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Question 1
ArithmeticFoundation

Arithmetic practice question 1

Arithmetic practice topics

Question sets mix direct skills with unfamiliar applications so method selection becomes part of the practice.

01

Fractions and mixed numbers

Add, subtract, multiply, and divide fractions, then convert between improper fractions and mixed numbers without a calculator.

02

Ratios, rates, and proportions

Find a unit rate from a pair of quantities and scale a ratio up or down to match a value you are given.

03

Percent change and discounts

Work out sale prices, increases, and successive changes, and decide which starting amount the percent is taken from.

04

Order of operations and estimation

Evaluate expressions with brackets and powers in the right order, and round numbers to check whether an answer is sensible.

Arithmetic practice questions with worked answers

These 8 questions are printed in full on this page, with every step of the arithmetic written out. Cover the options, solve the question on paper first, and only then open the worked answer to compare your method with the one shown.

Question 1: Add 3/4 + 5/6 and write the answer as a mixed number.

Foundation level · fractions and mixed numbers

  1. 1 7/12
  2. 1 1/2
  3. 8/10
  4. 1 5/12
Show the worked answer
  1. Both 4 and 6 divide into 12, so use 12 as the common denominator.
  2. 3/4 becomes 9/12, and 5/6 becomes 10/12.
  3. 9/12 + 10/12 = 19/12.
  4. 19 divided by 12 is 1 with 7 left over, so the answer is 1 7/12.

Answer: 1 7/12

Question 2: A recipe needs 2 1/4 cups of flour. You only want to make 2/3 of the recipe. How much flour do you need?

Exam level · fractions and mixed numbers

  1. 1 1/2 cups
  2. 1 3/4 cups
  3. 3 3/8 cups
  4. 1 1/3 cups
Show the worked answer
  1. Write 2 1/4 as an improper fraction: 2 1/4 = 9/4.
  2. Two thirds of that amount means 9/4 x 2/3.
  3. Multiply across the top and bottom: (9 x 2)/(4 x 3) = 18/12.
  4. 18/12 cancels by 6 to give 3/2, which is 1 1/2 cups.

Answer: 1 1/2 cups

Question 3: A car travels 210 miles in 3 hours at a steady speed. How far does it travel in 7 hours at that speed?

Foundation level · ratios, rates, and proportions

  1. 490 miles
  2. 420 miles
  3. 560 miles
  4. 630 miles
Show the worked answer
  1. Find the unit rate first: 210 miles / 3 hours = 70 miles per hour.
  2. Steady speed means the same 70 miles are covered every hour.
  3. In 7 hours the car covers 70 x 7 miles.
  4. 70 x 7 = 490, so the car travels 490 miles.

Answer: 490 miles

Question 4: Blue and yellow paint are mixed in the ratio 5:3. You pour in 24 liters of yellow paint. How much blue paint do you need?

Exam level · ratios, rates, and proportions

  1. 40 liters
  2. 14.4 liters
  3. 45 liters
  4. 36 liters
Show the worked answer
  1. The yellow part of the ratio is 3, and it stands for 24 liters.
  2. One ratio part is 24 / 3 = 8 liters.
  3. Blue is 5 parts, so blue = 5 x 8 liters.
  4. 5 x 8 = 40, so you need 40 liters of blue paint.

Answer: 40 liters

Question 5: A jacket costs $80 and is marked down by 25%. What is the sale price?

Foundation level · percent change and discounts

  1. $60
  2. $55
  3. $64
  4. $75
Show the worked answer
  1. 25% of $80 is 80 / 4 = $20, because 25% is one quarter.
  2. The discount of $20 is taken off the original price.
  3. 80 - 20 = 60.
  4. The sale price is $60. Check: 60 is 75% of 80, which matches a 25% cut.

Answer: $60

Question 6: A price goes up by 20%, and then the new price is cut by 20%. Compared with the starting price, what is the final price?

Challenge level · percent change and discounts

  1. 4% lower
  2. exactly the same
  3. 4% higher
  4. 20% lower
Show the worked answer
  1. Percent changes are easiest to test on a starting price of $100.
  2. The 20% rise gives 100 x 1.20 = $120.
  3. The 20% cut is taken off $120, not off $100: 120 x 0.80 = $96.
  4. 96 is $4 below the starting $100, so the final price is 4% lower.

Answer: 4% lower

Question 7: Work out 6 + 4 x (10 - 7)^2 / 2.

Exam level · order of operations and estimation

  1. 24
  2. 51
  3. 21
  4. 45
Show the worked answer
  1. Brackets first: 10 - 7 = 3, so the expression is 6 + 4 x 3^2 / 2.
  2. Powers next: 3^2 = 9, giving 6 + 4 x 9 / 2.
  3. Multiply and divide left to right: 4 x 9 = 36, then 36 / 2 = 18.
  4. Add last: 6 + 18 = 24.

Answer: 24

Question 8: Estimate 39 x 51 by rounding each number to the nearest ten. How far is your estimate from the exact answer?

Challenge level · order of operations and estimation

  1. The estimate is 11 too high
  2. The estimate is 11 too low
  3. The estimate is 1 too high
  4. The estimate is 100 too high
Show the worked answer
  1. Round each number: 39 rounds to 40 and 51 rounds to 50.
  2. The estimate is 40 x 50 = 2000.
  3. The exact product is 39 x 51 = 1989.
  4. 2000 - 1989 = 11, so the estimate sits 11 above the exact answer.

Answer: The estimate is 11 too high

How the three Arithmetic difficulty levels differ

The difficulty buttons above change what a question asks of you, not just the size of the numbers. Each example below is taken from the question set on this page.

Difficulty levels for Arithmetic practice, with an example question from this page.
LevelWhat it testsExample questionTime target
FoundationOne skill at a time, with the numbers kept small enough to check in your head.Add 3/4 + 5/6 and write the answer as a mixed number.About 1 minute
ExamThe wording of a real test paper: pick the method first, then carry out two or three steps.A recipe needs 2 1/4 cups of flour. You only want to make 2/3 of the recipe. How much flour do you need?2 to 3 minutes
ChallengeTwo ideas combined, or a result you have to interpret after the calculation ends.A price goes up by 20%, and then the new price is cut by 20%. Compared with the starting price, what is the final price?4 to 5 minutes

How to practice Arithmetic effectively

Begin without notes and explain your choice before checking. For every miss, identify whether the cause was a definition, setup, calculation, interpretation, or time decision. Re-solve the question from a blank page, then return to the same skill in a mixed set tomorrow.

What your Arithmetic answer review should show

A useful review shows more than the correct option. Compare the method with your first attempt, locate the earliest incorrect decision, and write one rule that would prevent the same error in a new Arithmetic problem.

Move from mixed Arithmetic questions to a complete course

This page targets flexible Arithmetic question practice. When you need a syllabus-aligned sequence with unit selection, use Pre-Algebra practice by unit and return here later for mixed retrieval.

Questions about Arithmetic practice

When should I change the difficulty?

Move up after you can solve several questions accurately without hints and explain the method. Move down for one short set when errors show that a definition or setup is still uncertain.

How often should I practice?

Short sessions on several days usually build stronger recall than one long session. Revisit missed Arithmetic skills the next day, then mix them with older topics later in the week.

Where can I review the lessons in order?

Use Pre-Algebra practice by unit for a syllabus-aligned sequence with unit selection, practice, and a complete answer review.

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