Question

Simplify the following expression
a) 2/3+ 4/5- 3/4
b) 2/4 - 4/3
c) 31/7 + 7/1
Please break it down in a way i will understand

Answer 1

I'll do each one step by step and keep things simple.

a) 2/3 + 4/5 − 3/4
- Find a common denominator: lcm(3,5,4) = 60.
- Convert each fraction to /60:
- 2/3 = 40/60 (because 2×20 = 40)
- 4/5 = 48/60 (because 4×12 = 48)
- 3/4 = 45/60 (because 3×15 = 45)
- Add/subtract the numerators: 40 + 48 − 45 = 43.
- Result: 43/60 (already in simplest form).

b) 2/4 − 4/3
- First simplify 2/4 = 1/2.
- Common denominator of 1/2 and 4/3 is 6.
- 1/2 = 3/6
- 4/3 = 8/6
- Subtract: 3/6 − 8/6 = −5/6.
- Result: −5/6.

c) 31/7 + 7/1
- 7/1 is just 7. Use denominator 7:
- 7 = 49/7 (because 7×7 = 49)
- Add: 31/7 + 49/7 = 80/7.
- You can leave it as the improper fraction 80/7 or as a mixed number: 11 3/7 (since 80 = 7×11 + 3).
- Result: 80/7 = 11 3/7.

Summary:
a) 43/60
b) −5/6
c) 80/7 (or 11 3/7)