What is...
-1/2+1/3=_____
-1 1/5+-(-6 1/2)=_____
5/8-(-2/8)=_____
-9/10-2/5=_____
6 3/5-(2 1/5)=_____
Sorry about #2, it should be
-3 1/5+(-6 1/2)=_____
And #5 should be (-2 1/5) not (2 1/5). Sorry about that :-/
first, find the common denominator for each problem.
Then you can work with the fractions more easily.
Thanks
To solve these addition and subtraction problems involving fractions and mixed numbers, follow these steps:
Step 1: Convert mixed numbers to improper fractions (if necessary):
If a mixed number is given (e.g., 1 1/5), convert it into an improper fraction. To do this, multiply the whole number by the denominator of the fraction, then add the numerator. Write the sum as the new numerator, and keep the denominator the same. For example:
1 1/5 = (1 × 5 + 1)/5 = 6/5
Step 2: Find a common denominator:
To add or subtract fractions, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions involved.
For example, the common denominator of 2/3 and 1/4 is 12.
Step 3: Perform the addition/subtraction:
Use the common denominator to add or subtract the fractions. Keep the denominator the same and perform the addition or subtraction on the numerators.
For addition: Add the numerators and keep the common denominator.
For subtraction: Subtract the second numerator from the first numerator and keep the common denominator.
Step 4: Simplify the result (if needed):
If the fraction can be simplified further, divide the numerator and denominator by their greatest common factor (GCF) to obtain the simplest form.
Now, let's solve the given equations:
1. -1/2 + 1/3:
- To find a common denominator, you multiply the denominators: 2 * 3 = 6.
- Convert the fractions to have a common denominator: (-1 * 3)/(2 * 3) + (1 * 2)/(3 * 2) = -3/6 + 2/6.
- Add the numerators: -3 + 2 = -1.
- Keep the common denominator: -1/6.
2. -1 1/5 + -(-6 1/2):
- Convert the mixed numbers to improper fractions: (-1 * 5 + 1)/5 = -4/5 and (-6 * 2 + 1)/2 = -11/2.
- To find a common denominator, multiply the denominators: 5 * 2 = 10.
- Convert the fractions to have a common denominator: (-4 * 2)/(5 * 2) + (-11 * 5)/(2 * 5) = -8/10 + 55/10.
- Add the numerators: -8 + 55 = 47.
- Keep the common denominator: 47/10.
3. 5/8 - (-2/8):
- The subtraction of a negative number is the same as adding the positive number.
- To find a common denominator, use the denominators: 8.
- Convert the fractions to have a common denominator: 5/8 + 2/8.
- Add the numerators: 5 + 2 = 7.
- Keep the common denominator: 7/8.
4. -9/10 - 2/5:
- To find a common denominator, multiply the denominators: 10 * 5 = 50.
- Convert the fractions to have a common denominator: (-9 * 5)/(10 * 5) - (2 * 10)/(5 * 10) = -45/50 - 20/50.
- Subtract the numerators: -45 - 20 = -65.
- Keep the common denominator: -65/50.
- Simplify the fraction by dividing the numerator and denominator by their GCF (5): (-65/5)/(50/5) = -13/10.
5. 6 3/5 - (2 1/5):
- Convert the mixed numbers to improper fractions: (6 * 5 + 3)/5 = 33/5 and (2 * 5 + 1)/5 = 11/5.
- To find a common denominator, use the denominators: 5.
- Convert the fractions to have a common denominator: 33/5 - 11/5.
- Subtract the numerators: 33 - 11 = 22.
- Keep the common denominator: 22/5.
Final answers:
1. -1/2 + 1/3 = -1/6
2. -1 1/5 + -(-6 1/2) = 47/10
3. 5/8 - (-2/8) = 7/8
4. -9/10 - 2/5 = -13/10
5. 6 3/5 - (2 1/5) = 22/5