Add - 1 3/10 + (-4 2/15
A. 5 13/30
B. 5 1/6
C. 2 5/6
D. 5 1/5
To add - 1 3/10 and -4 2/15, we need to find a common denominator. The common denominator for 10 and 15 is 30.
Converting -1 3/10 to an improper fraction, we get -10/10 + 3/10 = -13/10.
Converting -4 2/15 to an improper fraction, we get -60/15 + 2/15 = -58/15.
Now, we add the two fractions: -13/10 + (-58/15).
To add these fractions, we need to find a common denominator. The common denominator for 10 and 15 is 30.
-13/10 can be written as -39/30, and -58/15 can be written as -116/30.
Now, we add the fractions: -39/30 + (-116/30) = -155/30.
We can simplify -155/30 to -5 5/6.
Therefore, the correct answer is option C. 2 5/6.
To add the given numbers, we first need to convert the mixed numbers into improper fractions.
The first number: -1 3/10
To convert -1 3/10 into an improper fraction, we multiply the whole number (-1) by the denominator (10) and then add the numerator (3). The result will be the new numerator.
-1 x 10 = -10
-10 + 3 = -7
The new numerator is -7. So, the first number can be written as -7/10.
The second number: -4 2/15
To convert -4 2/15 into an improper fraction, we multiply the whole number (-4) by the denominator (15) and then add the numerator (2). The result will be the new numerator.
-4 x 15 = -60
-60 + 2 = -58
The new numerator is -58. So, the second number can be written as -58/15.
Now, we can add the two improper fractions:
-7/10 + (-58/15)
To add these fractions, we need to have a common denominator.
The least common multiple (LCM) of 10 and 15 is 30.
Next, we need to convert both fractions to have a denominator of 30.
For the first fraction (-7/10), we multiply both the numerator and denominator by 3:
(-7 x 3) / (10 x 3) = -21/30
For the second fraction (-58/15), we multiply both the numerator and denominator by 2:
(-58 x 2) / (15 x 2) = -116/30
Now, we can add the fractions:
-21/30 + (-116/30)
Since the denominators are the same, we can simply add the numerators:
-21 + (-116) = -137
So, the sum is -137/30.
To express the result as a mixed number, we can divide the numerator (-137) by the denominator (30):
-137 ÷ 30 = -4 remainder 17
Thus, the result can be written as -4 17/30.
The correct option is:
A. 5 13/30