− 24/21 + 24/20
Step by step
To add or subtract fractions with different denominators, we need to find a common denominator.
Step 1: Find the least common multiple (LCM) of 21 and 20.
The prime factorization of 21 is 3 x 7, and the prime factorization of 20 is 2 x 2 x 5.
The LCM is the product of the highest power of each prime factor: LCM(21, 20) = 2^2 x 3 x 5 x 7 = 420.
Step 2: Rewrite each fraction with the common denominator of 420.
- The first fraction, -24/21, can be simplified by dividing both numerator and denominator by the greatest common factor (GCF) of -24 and 21, which is 3. We get: -8/7.
- The second fraction, 24/20, can be simplified by dividing both numerator and denominator by the GCF of 24 and 20, which is 4. We get: 6/5.
- Now we have: -8/7 - 6/5, both with a common denominator of 420.
Step 3: Combine the fractions by adding their numerators and keeping the common denominator.
- To add fractions, we need to have a common denominator. In this case, it is 420.
- To add the fractions, we multiply each fraction by a factor that will give us a common denominator of 420.
- For -8/7, we multiply numerator and denominator by 60. We get: -8/7 x 60/60 = -480/420.
- For 6/5, we multiply numerator and denominator by 84. We get: 6/5 x 84/84 = 504/420.
- Now we have: -480/420 + 504/420 = 24/420.
Step 4: Simplify the result, if possible.
- The fraction 24/420 can be simplified by dividing both numerator and denominator by their GCF, which is 12. We get: 2/35.
- Therefore, - 24/21 + 24/20 = -8/7 - 6/5 = -480/420 + 504/420 = 24/420 = 2/35.
Step 1: Find a common denominator.
The least common multiple of 21 and 20 is 420, so the common denominator is 420.
Step 2: Convert the fractions to equivalent fractions with the common denominator.
- 24/21 = - 24 * 20/21 * 20 = - 480/420
+ 24/20 = 24 * 21/20 * 21 = 504/420
Step 3: Add or subtract the fractions.
- 480/420 + 504/420 = (-480 + 504) / 420 = 24/420
Step 4: Simplify the fraction if possible.
24/420 = 12/210 = 6/105
Answer: 6/105