Page 1 Mathematics: Computation Study Guide for the TABE
How to prepare for the TABE Math: Computation Test
The Computation section of the TABE Math test is really an assessment of your knowledge of the procedures to follow when doing operations (addition, subtraction, multiplication, and division) with numbers. It also tests your accuracy when performing these operations because you may not use a calculator for this section.
On the first two levels (E and M) of the TABE Math: Computation Test, you will be working mostly with whole numbers, along with a few decimals and fractions. In levels D and A, however, you need to be able to perform operations with other types of numbers. Here is a list of the number types and levels in which they appear.
- whole numbers (E,M)
- decimals (E, M, D)
- fractions (M, D, A)
- integers (D, A)
- percents (D, A)
- algebraic (A)
Following are some of the procedures you need to know. If you are not comfortable and fluent with any of them, seek extra practice materials. Drill and practice on these is the best way to improve accuracy and become proficient.
Procedures to Know
Adding Whole Numbers
Adding whole numbers without the aid of calculator is simplified by first writing the addends (the numbers to be added) vertically. Align digits according to their place value – ones at the first rightmost column, followed by the tens to the left, then hundreds and so on. To add 1045 and 34 write the addends vertically, carefully aligning the digits according to place value:
Start adding from the ones column, going to the left one place value at a time. Write the sum of each column below the horizontal line, aligned as to place value. For this example, the ones column sum is 9; the tens column sum is 7; the hundreds is 0; the thousands is 1. The sum of 1045 and 34 is, therefore, 1079.
However, if the sum of any of the columns is more than 9, as in the following example, you need to regroup the digits.
Add the first column: , but 12 is 10 + 2 (or 1 tens and 2 ones), so write 2 below the horizontal line at the ones column, and add 1 on top of the tens column.
Then proceed to add the tens column including the 1 on top: (which is 1 hundreds and 0 tens), so we write 0 at the tens column and 1 on top of the hundreds column.
Add the hundreds column (), then the thousands column (). The sum of 1057 and 3145 is 4202.
Subtracting Whole Numbers
Subtraction, as with other arithmetic operations, is much easier to perform if done vertically. Start subtracting from the ones column, moving to the left or the bigger place values. In , is the minuend while is the subtrahend. Write the minuend on top, the subtrahend below, carefully aligning the digits that correspond to the same place value.
Write the difference of the digits in each column under the horizontal line. The difference for the ones column is , and the difference for the tens column is . The result of subtracting 25 from 76 is, therefore, 51. This calculation can be verified by adding the resulting answer, 51, with the portion subtracted, 25, to arrive back at the original whole of 76.
When any digit of the subtrahend, however, is larger than the minuend, there is a need to perform regrouping, as in this example:
Expand each number to show the value of each digit:
Since we cannot subtract a number from another number which is smaller within a column (such as, 3 from 1 and 500 from 0), we borrow one unit from the number on the left column. So we regroup the minuend by borrowing 1 unit from the tens column and adding that to the number in the ones column, and by borrowing 1 unit from the thousands column and adding that to the number in the hundreds column.
Multiplication of Whole Numbers
To perform long-hand or manual multiplication start off by writing the factors (or the numbers to be multiplied) vertically. The number written on top is also called multiplicand, while the one below is called the multiplier. Align digits according to their place value – with ones on the right and increasing place values toward the left. To multiply 1234 by 567, write first as:
We start by multiplying the ones digit (7) of the multiplier with every digit of the multiplicand. Write the result directly below the horizontal line, properly aligning the last digit under the ones column. At this point, don’t mind the commas:
We then proceed by multiplying the tens digit (6) of the multiplier with every digit of the multiplicand. Write the result below the previous result, aligning the last digit with the tens column. You can use a “placeholder zero”, as shown here, to remind you to align with the proper column each time.
Repeat the same procedure, but this time using the hundreds digit (5) of the multiplier to multiply with each digit of the multiplicand. Two “placeholder zeroes” are used here.
Vertically add the results of the multiplication to get the product of 1234 and 567; separate the final result with commas:
Division of Whole Numbers
Division of some numbers may simply require a quick recall from memory, such as or . This test, however, usually involves multi-step division, with or without a remainder or decimal in the result.
The larger number is called the dividend; the smaller number is the divisor. The divisor is written before the long division symbol, the dividend is written inside; while the result is written on top of the symbol.
Step 1: To calculate , write the numbers as:
Step 2: Divide every digit of the dividend by the divisor and write the answer on top of the digit being divided. In this example, we can start by examining the dividend to see whether the first digit is large enough to be divided by the divisor – we find that it’s not (8 is smaller than 41). So we take 2 digits (85), and divide 85 by 41 to get 2. Write 2 on top of the symbol and align it with 5:
Step 3: Multiply 41 by 2 and write the product below 85:
Step 4: Subtract 82 from 85 to get 3. Bring down 2 from the dividend:
Step 5: Divide 32 by 41 to get 0. Repeat Step 3 and Step 4:
Step 6: Divide 328 by 41 to get 8. Repeat Step 3 and Step 4:
The answer is 208. The procedure is simply repeated until the last digit. Remainders (when the result of subtraction in the last step is not 0) can be presented in three ways:
- as r. followed by the remainder
- as a fraction with the remainder as the numerator, and the divisor as the denominator
- as digits after a decimal point when division is continued after the whole-number part of the quotient (This involves adding zeroes after the last digit of the dividend.)