A)Round -7.86 up to the next integer.

B) Round -0.04837 to the nearest hundredth.
C)Round -437 down to the preceding ten.
D)Estimate 64.2789 + 37.7825 to the nearest integer.

A) 7.9

B) .05
c) 440
D) 102

To round numbers, you typically follow certain rules:

A) To round a number up to the next integer, you need to check the decimal part. If it's greater than or equal to 0.5, you add 1 to the integer part. In this case, you have -7.86. The integer part is -7, and the decimal part is 0.86, which is greater than 0.5. So, rounding it up to the next integer, you get -7.

B) To round a number to the nearest hundredth, you need to look at the decimal place two positions after the decimal point. If it's less than 0.5, you keep the same number. If it's greater than or equal to 0.5, you add 1 to the hundredth place. In this case, you have -0.04837. The hundredth place is 8, which is greater than 5, so rounding it to the nearest hundredth gives you -0.05.

C) To round a number down to the preceding ten, you need to look at the units place. If the units place is greater than or equal to 5, you round up, and if it's less than 5, you round down. In this case, you have -437. The units place is 7, which is greater than 5, so rounding it down to the preceding ten gives you -440.

D) To estimate the sum of two numbers to the nearest integer, you add the numbers and then round the result to the nearest integer. In this case, you have 64.2789 + 37.7825, which equals 102.0614. Rounding it to the nearest integer gives you 102.

So, the answers are:
A) -7
B) -0.05
C) -440
D) 102