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Fractions Operations: Addition, Subtraction, Multiplication, and Division
Published on June 29, 2026
Pre-Algebra
This problem set covers fundamental fraction operations including addition, subtraction, multiplication, and division, with an emphasis on simplifying results.
Question
Answer
Based on the provided image, here are the step-by-step solutions for the math problems presented in the final exam.
Exercise 1: Perform the following operations. Simplify whenever possible.
1.
- Find a common denominator: The least common multiple of 6 and 3 is 6.
- Convert
to . - Subtract:
. - Simplify:
. - Answer:
2.
- Convert the whole number 2 to a fraction with a denominator of 5:
. - Add:
. - Convert to a mixed number:
. - Answer:
or
3.
- Convert mixed numbers to improper fractions:
and . - Find a common denominator: The LCM of 4 and 5 is 20.
- Convert fractions:
and . - Add:
. - Convert to a mixed number:
. - Answer:
or
4.
- Multiply the numerators and denominators:
. - Simplify by dividing by 20:
. - Answer:
5.
- Solve inside the parentheses first. Common denominator for 8 and 4 is 8:
. - Perform the division by multiplying by the reciprocal:
. - Multiply:
. - Simplify by dividing by 2:
. - Answer:
Exercise 2:
1.a. Calculate
- Divide 6 by 4:
with a remainder of 2. - Bring down the 4 (making it 24 tenths):
. - The result is
. - Answer:
1.b. Does this division end? Explain.
- Answer: Yes.
- Explanation: The division ends (terminates) because the remainder becomes zero after the first decimal place.
is exactly divisible by .