ACT Math: Master Order of Operations with Fractions to Avoid Careless Errors

PEMDAS is the order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students understand PEMDAS but make careless errors when fractions or multiple operations appear. Example: 1/2+3/4*2. Wrong approach: 1/2+3=3.5, then 3.5/4=0.875, then 0.875*2=1.75 (wrong because this violates PEMDAS). Correct approach: Multiply first: 3/4*2=3/2. Then add: 1/2+3/2=4/2=2. PEMDAS with fractions requires careful tracking; write out each step explicitly to avoid jumbling operations.

Another example: 3+4^2*2. Exponent first: 4^2=16. Then multiply: 16*2=32. Then add: 3+32=35. Many students calculate 3+4=7, then 7^2=49, then 49*2=98 (wrong because they calculated 3+4 before the exponent, violating PEMDAS). Writing steps explicitly prevents these errors.

Trap 1: Treating a fraction bar as lower priority than it actually is. The fraction bar is a grouping symbol (like parentheses), so the numerator and denominator must be fully calculated before dividing. Example: (2+3)/(4-1)=5/3. Many students calculate 2+3=5, then jump to 5/4 without calculating the denominator first. Trap 2: Forgetting that multiplication and division are equal priority and calculated left to right. 8/2*4 is NOT 8/(2*4)=8/8=1. It's (8/2)*4=4*4=16, calculated left to right. Write out each step explicitly, especially with fractions. Fraction bars are grouping symbols; calculate the whole numerator, whole denominator, then divide.

When you see a complex expression with fractions and operations, write it out step by step. Mark which operation you're doing at each stage. This explicit work prevents careless errors that cost points.

Problem 1: 3/4+1/2*8. Multiply first: 1/2*8=4. Then add: 3/4+4=3/4+16/4=19/4. Problem 2: (1+2)^2-5*2. Parentheses: (1+2)=3. Exponent: 3^2=9. Multiply: 5*2=10. Subtract: 9-10=-1. Problem 3: 2+3*4/2. Multiply and divide left to right: 3*4=12, 12/2=6. Then add: 2+6=8. Problem 4: (6+2)/(4-1)+1. Parentheses: numerator (6+2)=8, denominator (4-1)=3. Divide: 8/3. Add: 8/3+1=8/3+3/3=11/3. All four problems require careful step-by-step execution of PEMDAS; rushing leads to errors.

Do ten more PEMDAS problems with fractions and operations. Write every step. By test day, careful execution will prevent careless errors and ensure you get these problems right.

Many ACT Math errors are careless mistakes from incorrect order of operations, not from misunderstanding the concept. If you develop a habit of writing out steps explicitly and following PEMDAS rigorously, you'll eliminate most careless errors and see an immediate boost in your Math accuracy.

This week, write out every step for every PEMDAS problem you solve. By test day, careful execution will be your default, earning you points you might otherwise lose to careless mistakes.