Adding and Subtracting Fractions with Unlike Denominators — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The least common denominator is the smallest number both denominators divide into evenly.
The Least Common Denominator (LCD) is the smallest common multiple of the denominators. Using the LCD keeps numbers smaller and simplifies computation.
2. Fractions that name the same amount, like 24 and 12, are called equivalent fractions.
Equivalent fractions represent the same value. 24 and 12 are equivalent because 2÷2=1 and 4÷2=2. Creating equivalent fractions is essential for adding/subtracting unlike denominators.
3. Before adding 13 + 25, you must find a common denominator.
A common denominator allows you to express both fractions in terms of equal-sized pieces before combining them.
4. A fraction is in simplest form when the numerator and denominator share no common factor > 1.
A fraction in simplest form (also called lowest terms) has a GCF of 1 between numerator and denominator. For example, 68 simplifies to 34.
5. The LCD of 4 and 6 is 12.
Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... The first common multiple is 12, so LCD = 12.
6. To rename 35 with a denominator of 20, multiply numerator and denominator by 4.
5 × 4 = 20, so multiply both parts by 4: 35 = 1220.
7. 16 + 34 = 212 + 912 = 1112 in simplest form.
LCD of 6 and 4 is 12. 16 = 212, 34 = 912. Sum = 1112. GCF(11,12)=1, already in simplest form.
8. 58 − 13 = 1524 − 824 = 724.
LCD of 8 and 3 is 24. 58 = 1524, 13 = 824. Difference = 724. GCF(7,24)=1, already in simplest form.
9. When a fraction like 68 can be reduced, divide both parts by their greatest common factor.
To simplify, find the Greatest Common Factor (GCF) of numerator and denominator and divide both by it. GCF(6,8)=2, so 68 = 34.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
12 + 13
→ 56
712
34 − 16
→ 712
13
25 + 14
→ 1320
56
56 − 12
→ 13
1320
12+13=36+26=56; 34−16=912−212=712; 25+14=820+520=1320; 56−12=56−36=26=13.