations quickly

Always check if your answer can be simplified further

For SAT math fractions and operations, work systematically through each step

When in doubt, find common denominators to make calculations clearer