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. To rename a fraction with a new denominator, multiply both the numerator and denominator by the same number.
Multiplying both the numerator and denominator by the same number creates an equivalent fraction. This keeps the fraction's value the same while changing its denominator to match another fraction.
2. The LCD of 3 and 7 is 21.
Since 3 and 7 are both prime numbers with no shared factors, their LCD is 3 times 7 = 21.
3. 45 rewritten with a denominator of 15 is 12 15 .
To change the denominator from 5 to 15, multiply by 33. The numerator becomes 4 times 3 = 12, so 45 = 1215.
4. 29 + 56 = 418 + 1518 = 1118 as a mixed number.
Using the LCD of 18, convert to 418 + 1518 = 1918. Since 1918 is greater than 1, rewrite it as 1 whole and 118, giving 1118.
5. After adding or subtracting fractions, always check if the answer can be simplified.
After computing the answer, check whether the numerator and denominator share a common factor. If they do, divide both by that factor to write the fraction in simplest form.
6. 710 − 13 = 2130 − 1030 = 1130.
The LCD of 10 and 3 is 30. Converting gives 2130 − 1030 = 1130, and since 11 is prime, the fraction cannot be simplified further.
7. The LCD of 8 and 12 is 24.
Listing multiples of 8 (8, 16, 24) and 12 (12, 24) shows that 24 is the smallest number both divide into evenly, making it the LCD.
8. 34 + 56 = 912 + 1012 = 1712 as a mixed number in simplest form.
With the LCD of 12, add 912 + 1012 = 1912. Since 1912 is improper, convert to 1712, which is already in simplest form because 7 and 12 share no common factors.
9. When the sum of two fractions is greater than 1, the result is an improper fraction or a mixed number.
When the numerator is larger than the denominator, the fraction is worth more than 1 whole, which makes it an improper fraction that can be rewritten as a mixed number.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
37 + 12
→ 1314
1215
59 − 16
→ 718
1314
45 + 13
→ 1215
718
78 − 310
→ 2340
2340
Correct matches: 37 + 12 → 1314; 59 − 16 → 718; 45 + 13 → 1215; 78 − 310 → 2340.