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Secondary 2 Fractions, Decimals and Percentages Worksheet

By Marius — private math tutor in Montreal. Updated 30 August 2026

This is the year fraction work stops being about drawing pizzas. The set covers the operation Secondary 2 adds — division, where you multiply by the inverse and the answer can come out larger than what you started with — together with the two conversions that need a method rather than a guess: a mixed number into a decimal and back, and a periodic decimal into an exact fraction using the multiply-and-subtract trick. Around them sit the skills everything else leans on: reducing, building equivalent fractions, comparing over a common denominator, and the difference between rounding a number and truncating it. Several questions hand you a plausible-looking piece of someone's work and ask you to find the flaw. Read it here and print it free.

Practice worksheet — free PDF

5 pages 7 questions Letter size, print-ready

Download the worksheet Read the questions here

No email, no account, no watermark. Teachers: photocopy it for your classes freely. Worked solutions and 7 harder problems come with the Secondary 2 Math bundle.

All 7 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one.

Q1Approximation and Rounding a Number

The water meter at the Parc Molson community pool reads $3048.472 m^{3}$ at the end of the season.
1. Round this reading to the nearest whole cubic metre.
2. Round it to the nearest tenth of a cubic metre.
3. Round it to the nearest hundred cubic metres.
4. Truncate the reading at the tenths place, and say how your truncated value compares with your answer to b).
Q2Dividing Fractions

Carry out each division. Give every answer in lowest terms, as a mixed number when it is greater than $1$ .
1. $\frac{3}{4} \div \frac{2}{5}$
2. $\frac{5}{6} \div \frac{10}{9}$
3. $2 \frac{1}{4} \div \frac{3}{8}$
4. A community garden club has $4 \frac{2}{3}$ kg of sunflower seed to divide into bags holding $\frac{7}{12}$ of a kilogram each. How many bags does the club fill?
Q3Expressing a Fraction as a Periodic Number and Vice Versa
1. Write $\frac{7}{11}$ in decimal notation, placing a bar over the period.
2. Write $\frac{5}{6}$ in decimal notation, placing a bar over the period.
3. Write $0 . \overset{―}{4}$ as a fraction in lowest terms.
4. Write $0 . \overset{―}{27}$ as a fraction in lowest terms.
Q4Expressing a Mixed Number as a Decimal Number and Vice Versa
1. Write $3 \frac{5}{8}$ in decimal notation.
2. Write $2 \frac{7}{20}$ in decimal notation.
3. Write $4.16$ as a mixed number whose fraction is in lowest terms.
4. Write $6.375$ as a mixed number whose fraction is in lowest terms.
Q5Fractional Notation (Fractions)
1. Reduce $\frac{84}{126}$ to lowest terms.
2. Complete the equivalent fraction: $\frac{5}{12} = \frac{}{84}$ .
3. Which is greater, $\frac{7}{9}$ or $\frac{11}{14}$ ? Show how you know.
4. In a school of $152$ students, $\frac{3}{8}$ of them take the bus. How many students is that?
Q6The Common Denominator - Secondary 1, 2 and 3
1. Compute $\frac{5}{12} + \frac{7}{18}$ .
2. Compute $\frac{3}{4} - \frac{5}{8} + \frac{1}{6}$ .
3. Place $\frac{5}{8}$ , $\frac{7}{12}$ and $\frac{3}{5}$ in order from smallest to greatest, using a common denominator.
Q7Synthesis — drawing on several sheets in this topic

A sugar shack has $19 \frac{1}{2}$ litres of syrup left in its tank and bottles it in containers holding $\frac{5}{8}$ of a litre each.
1. How many containers can be filled completely, and what fraction of a litre stays in the tank?
2. Write that leftover volume in decimal notation.
3. The producer records the volume actually bottled as a decimal number rounded to the nearest tenth of a litre. What does he write?

The 7 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

Which stream is this for? None yet — streams begin in Secondary 4, and this is the mathematics every Secondary 2 student in Québec takes. Every value here is positive, which is what the Progression of Learning specifies for moving between fractional, decimal and percentage notation at this level. Scientific notation and the laws of exponents arrive in a later year and are not on this sheet.

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

Dividing fractions: multiply by the inverse, then ask what the answer means

The method is one line — turn the second fraction upside down and multiply — and mixed numbers are converted to fractions first, before anything else happens.

