5.2 Fractions

5.2 Fractions

Quick Summary: OPM names fractions directly as Occupational Math content and its preparation tip is to brush up on basic math concepts, such as percentages, fractions, decimals, proportions, basic algebra, basic geometry, and basic probability. Because a calculator is permitted, the practical skill is knowing which fraction operation a problem calls for, and recognising when converting to a decimal is faster than working in fractions.

The four operations

Addition and subtraction need a common denominator

You cannot add halves to thirds until both are expressed in the same parts.

• 1/2 + 1/3: the least common denominator of 2 and 3 is 6. So 1/2 = 3/6 and 1/3 = 2/6, giving 3/6 + 2/6 = 5/6.
• 3/4 − 2/5: the least common denominator of 4 and 5 is 20. So 3/4 = 15/20 and 2/5 = 8/20, giving 15/20 − 8/20 = 7/20.

A shortcut when the denominators share no common factor: multiply them. For 3/4 − 2/5, 4 × 5 = 20 is already the least common denominator.

Multiplication needs no common denominator

Multiply the numerators, multiply the denominators, then simplify.

• 2/3 × 3/5 = 6/15 = 2/5.
• 3/8 × 4/9 = 12/72 = 1/6.

Cancelling before multiplying is faster and reduces simplification errors. In 3/8 × 4/9, the 3 and the 9 share a factor of 3, and the 4 and the 8 share a factor of 4, leaving 1/2 × 1/3 = 1/6.

Division means multiplying by the reciprocal

To divide by a fraction, flip it and multiply.

• 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1.5.

The result is larger than 3/4, which surprises candidates who expect division to shrink things. Dividing by a number less than 1 always increases the value. That instinct is a useful magnitude check.

• 5/6 ÷ 5/3 = 5/6 × 3/5 = 15/30 = 1/2.

Mixed numbers

Convert to improper fractions before operating.

To convert 3 1/4: multiply the whole number by the denominator and add the numerator, keeping the denominator. So 3 × 4 = 12, plus 1 gives 13, and the result is 13/4.

A form takes 2 1/2 minutes to process. How long do 14 forms take?

2 1/2 = 5/2. Then 5/2 × 14 = 70/2 = 35 minutes.

Converting back: an improper fraction becomes a mixed number by dividing. 17/5 = 3 remainder 2, so 3 2/5.

Fraction of a quantity

This is the most common fraction item on the assessment, and it is built on one rule: "of" means multiply.

A unit received 240 requests. Two-thirds were submitted online. How many were submitted online?

(2/3) × 240 = 480/3 = 160.

A two-step version follows naturally:

Of the 240 requests, two-thirds were submitted online, and one-quarter of those online requests required follow-up. How many required follow-up?

Online: (2/3) × 240 = 160. Follow-up: (1/4) × 160 = 40.

The trap here is applying the second fraction to the original total. (1/4) × 240 = 60, and 60 is reliably offered as an option. Read carefully whether a fraction applies to the whole or to a previously computed part — the phrase of those is the signal.

Comparing fractions

To compare 5/8 and 7/11 quickly, cross-multiply: 5 × 11 = 55 and 7 × 8 = 56. Because 56 is larger and it sits above the 7/11 side, 7/11 is the larger fraction.

With a calculator, dividing is just as fast: 5 ÷ 8 = 0.625 and 7 ÷ 11 ≈ 0.636. The decimal route also makes ordering three or more fractions trivial.

When to convert to decimals

Since a calculator is permitted, converting is often the efficient choice. Divide the numerator by the denominator.

Convert to decimals when the answer options are decimals or currency, the problem mixes fractions with decimals or percentages, or you need to compare several values.

Stay in fractions when the options are fractions, or when repeating decimals such as 1/3 would introduce rounding drift through several steps. Working 1/3 as 0.33 across a three-step problem can move the result far enough to land on a distractor.