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← Pre-Algebra
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Practice deliberately

Work through Pre-Algebra unit by unit, then test yourself under time.

Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 5 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.

Pre-Algebra coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

This page follows the Pre-Algebra syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use arithmetic practice questions with answers.

01

Integers and rational numbers

Build number sense with exact representations, estimation, and inverse-operation checks before applying the skill in multi-step contexts.

Goal: recognise a integers and rational numbers problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Ratios and proportions

Build number sense with exact representations, estimation, and inverse-operation checks before applying the skill in multi-step contexts.

Goal: recognise a ratios and proportions problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Expressions and variables

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a expressions and variables problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Linear relationships

Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.

Goal: recognise a linear relationships problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Geometry foundations

Draw and label the givens, establish every theorem condition, calculate with exact relationships, and check scale and units.

Goal: recognise a geometry foundations problem from its wording, carry out the governing method, and check that the result is reasonable.

Pre-Algebra questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 5 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: Work out -7 + 12 - (-5).

Pre-Algebra · Integers and rational numbers

  1. 10
  2. 0
  3. -10
  4. 24
Show the worked answer
  1. Subtracting a negative number is the same as adding, so -(-5) becomes +5.
  2. The expression is now -7 + 12 + 5.
  3. -7 + 12 = 5.
  4. 5 + 5 = 10, so the answer is 10.

Answer: 10

Question 2: Which of these numbers is the greatest: -3/4, -0.7, -5/8, or -0.71?

Pre-Algebra · Integers and rational numbers

  1. -5/8
  2. -0.7
  3. -0.71
  4. -3/4
Show the worked answer
  1. Write every number as a decimal so they can be compared directly.
  2. -3/4 = -0.75 and -5/8 = -0.625.
  3. The four values are -0.75, -0.7, -0.625, and -0.71.
  4. On a number line the greatest negative number is the one closest to zero, and that is -0.625, which is -5/8.

Answer: -5/8

Question 3: Three pounds of apples cost $7.50. At the same rate, what do 8 pounds cost?

Pre-Algebra · Ratios and proportions

  1. $20.00
  2. $18.75
  3. $22.50
  4. $15.00
Show the worked answer
  1. Find the price for one pound first. That is the unit rate.
  2. 7.50 / 3 = 2.50, so apples cost $2.50 per pound.
  3. Eight pounds cost 8 x 2.50.
  4. 8 x 2.50 = 20, so 8 pounds cost $20.00.

Answer: $20.00

Question 4: On a map, 1 cm stands for 15 km. Two towns are 4.5 cm apart on the map. How far apart are they in real life?

Pre-Algebra · Ratios and proportions

  1. 67.5 km
  2. 19.5 km
  3. 3.3 km
  4. 60 km
Show the worked answer
  1. Every 1 cm on the map is 15 km on the ground, so multiply by 15.
  2. 4.5 x 15 is the real distance in kilometers.
  3. 4 x 15 = 60 and 0.5 x 15 = 7.5.
  4. 60 + 7.5 = 67.5, so the towns are 67.5 km apart.

Answer: 67.5 km

Question 5: Evaluate 5x - 3y when x = -2 and y = 4.

Pre-Algebra · Expressions and variables

  1. -22
  2. -2
  3. 22
  4. 2
Show the worked answer
  1. Replace each letter with its value: 5(-2) - 3(4).
  2. 5 x (-2) = -10.
  3. 3 x 4 = 12, and that amount is subtracted.
  4. -10 - 12 = -22.

Answer: -22

Question 6: A line passes through the points (2, 3) and (6, 11). What is its slope?

Pre-Algebra · Linear relationships

  1. 2
  2. 1/2
  3. 4
  4. 8
Show the worked answer
  1. Slope is the change in y divided by the change in x.
  2. The y values change by 11 - 3 = 8.
  3. The x values change by 6 - 2 = 4.
  4. 8 / 4 = 2, so the slope is 2.

Answer: 2

Question 7: Solve 4x + 7 = 31 for x.

Pre-Algebra · Linear relationships

  1. 6
  2. 9.5
  3. 24
  4. 7
Show the worked answer
  1. Undo the addition first. Subtract 7 from both sides.
  2. 4x + 7 - 7 = 31 - 7 gives 4x = 24.
  3. Now undo the multiplication. Divide both sides by 4.
  4. 24 / 4 = 6, so x = 6. Check: 4(6) + 7 = 31.

Answer: 6

Question 8: A rectangle has a perimeter of 34 cm and a length of 11 cm. What is its area?

Pre-Algebra · Geometry foundations

  1. 66 square cm
  2. 374 square cm
  3. 132 square cm
  4. 72 square cm
Show the worked answer
  1. Perimeter counts each length and each width twice: 2(length) + 2(width) = 34.
  2. The two lengths use 2 x 11 = 22 cm of the perimeter.
  3. That leaves 34 - 22 = 12 cm for the two widths, so each width is 12 / 2 = 6 cm.
  4. Area = length x width = 11 x 6 = 66 square cm.

Answer: 66 square cm

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed Pre-Algebra questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1Integers and rational numbersWork out -7 + 12 - (-5).10
2Integers and rational numbersWhich of these numbers is the greatest: -3/4, -0.7, -5/8, or -0.71?-5/8
3Ratios and proportionsThree pounds of apples cost $7.50. At the same rate, what do 8 pounds cost?$20.00
4Ratios and proportionsOn a map, 1 cm stands for 15 km. Two towns are 4.5 cm apart on the map. How far apart are they in real life?67.5 km
5Expressions and variablesEvaluate 5x - 3y when x = -2 and y = 4.-22
6Linear relationshipsA line passes through the points (2, 3) and (6, 11). What is its slope?2
7Linear relationshipsSolve 4x + 7 = 31 for x.6
8Geometry foundationsA rectangle has a perimeter of 34 cm and a length of 11 cm. What is its area?66 square cm

How the generated Pre-Algebra sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this Pre-Algebra practice page

What does this page cover?

It covers all 5 Pre-Algebra units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.

When can I see correct answers and explanations?

The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.