Adding and subtracting Rational Numbers
1. -1/2 + 1/3
2.-3 1/5 + (-6 1/2)
3. 5/8 - (-2/8)
4.-9/10 - 2/5
5.6 3/5 - (-2 1/5)
1. -1/2 + 1/3
= -3/6 + 2/6
2.-3 1/5 + (-6 1/2)
= -3 2/10 - 6 5/10
3. 5/8 - (-2/8)
= 5/8 + 2/8
4. -9/10 - 2/5
= -9/10 - 4/10
5. 6 3/5 - (-2 1/5)
= - 6 3/5 + 2 1/5
To add and subtract rational numbers, follow these steps:
1. Find a common denominator for the fractions involved. This is the least common multiple (LCM) of the denominators.
2. Convert each fraction to an equivalent fraction with the common denominator found in step 1.
3. Perform the addition or subtraction operation on the numerators.
4. Simplify the resulting fraction, if possible.
Now, let's solve the given problems using these steps:
1. -1/2 + 1/3:
To find a common denominator, we multiply the denominators 2 and 3, which gives us 6. Now, we need to convert each fraction to an equivalent fraction with a denominator of 6:
-1/2 = -3/6 (multiply the numerator and denominator by 3)
1/3 = 2/6 (multiply the numerator and denominator by 2)
Now, we can add the numerators: -3/6 + 2/6 = -1/6
So, -1/2 + 1/3 = -1/6
2. -3 1/5 + (-6 1/2):
First, convert the mixed numbers to improper fractions:
-3 1/5 = -16/5 (multiply 3 by 5 and add 1 to get 16, and keep the denominator)
-6 1/2 = -13/2 (multiply 6 by 2 and add 1 to get 13, and keep the denominator)
Now, we need to find a common denominator. The LCM of 5 and 2 is 10. Convert both fractions to have a denominator of 10:
-16/5 = -32/10 (multiply the numerator and denominator by 2)
-13/2 = -65/10 (multiply the numerator and denominator by 5)
Now, we can add the numerators: -32/10 + (-65/10) = -97/10
So, -3 1/5 + (-6 1/2) = -97/10
3. 5/8 - (-2/8):
We don't need to find a common denominator here since the fractions already have the same denominator. To subtract fractions, we must change the operation to addition and take the negative of the second fraction:
5/8 + 2/8 = 7/8
So, 5/8 - (-2/8) = 7/8
4. -9/10 - 2/5:
To find a common denominator, we can see that 10 and 5 have a common multiple of 10. Convert each fraction to have a denominator of 10:
-9/10 = -9/10
2/5 = 4/10
Now, we can subtract the numerators: -9/10 - 4/10 = -13/10
So, -9/10 - 2/5 = -13/10
5. 6 3/5 - (-2 1/5):
First, convert the mixed numbers to improper fractions:
6 3/5 = 33/5 (multiply 6 by 5 and add 3 to get 33, and keep the denominator)
-2 1/5 = -11/5 (multiply 2 by 5 and add 1 to get 11, and keep the denominator)
We don't need to find a common denominator here since the fractions already have the same denominator. To subtract fractions, we must change the operation to addition and take the negative of the second fraction:
33/5 + 11/5 = 44/5
So, 6 3/5 - (-2 1/5) = 44/5