Why this matters for FAST: Adding and subtracting fractions with unlike denominators is a fundamental skill tested extensively on FAST. Students must find common denominators, perform operations correctly, and express answers in simplest form.
Students think 1/2 + 1/3 = 2/5 by adding across (1+1=2 and 2+3=5). This is the most common error!
"We can only add fractions when they have the SAME denominator. The denominator tells us what SIZE pieces we have. We can't add halves and thirds directly - we need to convert them to the same-sized pieces first!"
Students convert only one fraction: 1/2 + 1/4, they change 1/2 to 2/4 but then write 2/4 + 1/4 = 3/8 (using wrong denominator).
"After converting, check: Do BOTH fractions now have the same denominator? 2/4 + 1/4 - yes! Now add just the numerators: 2+1=3, keep the denominator: 3/4."
Students get 4/8 as their answer but don't recognize it should be simplified to 1/2.
"Always check: Can both the numerator and denominator be divided by the same number? If yes, simplify! 4/8 - both divide by 4, so 4/8 = 1/2."
Review: "What is 2/5 + 1/5?" (3/5) "Why can we just add the numerators?" (Because they have the same denominator - same-sized pieces!) "What if the denominators are different?"
"To add or subtract fractions with different denominators, we need to find a COMMON denominator - a number that both denominators can divide into evenly. The easiest way is to find the Least Common Multiple (LCM) of the denominators."
Example: 1/2 + 1/3 = ?
Step 1: Find LCD of 2 and 3
Multiples of 2: 2, 4, 6, 8...
Multiples of 3: 3, 6, 9...
LCD = 6
Convert both fractions to sixths:
12 = 1 x 32 x 3 = 36
13 = 1 x 23 x 2 = 26
"Ask yourself: What do I multiply each denominator by to get 6? Then multiply BOTH the numerator and denominator by that same number."
36 + 26 = 56
Add numerators, keep the denominator!
5/6 is already in simplest form (5 and 6 share no common factors)
Work through these together:
"What is 2/3 + 1/4?"
A) 3/7 B) 11/12 C) 3/12 D) 8/12
Correct answer: B) 11/12 (LCD=12: 8/12 + 3/12 = 11/12)
For struggling students: Use fraction strips to visualize why we need common denominators. Start with denominators where one is a multiple of the other (like 2 and 4, or 3 and 6).
For advanced students: Challenge with three-fraction problems or fractions with larger denominators that require finding LCM (like 1/4 + 1/6 + 1/8).
For home: Send Parent Activity sheet. Families can practice with cooking measurements (combining 1/2 cup and 1/4 cup).