October 2026 - Fractions & Decimals Study Guide

Adding and subtracting

You can only add or subtract parts of the same size, which is what a common denominator gives you.

• Find the smallest number both denominators divide into. For 3/4 and 2/5, that is 20.
• Rescale each fraction: multiply top and bottom by the same amount — 3/4 = 15/20, 2/5 = 8/20.
• Add or subtract the numerators only. The denominator does not change: 15/20 + 8/20 = 23/20.
• Convert an improper result to a mixed number if the answer choices are mixed: 23/20 = 1 3/20.

Subtracting mixed numbers

Comparing fractions fast

To decide which of two fractions is larger, cross-multiply: for 5/8 against 7/11, compare 5 × 11 = 55 with 7 × 8 = 56. The larger product sits above the larger fraction, so 7/11 is bigger. It is quicker than dividing and it never introduces a rounding error.

Two shortcuts help as well. With the same denominator, the bigger numerator wins. With the same numerator, the *smaller* denominator wins, because the whole has been cut into fewer pieces.

Decimal place value

Ordering decimals goes wrong when digits are compared by count rather than by place.

Where marks are lost

• Adding denominators. 1/2 + 1/3 is not 2/5. Only numerators are added, once the denominators match.
• Leaving an answer unsimplified. 6/8 and 3/4 are the same number, but the unsimplified version is a favourite distractor.
• Losing a decimal place when multiplying. Count the decimal places in both factors and give the answer that many.
• Forgetting to convert a mixed number before multiplying or dividing.

Terms to know

Numerator

The top number of a fraction: how many parts you have.

Denominator

The bottom number: how many parts the whole is divided into.

Common denominator

A shared denominator that lets two fractions be added or subtracted.

Improper fraction

A fraction whose numerator is larger than its denominator, such as 19/12.

Mixed number

A whole number with a fraction, such as 1 7/12.

Equivalent fractions

Different fractions with the same value, such as 6/8 and 3/4.

Simplify

Divide top and bottom by their largest common factor.

What the TEAS asks most

The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.

Key points

• Common denominators are needed to add and subtract, never to multiply.
• Cross-multiply to compare two fractions — faster and exact.
• Same numerator: the smaller denominator is the bigger fraction.
• Pad decimals with zeros before ordering them.
• Always simplify, and check whether the choices want a mixed number.