For example, if you are calculating 11,876÷39{\displaystyle 11,876\div 39}, you can round 11,876 up to 12,000, and 39 up to 40. Then, you can calculate in your head using basic math facts that 12,000÷40=300{\displaystyle 12,000\div 40=300}. Then complete you exact calculation. If you get that 11,876÷39=304{\displaystyle 11,876\div 39=304}, remainder 20{\displaystyle 20}, you can see that your answer and estimate are close, and therefore your calculation is likely correct.
If you discover with the calculator that your answer is incorrect, don’t simply change your answer. Go back through your work and see where you made a mistake in the calculating process, then show the necessary work needed to find the right answer. If you don’t show your work on a math problem, your teacher might think you did everything on a calculator and won’t give you any credit.
For example, if you find that 560÷16=35{\displaystyle 560\div 16=35}, you should be able to make a multiplication problem with the same three numbers by multiplying the divisor (the number you are dividing by) by the product: 16×35=560{\displaystyle 16\times 35=560}. If the equation you make with the inverse operation is true, then your calculation is correct.
For example, if you are working with the equation 4x=24+6x{\displaystyle 4x=24+6x}, and you find that x=12{\displaystyle x=12}, substitute 12 into the equation for x{\displaystyle x} to see if it makes the equation true:4(12)=24+6(12){\displaystyle 4(12)=24+6(12)}48=24+72{\displaystyle 48=24+72}48=96{\displaystyle 48=96}Since the equation isn’t true, you know that 12 isn’t the correct solution, and you need to go back and check your work.
For example, if you are solving the equation 3(2x+3)+14−2(42){\displaystyle 3(2x+3)+14-2(4^{2})} and you go back and see that your first step was to subtract 2 from 14, you know your answer is wrong, because you should have calculated the values in parentheses and exponents first, and then completed multiplication, before you did any adding and subtracting.
Subtracting a negative number is the same as adding it. (3−(−7)=3+7=10{\displaystyle 3-(-7)=3+7=10})[6] X Research source Adding two negative numbers together results in a negative number. (−3+−7=−10{\displaystyle -3+-7=-10}) A negative time a negative equals a positive. (−3×−7=21{\displaystyle -3\times -7=21}) A negative times a positive equals a negative. (−3×7=−21{\displaystyle -3\times 7=-21})[7] X Research source The variable −x{\displaystyle -x} is not necessarily negative. The negative sign indicates that it is the opposite of whatever x{\displaystyle x} is. So, if x{\displaystyle x} is positive, −x{\displaystyle -x} is negative. If x{\displaystyle x} is negative, −x{\displaystyle -x} is positive. [8] X Research source
As when using a regular calculator, don’t use an algebra calculator to do your work for you. Do the problems first, then use the algebra calculator to check your solutions. If your answer is incorrect, go back and rework the problem; don’t just copy the solution from the calculator.
For example: “Fred picks 8 apples on Sunday, and 6 apples on Monday. George picks 2 more apples than Fred each day. Charlie picks 5 less apples than George on Sunday, and 1 more apple on Friday. How many apples does George pick?” Here, make sure to solve for the amount of apples George picks, not the amount Charlie picks or the amount all of them pick together. Also, make sure you understand all of the details of the problem. For example, each day, George picks 2 more than Fred’s daily total. He doesn’t pick 2 more than Fred’s 2-day total.
Some common keywords include “combined” (addition), “decreased” (subtraction), “of” (multiplication), and “per” (division). [13] X Research source For example: “Carlos has 15 books per book shelf. He has 120 books. How many shelves does he have?” The key word “per” should tell you this is a division problem. If you go back to your work and see that you calculated 15×120{\displaystyle 15\times 120}, you know that you did the wrong calculation.
For example: “Mr. Ripley needs to book buses for the fourth grade field trip. Each bus holds 52 people. He has 30 students. The two other fourth grade teachers have 28 students and 26 students, respectively. There will also be one adult chaperoning each class, plus the three teachers. How many buses does Mr. Ripley need to book for the field trip?” If you add up all of the people going on the field trip (90), and divide by the number of people that fit on one bus (52), you get 1. 731. But Mr. Ripley can’t book seven-tenths of a bus. So, if you put down 1. 731 as your answer to this problem, you know it is not a reasonable answer. You need to round up your answer to 2.
