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MTH1W Number Sense
Grade 9 Unit 1 — practice questions with full solutions

Integers, fractions, decimals, powers, ratios, rates and percent. Almost every later unit leans on these skills, so this is the one to get airtight first.

MTH1W · Grade 9 Strand B — Number 12 core 1 challenge
1Core
Evaluate: −3 + 5 × (−2)2 − 12 ÷ (−4)
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  1. Follow BEDMAS. Powers first: (−2)2 = 4.
  2. Expression becomes −3 + 5 × 4 − 12 ÷ (−4).
  3. Multiply and divide, left to right: 5 × 4 = 20 and 12 ÷ (−4) = −3.
  4. Now: −3 + 20 − (−3) = −3 + 20 + 3.
Final answer20
2Core
Simplify: 2⁄3 − 5⁄6 + 3⁄4
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  1. The lowest common denominator of 3, 6 and 4 is 12.
  2. Rewrite each fraction: 8⁄12 − 10⁄12 + 9⁄12.
  3. Combine the numerators: 8 − 10 + 9 = 7.
Final answer7⁄12
3Core
Evaluate (−2)4 and −24. Explain why the answers are different.
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  1. In (−2)4 the brackets mean the whole number −2 is the base: (−2)(−2)(−2)(−2) = 16.
  2. In −24 there are no brackets, so only 2 is the base and the negative sign is applied at the end: −(2 × 2 × 2 × 2) = −16.
  3. The brackets decide what the base actually is — this is one of the most common places students lose marks.
Final answer(−2)4 = 16    −24 = −16
4Core
-3-2-10123PQR
Use the number line above to answer: (a) State the value at each of P, Q and R. (b) Find the distance from P to R. (c) Find the midpoint of Q and R.
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  1. (a) Each small tick is 0.5. P sits half a unit left of −2, so P = −2.5. Q is half a unit right of 0, so Q = 0.5. R sits exactly on 2, so R = 2.
  2. (b) Distance is always positive — subtract the smaller from the larger: 2 − (−2.5) = 2 + 2.5 = 4.5.
  3. (c) The midpoint is the average of the two values: (0.5 + 2) ÷ 2 = 2.5 ÷ 2 = 1.25.
Final answer(a) P = −2.5, Q = 0.5, R = 2   (b) 4.5 units   (c) 1.25
5Core
A recipe uses 3⁄4 cup of sugar to make 12 cookies. How much sugar is needed for 30 cookies?
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  1. Find the scale factor: 30 ÷ 12 = 5⁄2.
  2. Multiply the sugar by that factor: 3⁄4 × 5⁄2 = 15⁄8.
  3. Convert to a mixed number: 15⁄8 = 1 7⁄8.
Final answer1 7⁄8 cups
6Core
Order from least to greatest:   2⁄3,   0.6,   5⁄8,   0.67
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  1. Convert every value to a decimal so they can be compared fairly.
  2. 2⁄3 = 0.666… and 5⁄8 = 0.625.
  3. Now compare: 0.6, 0.625, 0.666…, 0.67.
  4. Careful with the last two — 0.666… is slightly less than 0.67.
Final answer0.6,   5⁄8,   2⁄3,   0.67
7Core
A jacket is priced at $85. It is marked down 15%, and then 13% HST is added to the reduced price. What is the final cost?
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  1. A 15% discount means you pay 85% of the price: 85 × 0.85 = $72.25.
  2. Adding 13% tax means multiplying by 1.13: 72.25 × 1.13 = 81.6425.
  3. Round to the nearest cent.
Final answer$81.64
8Core
Each small rectangle is one equal part of the whole
The grid above is divided into equal parts, with some shaded. Write the shaded portion as (a) a fraction in lowest terms, (b) a decimal, and (c) a percent.
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  1. Count the parts: the grid is 5 columns by 4 rows, so there are 20 equal parts in total.
  2. Count the shaded parts: 12 are shaded.
  3. (a) The fraction is 12⁄20. Divide both parts by 4 to reduce: 3⁄5.
  4. (b) Convert to a decimal: 3 ÷ 5 = 0.6.
  5. (c) Multiply by 100 to get a percent: 60%.
Final answer(a) 3⁄5   (b) 0.6   (c) 60%
9Core
Three friends share $450 in the ratio 2 : 3 : 4. How much does each person receive?
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  1. Add the ratio parts: 2 + 3 + 4 = 9 parts in total.
  2. Find the value of one part: $450 ÷ 9 = $50.
  3. Multiply each share by $50: 2 × 50, 3 × 50, 4 × 50.
  4. Check: 100 + 150 + 200 = 450. ✔
Final answer$100, $150 and $200
10Core
Car A travels 240 km in 3 hours. Car B travels 180 km in 2 hours. Which car is faster, and by how much?
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  1. Unit rate for Car A: 240 ÷ 3 = 80 km/h.
  2. Unit rate for Car B: 180 ÷ 2 = 90 km/h.
  3. Compare: 90 − 80 = 10.
Final answerCar B is faster by 10 km/h
11Core
Simplify using exponent laws:   (23 × 25) ÷ 24
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  1. When multiplying powers with the same base, add the exponents: 23 × 25 = 28.
  2. When dividing powers with the same base, subtract the exponents: 28 ÷ 24 = 24.
  3. Evaluate: 24 = 16.
Final answer24 = 16
12Core
Sam earns $17.50 per hour and works 22 hours. He spends 2⁄5 of his earnings. How much does he have left?
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  1. Total earnings: 17.50 × 22 = $385.
  2. Amount spent: 2⁄5 × 385 = $154.
  3. Amount left: 385 − 154 = $231.
  4. Shortcut check: he keeps 3⁄5, and 3⁄5 × 385 = 231. ✔
Final answer$231
13Challenge
A number is increased by 20%, and the result is then decreased by 20%. The final value is 96. What was the original number?
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  1. Let the original number be x.
  2. Increasing by 20% multiplies by 1.2; decreasing by 20% multiplies by 0.8.
  3. So 1.2 × 0.8 × x = 0.96x, and 0.96x = 96.
  4. Divide: x = 96 ÷ 0.96 = 100.
  5. Notice the result is not back to where it started — a 20% rise followed by a 20% fall always loses 4%.
Final answer100

MTH1W Number Sense — common questions

Short answers to the things students ask most about this unit.

What topics are on the Grade 9 number sense unit test?

Integers, fractions, decimals, order of operations (BEDMAS), powers and exponent rules, ratios, rates, proportions and percent problems.

Is MTH1W the same as Grade 9 academic math?

MTH1W replaced both the academic (MPM1D) and applied (MFM1P) Grade 9 courses when Ontario de-streamed Grade 9 math in 2021. Every Grade 9 student now takes the same course.

How do I get better at BEDMAS questions?

Work one operation at a time and write a new line for each step. Most lost marks come from doing two steps mentally at once, especially with negatives and powers.

More MTH1W practice — grade 9 math

MTH1W Algebraic Expressions & Exponent LawsMTH1W Solving Linear EquationsMTH1W Linear Relations & GraphingMTH1W Geometry & MeasurementAll MTH1W units
← All assignmentsUnit 2: Algebraic Expressions & Exponent Laws →
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