Simplify: Negative four and one-fifth minus negative thirteen and one-tenth

-4 1:5 - ( - 13 1:10)

first we should turn these into improper fractions by multiplying the whole number by the denominator then add the numerator.

4 * 5 = 20 + 1 = 21

13 * 10 = 130 + 1 = 131

(-21/5) - (-131/10)

To subtract fractions we want to find a common denominator so we can multiply the numerator and denominator of (-21/5) by 2 to get (-42/10)

(-42/10) - (-131/10)

Since we are subtracting a negative, that becomes a positive

(-42/10) + 131/10

131 - 42 = 89

89/10

Now we can change it back into a mixed fraction:

8 and nine-tenths or 8 9:10