14⁄3 ÷ 7⁄12 = 14⁄3 × 12⁄7 = 168⁄21 = 8

Dividing does not always make things smaller. Seven metres of ribbon cut into two-thirds of a metre gives ten and a half pieces, which is more than seven. The rule that actually holds, for positive numbers: dividing by something less than 1 makes the answer larger, dividing by something greater than 1 makes it smaller, and dividing by 1 changes nothing. It follows from the method — dividing by a fraction below 1 means multiplying by an inverse above 1.

The quotient is often not the answer. Ten and a half pieces of ribbon means ten usable pieces, because half a piece is not a piece; here you round down, and the leftover is what remains on the roll. Compare that with a question about how many packs to order for a group, where the answer must be rounded up. The digits do not decide this — the situation does, and the sheet puts both cases in front of you.

Periodic decimals, and the method that makes them exact

Some fractions produce a decimal that repeats forever, and the bar goes over the repeating block alone: 5⁄6 is 0.8̅3̅ with only the 3 repeating, while 7⁄11 repeats a block of two digits. Going the other way looks like a trick and is really one idea — multiply by the power of ten that shifts the decimal by exactly one period, then subtract to make the tails cancel.

x = 0.27̅ → 100x = 27.27̅ → 99x = 27 → x = 3⁄11

Match the power of ten to the length of the period: one repeating digit needs 10, two need 100. When the repetition starts late, as in 0.58̅, you shift twice — once to reach the start of the period and once further — and subtract those. Then reduce.

The famous consequence. One-ninth is 0.1̅, two-ninths is 0.2̅, and the pattern continues — so nine-ninths is 0.9̅. Nine-ninths is also 1. That is not the pattern breaking down; it is one number carrying two decimal names, and the multiply-and-subtract method proves it in two lines. A question here walks you into it deliberately.

Mixed numbers and decimals: the fraction bar is a division sign

Three and four-fifths is 3.8, because 4 ÷ 5 = 0.8. It is not 3.45, and the error that produces 3.45 is copying the digits across instead of dividing. A size check kills it instantly: four fifths is nearly a whole unit, so the answer has to be close to 4.

Coming back the other way, read the place value carefully. In 7.08 the 8 stands in the hundredths column, so the fraction is 8⁄100 — reduced, 2⁄25. Reading it as eight tenths makes the fractional part ten times too big, and again a size check catches it.

Common denominators are for comparing as well as adding

To add, subtract or order fractions, put them over the least common multiple of the denominators. Prime factorisation is the reliable way to find it: 12 = 2² × 3 and 18 = 2 × 3², so the least common multiple is 36. Then the comparison is just a comparison of numerators.

Adding numerators and denominators is not addition. Two-fifths plus three-sevenths is not five-twelfths, and you can see it without calculating: adding two positive numbers gives something bigger than both, and five-twelfths is smaller than either. The same invented rule would make a half plus a half equal a half. Curiously, the number it produces does land between the two fractions — which is why a student can check it and be reassured. Landing between them is not the test; being larger than both is.

Rounding, truncating, and what a rounded number can be used for

Rounding looks at the next digit and adjusts; truncating simply cuts and never adjusts, so a truncated value is never above the true one while a rounded value may land on either side.

Round the original, in one step, to the place asked for. Rounding 9.46 to the nearest tenth gives 9.5, and rounding that to the nearest unit gives 10 — but 9.46 to the nearest kilogram is 9. Two small pushes in the same direction added up to a whole unit of error, because the second rounding was applied to a number that had already moved.

Equal rounded values do not mean equal numbers. Two shares that both round to 0.58 can still differ, and the last question on the sheet is exactly that: three classes whose shares are close enough that rounding hides the order. Rounding is a way of reporting a number briefly. To decide which of two numbers is greater, compare them over a common denominator, or compare their exact decimals far enough to the right.

Three notations, one number

A fraction, a decimal and a percentage are three ways of writing the same quantity, and each is convenient for something different — a jug marked in quarters wants a fraction, a comparison wants a percentage, a calculation usually wants a decimal. When several values arrive in mixed notations, convert them all to one form before comparing. Doing it by eye is how "62 is a big number, so 62% must be the largest" happens.

Getting the most out of it

Convert everything to one notation before you compare

Fractions against decimals against percentages cannot be compared as they stand. Pick one form — usually decimals, or a common denominator when the values are close — convert all of them, and only then order. Two of the questions here are unwinnable by eye and straightforward this way.

Estimate before you compute, and check the size afterwards

Four-fifths is nearly one, so three and four-fifths is nearly four. Dividing by a number below one makes the answer bigger. A rough expectation held in your head is what turns a wrong answer into an obviously wrong answer, and it costs nothing.

On every context question, ask which way to round

Containers you can actually fill round down; packs you must order to cover everyone round up. Get into the habit of writing the unrounded value, then a clause saying which way the situation forces it and why. That clause is where the reasoning marks live.

