November 2026 - Fractions & Decimals Study Guide for nursing students in
Adding and subtracting fractions needs a common denominator; multiplying does not. Comparing them is faster by cross-multiplying than by converting to decimals. Almost every mark lost here comes from one of three places: a missing common denominator, an unsimplified answer, or a misplaced decimal point.
Try 4 short questions throughout this guide. Check each answer to learn from the explanation.
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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
Worked example
A bottle holds 3 1/4 litres. A patient drinks 1 2/3 litres. How much is left?
Convert to improper fractions: 3 1/4 = 13/4 and 1 2/3 = 5/3.
Common denominator of 4 and 3 is 12: 13/4 = 39/12, 5/3 = 20/12.
Subtract numerators: 39/12 - 20/12 = 19/12.
Convert back: 19/12 = 1 7/12.
1 7/12 litres remain. Converting to improper fractions first avoids borrowing from the whole number, which is where mixed-number subtraction usually goes wrong.
Question 1 of 4
What is 2/3 + 1/4?
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Correct answer: B. 11/12
With a common denominator of 12, 2/3 = 8/12 and 1/4 = 3/12, giving 11/12. Choice A adds the numerators and denominators separately, which is the classic error; 3/12 comes from adding numerators without rescaling; and 1 1/12 is 13/12, an answer larger than 1 when both fractions together are still under it.
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.
Question 2 of 4
A patient is prescribed 1 1/2 tablets twice a day. How many tablets are needed for four days?
Choose one answer, then check it.
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Correct answer: C. 12
1 1/2 twice a day is 3 tablets daily, and over four days that is 12. Choice A stops after multiplying the dose by two doses without extending to four days; 8 ignores the half; and 16 doubles the daily total again.
Decimal place value
Ordering decimals goes wrong when digits are compared by count rather than by place.
Place
Position
Example
As a fraction
Tenths
First digit after the point
0.7
7/10
Hundredths
Second digit
0.07
7/100
Thousandths
Third digit
0.007
7/1000
Length is not size. 0.5 is larger than 0.45, even though 45 is larger than 5, because the comparison happens place by place. Pad the shorter decimal with zeros — 0.50 against 0.45 — and the comparison becomes obvious.
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.
Add or subtract these two fractions.
Common denominator, combine numerators, simplify, and match the format of the answer choices.
Which of these fractions is largest?
Cross-multiply pairs, or use the same-numerator and same-denominator shortcuts.
Order these decimals from least to greatest.
Pad with zeros to equal length, then compare place by place.
Express this fraction as a decimal, or the reverse.
Divide numerator by denominator; for the reverse, read the last place value as the denominator.
Question 3 of 4
Which fraction is the largest?
Choose one answer, then check it.
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Correct answer: C. 3/5
Cross-multiplying 3/5 against 4/7 gives 21 against 20, so 3/5 is larger, and it beats the others the same way. All four sit close to a half, which is what makes eyeballing them unreliable — 3/5 is 0.6, the highest of the set.
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.
Question 4 of 4
Which list is ordered from least to greatest?
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Correct answer: B. 0.35, 0.4, 0.409
Padded to three places these are 0.350, 0.400 and 0.409, so the order is 0.35, 0.4, 0.409. The wrong choices come from judging by digit count — treating 0.409 as smaller than 0.4 because it has more digits, or larger than everything for the same reason.
TEAS · Fractions and decimals
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