4. divide. write each quotient as either a whole number or a mixed number in lowest terms. show your work
12 5/8 ÷ 3 1/4
5. solve the equation. show your work
-1/2 + m = -5 3/7

4. First you convert it into fractions: 101/8 / 13/4. Then you flip the second one to make it multiplication. 101/8 * 4/13. Then you simplify things there. You can cross cancel 8 and 4, changing them to 2 and 1. That makes the problem now: 101/2 * 1/13. Then you multiply across. That makes it 101/26. The answer is 101/26 because 101 is a prime number and cannot be divisible by any number besides 1 and itself.
5. First thing you've gotta do is convert -5 3/7 into a fraction. That is -38/7. Next, you have to add 1/2 to each side, to cancel out the 1/2 on the one side. You also have to convert the fractions together to make them able to be added together. The LCD of 2 and 7 is 14. So, you have to multiply 7 by 2 and 38 by 2 and multiple 2 by 7 and 1 by 7. That makes it -76/14 + 7/14. Add them together to get -69/14. Now you can convert this back into a mixed number. That mixed number is -4 13/14. So the answer is: m= -4 13/14