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. A number made up of a whole number and a fraction, like 214, is called a mixed number.
A mixed number combines a whole number and a proper fraction, such as 214. They arise when adding fractions produces a sum greater than 1.
2. To add mixed numbers, first add the fraction parts, then add the whole numbers.
When adding mixed numbers, handle the fractional parts first (finding a common denominator), then add the whole number parts. Regroup if the fractional sum is improper.
3. An improper fraction has a numerator greater than or equal to its denominator, like 73.
An improper fraction has a numerator ≥ denominator. It represents a value greater than or equal to 1 and can be converted to a mixed number.
4. 310 + 45 = 310 + 810 = 1110 as a mixed number.
LCD of 10 and 5 is 10. 45 = 810. Sum = 310 + 810 = 1110 = 1110.
5. To convert 114 to a mixed number, divide 11 by 4 to get 234.
11 ÷ 4 = 2 remainder 3. So 114 = 234.
6. When subtracting mixed numbers, you may need to regroup from the whole number part.
If the fraction being subtracted is larger than the fraction it's being subtracted from, borrow 1 from the whole number and add it (as an equivalent improper fraction) to the fractional part.
7. 213 + 114 = 2412 + 1312 = 3712.
LCD of 3 and 4 is 12. 13 = 412, 14 = 312. Fraction sum: 412 + 312 = 712. Whole number sum: 2+1=3. Result: 3712.
8. 512 − 223 requires regrouping because 12 is less than 23.
Since 12 = 36 and 23 = 46, the fraction 12 is less than 23. You cannot subtract the larger fraction from the smaller, so you must regroup 1 from the 5.
9. The sum 78 + 58 = 128, which simplifies to the mixed number 112.
128 is an improper fraction. 12 ÷ 8 = 1 remainder 4, so 128 = 148 = 112 in simplest form.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
112 + 213
→ 356
2712
434 − 116
→ 3712
3910
225 + 112
→ 3910
356
513 − 234
→ 2712
3712
1½+2⅓=3+56=356; 4¾−1⅙=3+712=3712; 2⅖+1½=3+910=3910; 5⅓−2¾=2+712=2712.