1.2 Basic operations: whole numbers, fractions, decimals & one-step workplace problems

Basic Operations on the Job

Level 3 and Level 4 Applied Math questions are built almost entirely from the four basic operations — addition, subtraction, multiplication, and division — applied to whole numbers, fractions, and decimals. Master these and you secure the foundation the whole test is built on, because even a hard Level 7 problem is usually just a chain of these same simple steps. A calculator is allowed, so the real goal is knowing which operation a workplace situation calls for.

Whole Numbers

Whole numbers are the counting numbers (0, 1, 2, 3, and so on) with no fraction or decimal part. On the test they appear as counts of parts, boxes, hours, or people. Clue words tell you the operation:

• Addition — "total," "combined," "altogether," "sum"
• Subtraction — "how many more," "difference," "left over," "remaining"
• Multiplication — "each," "per," repeated equal groups
• Division — "split evenly," "how many per," "share"

Worked example — whole numbers

A warehouse receives 6 pallets, and each pallet holds 48 cartons. How many cartons arrived in total? The word "each" signals multiplication: 6 x 48 = 288 cartons. If those 288 cartons must be split evenly among 4 delivery trucks, divide: 288 / 4 = 72 cartons per truck.

Fractions

A fraction shows part of a whole, written as a numerator over a denominator (for example, 3/4). Three rules cover almost every workplace fraction problem.

Adding and subtracting fractions

You can add or subtract fractions only when they share a common denominator (the bottom numbers match). If the denominators differ, rewrite each fraction so they are equal, then add or subtract only the numerators and keep the denominator.

Worked example: A machinist removes 1/8 inch and then another 3/8 inch from a rod. Total removed = 1/8 + 3/8 = 4/8 = 1/2 inch. If instead she starts with 3/4 inch of stock and cuts away 1/2 inch, first make the denominators match: 1/2 = 2/4. Then 3/4 - 2/4 = 1/4 inch remaining.

Multiplying fractions

To multiply, multiply the numerators together and the denominators together — no common denominator needed. Worked example: A recipe for one full batch uses 2/3 cup of oil, and you need only 1/2 of a batch. Multiply: 2/3 x 1/2 = 2/6 = 1/3 cup.

Dividing fractions

To divide, flip the second fraction (use its reciprocal) and multiply. Worked example: You have 3/4 pound of a compound and each part needs 1/8 pound. How many parts can you make? 3/4 / 1/8 = 3/4 x 8/1 = 24/4 = 6 parts.

Decimals

Decimals are another way to write fractions of a whole, and money is the most common workplace decimal. The rule that trips people up is lining up the decimal point.

• Adding or subtracting — line up the decimal points vertically so tenths sit under tenths and hundredths under hundredths, then add or subtract as usual.
• Multiplying — multiply as if there were no decimal points, then count the total number of decimal places in both factors and place that many in the answer.
• Dividing — move the decimal point in the divisor to make it a whole number, move the dividend's point the same number of places, then divide.

Worked example — decimals

An employee buys supplies for $12.50, $3.75, and $0.99. Lining up the points and adding gives $17.24. Paying with a $20 bill, the change is 20.00 - 17.24 = $2.76. If one item costs $4.20 and you buy 3 of them, then 4.20 x 3 = $12.60.

Converting between fractions and decimals

Workplace problems often mix the two forms — a measurement given as 3/4 inch may need to be added to one given as 0.5 inch. To turn a fraction into a decimal, divide the numerator by the denominator: 3/4 = 3 / 4 = 0.75. To turn a decimal into a fraction, write it over its place value and reduce: 0.5 = 5/10 = 1/2. With both values in the same form, 3/4 inch + 0.5 inch = 0.75 + 0.50 = 1.25 inches. Converting first prevents the common mistake of adding a fraction and a decimal without matching their forms.

Rounding

Rounding gives a clean, practical answer. Find the place value you are rounding to, then look at the digit immediately to its right: if that digit is 5 or more, round up; if it is 4 or less, round down (leave the target digit unchanged). Money is normally rounded to the nearest cent, which is two decimal places.

Worked example: A job costs $18.276 per unit. Rounded to the nearest cent, the digit after the second decimal place is 6, so round up to $18.28. A drive of 47.3 miles rounded to the nearest whole mile drops the .3 (4 or less), giving 47 miles.

Putting It Together: One-Step Workplace Problems

Most Level 3 items are a single operation dressed up as a job scenario. The reliable routine is: read what is asked, pick the operation from the clue words, do the arithmetic on your calculator, then check that the units and the size of the answer make sense.

Worked example: A nurse works 8.5 hours Monday, 7.75 hours Tuesday, and 9.25 hours Wednesday. The word "total" signals addition: 8.5 + 7.75 + 9.25 = 25.5 hours. A quick estimate (about 8 + 8 + 9 = 25) confirms the answer is reasonable, so a calculator typo would stand out immediately.