- 3 1/5 + (-6 1/2
Please understand that just handing out answers to other students is a form of cheating. If you include explanation, but not THE answer, that's teaching or tutoring.
Be careful.
(- 3 1/5) + (-6 1/2)
= -16/5 - 13/2
= -32/10 - 65/10
...
To add these mixed numbers, you can follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add it to the numerator. Write the sum over the original denominator.
For the first mixed number, 3 1/5:
3 * 5 + 1 = 16
So, 3 1/5 as an improper fraction is 16/5.
For the second mixed number, -6 1/2:
-6 * 2 + 1 = -11
So, -6 1/2 as an improper fraction is -11/2.
Step 2: Add the improper fractions.
To add fractions, the denominators must be the same. In this case, both fractions have a denominator of 5. Add the numerators together and keep the denominator the same.
16/5 + (-11/2) = (16/5) + (-11/2)
Step 3: Find a common denominator.
To add fractions with different denominators, find the least common multiple (LCM) of the denominators. In this case, the LCM of 5 and 2 is 10.
Step 4: Convert both fractions to have a common denominator.
Multiply the numerator and denominator of the first fraction by 2 (since 5 * 2 = 10) and multiply the numerator and denominator of the second fraction by 5 (since 2 * 5 = 10). This will give both fractions a common denominator of 10.
(16/5) * (2/2) + (-11/2) * (5/5) = (32/10) + (-55/10)
Step 5: Add the fractions.
Now that the fractions have a common denominator, add the numerators and keep the denominator the same.
(32/10) + (-55/10) = (32 - 55) / 10 = -23/10
Therefore, the sum of 3 1/5 and -6 1/2 is -23/10.