Want the solutions, or something more challenging?

The worksheet, the questions above and every explanation on this page stay free permanently. Three more PDFs exist for this topic — the worked answer key, a harder problem set, and the answer key to that. They come with the Secondary 2 Math Solutions Bundle, which is what keeps the rest of the series free.

What else exists for Fractions, Decimals and Percentages

Three PDFs · 9 pages · all three are in the bundle below.

Answer key — 2 pages. All 7 questions worked step by step, including the restrictions and the justifications. Not a list of final answers.
Challenge problems — 5 pages, 7 problems. A separate sheet at exam-plus difficulty covering the same 6 concepts. Harder than anything on the free sheet.
Challenge answer key — 2 pages. Every challenge problem worked to the same standard, with the checks shown.
PDF, letter size, print-ready.

In the bundle See what's in it Not sold separately

The one thing that's for sale

Best value for the whole year

Every Secondary 2 Math topic — the complete Solutions Bundle

One download, one payment, the whole program. Every answer key and every challenge set for all 14 Secondary 2 Math worksheet sets — including this one.

14 sets · 42 PDFs · 181 pages$19.99

Worked solutions, not answer lists — every step written out
Covers the whole year's program at this level
Less than the price of one hour of tutoring — for the entire year's solutions

Everything paid, in one file $19.99CAD · one payment Secondary 2 Math bundle — coming soon Not on sale yet

Taking Secondary 1 Math as well? The Secondary 1 Math bundle covers all 15 of its sets — 45 PDFs, 182 pages — on the same terms.

Taking Secondary 3 Math as well? The Secondary 3 Math bundle covers all 11 of its sets — 33 PDFs, 154 pages — on the same terms.

Taking Secondary 4 Math as well? The Secondary 4 Math bundle covers all 17 of its sets — 51 PDFs, 154 pages — on the same terms.

Taking Secondary 5 Math as well? The Secondary 5 Math bundle covers all 21 of its sets — 63 PDFs, 228 pages — on the same terms.

Taking CEGEP Calculus I as well? The CEGEP Calculus I bundle covers all 8 of its sets — 24 PDFs, 82 pages — on the same terms.

Taking CEGEP Calculus II as well? The CEGEP Calculus II bundle covers all 8 of its sets — 24 PDFs, 90 pages — on the same terms.

Taking CEGEP Linear Algebra as well? The CEGEP Linear Algebra bundle covers all 7 of its sets — 21 PDFs, 82 pages — on the same terms.

Taking AP Calculus AB as well? The AP Calculus AB bundle covers all 8 of its sets — 24 PDFs, 126 pages — on the same terms.

Common questions

Is this worksheet really free?

Yes — the questions are on this page to read, and the PDF downloads directly, no email and no account. The one paid item is optional: the complete Secondary 2 Solutions Bundle, which covers every set at this level.

Why does dividing by a fraction make the answer bigger?

Because dividing by a number smaller than one means multiplying by its inverse, which is larger than one. Seven metres of ribbon cut into two-thirds of a metre gives ten and a half pieces. For positive numbers: dividing by less than one makes the answer larger, dividing by more than one makes it smaller, and dividing by one changes nothing.

How do I turn a repeating decimal into a fraction?

Call the number x and multiply by the power of ten that shifts it by exactly one period — 10 for a single repeating digit, 100 for a block of two. Subtract the original from the shifted copy so the repeating tails cancel, then solve for x and reduce. If the repetition starts late, shift twice and subtract those two.

Why is three and four-fifths not 3.45?

Because the fraction bar means a division: four divided by five is 0.8, so the number is 3.8. Copying the digits across is the commonest error here, and a size check catches it — four fifths is nearly a whole unit, so the answer has to be close to four.

Can I add fractions by adding the tops and the bottoms?

No. Adding two positive numbers gives a result larger than both, and that rule always produces something in between them instead. Put both fractions over a common denominator, add the numerators only, and leave the denominator alone.

Two numbers round to the same value. Are they equal?

No — they only fall in the same narrow interval. Rounding is a way of reporting a number briefly, and it can hide a real difference, which is what the last question on this sheet is built around. To decide which is greater, compare over a common denominator or compare the exact decimals far enough to the right.

Can teachers use this in class?

Yes. Print and photocopy it for your own classes freely — I just ask that the tutorinmontreal.ca footer stays on the page.

I'm stuck on one question. Can you help?

Yes — through one-on-one tutoring, in Montreal or online. Get in touch to arrange a session, or see the current rates.

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