Basic Math
Fractions & Decimals
Operations with mixed fractions, finding Lowest Common Denominators (LCD), rounding decimals, and converting between the two.
Questions appear in accounting and office contexts. Expect inventory quantities, distances, and file counts expressed as fractions or decimals.
What the exam tests
Conversion Exercises
Transform a fraction into its decimal equivalent (e.g., 3/4 = 0.75) or vice versa.
Mixed Fraction Arithmetic
Addition or subtraction problems involving mixed numbers, often in word problems (e.g., adding 5½ cans and 2¼ cans).
Place Value Identification
Identify the specific name of a decimal position, such as 'one thousandth' for 0.001.
Rounding and Approximation
Round a decimal to a specific number of decimal places or significant figures.
Applied Word Problems
Office or accounting scenarios requiring fractions or decimals to solve for a total, such as calculating percentages of files used or map distances.
Multiple-Choice Challenges
Trap options include reversed numbers (e.g., 421.25 vs. 421.52) or results from using the wrong operation.
Fraction Operations
Key rules
- ›To convert an improper fraction to a mixed number, divide the numerator by the denominator.
- ›To convert back to an improper fraction, multiply the whole number by the denominator and add the numerator.
- ›To add or subtract fractions, first find the Lowest Common Denominator (LCD): the smallest number all denominators divide into evenly.
- ›Simplify (cancel down) by dividing both numerator and denominator by the same number to reach the simplest form.
Common traps
- !Final answers must be in simplest form. Unsimplified fractions are often listed as wrong-answer traps.
Decimal Place Value and Alignment
Key rules
- ›Values right of the decimal decrease by powers of ten: tenths, hundredths, thousandths.
- ›For addition and subtraction, align decimal points vertically before calculating.
- ›For multiplication, count the total decimal digits in both factors and shift the point that many places left in the product.
- ›For division by powers of ten, shift the decimal point left by the number of zeros.
Common traps
- !Misaligned decimal points are the most common arithmetic error. Always line up the point before adding or subtracting.
Rounding and Estimation
Key rules
- ›Rounding rule: if the digit immediately to the right of the rounding position is less than 5, leave the rounding digit unchanged; if 5 or more, round up.
- ›Use mental approximation to eliminate implausible choices before calculating (e.g., estimate 48 × 12 as 50 × 10 = 500).
- ›Plug answer choices back into the original equation to verify. This is especially useful for multiple-choice fraction problems.
Common traps
- !Watch for reversed-digit trap answers (e.g., 421.25 vs. 421.52). Always confirm digit order after calculating.
Try one
Which of the following is an improper fraction?
An improper fraction has a numerator greater than its denominator. 11/10 is the only value greater than 1. All others are proper fractions (numerator < denominator).
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