Operations with Integers & Rational Numbers
Multiplying Integers
Circle the correct answer.
−4 × 3
−5 × (−6)
7 × (−2)
−8 × (−4)
Dividing Integers
Circle the correct answer.
−24 ÷ 6
−36 ÷ (−9)
45 ÷ (−5)
−56 ÷ (−7)
Sign Rules
Draw a line to match each sign combination to its result sign.
Order of Operations with Integers
Use BODMAS. Circle the correct answer.
−3 + 4 × 2
(−2 + 5) × (−3)
−10 − (−4) × 2
12 ÷ (−4) + 5
Operations with Rational Numbers
Circle the correct answer.
3/4 ÷ 1/2
2/3 × 9/4
1 3/4 + 2 1/2
3 1/3 − 1 2/3
Positive, Negative or Zero?
Without calculating, sort each expression by sign of result.
Integer Word Problems
Show all working.
The temperature drops 3°C each hour for 5 hours from 8°C. What is the final temperature?
A diver is at −18 m and ascends at 3 m per minute. How long until she reaches the surface?
Expand and simplify: (−3) × (4 − 7) + 2 × (−5)
BODMAS Chains with Integers
Apply BODMAS carefully. Circle the correct answer.
−2 × (3 + (−5))
(−4)² − 3 × (−2)
−18 ÷ (−3) + (−4) × 2
5 − 2 × (−3) + (−1)
Four Operations with Mixed Numbers
Circle the correct answer. Convert to improper fractions to help.
2½ + 1¾
3⅓ − 1⅔
1½ × 2⅔
2¼ ÷ ¾
Absolute Value
Draw a line to match each expression to its value. |x| means the distance of x from zero.
Temperature and Depth Word Problems
Show all working. Include units.
A submarine descends 15 m, then a further 23 m, then rises 8 m. If it started at the surface (0 m), what is its final depth? Write as an integer.
On Monday the temperature is −3°C. By Wednesday it has tripled in coldness (multiplied by 3). What is Wednesday's temperature?
A bank account has a balance of −$240. If the owner deposits $75 each week for 4 weeks, what is the new balance?
Operation Rules for Fractions
Sort each step into the correct operation column.
Integers in the Real World
Look for integers in everyday life this week.
- 1Check the weather forecast for your city and three other cities. Record minimum temperatures as integers. Find the difference between the highest and lowest.
- 2Look up the elevation (in metres) of three mountains and three ocean trenches. List them as positive and negative integers and order them from deepest to highest.
- 3Find a recipe that serves 4 people. Multiply each ingredient by −1/2 — what does that mean? Discuss why we can't actually have a negative amount of an ingredient.
Integer Operations — Harder
Calculate each expression using correct sign rules.
(−3)² =
(−2)³ =
−(−5)² =
(−4)² − 4² =
Evaluate and Sort
Evaluate each expression and sort from smallest to largest.
Adding and Subtracting Integers — Number Line Method
Use a number line drawn from −20 to 20 to solve each problem. Show your movements.
Start at −8. Add 13. Where do you end up?
Start at 5. Subtract 18. Where do you end up?
Start at −10. Subtract −6. Where do you end up? (Subtracting a negative = adding a positive.)
Adding Fractions — LCD Method
Use the LCD to add. Circle the correct answer.
1/2 + 1/3 =
3/4 + 1/6 =
2/5 + 3/10 =
1/3 + 1/4 + 1/6 =
Subtracting Fractions
Subtract using the LCD. Circle the correct answer.
5/6 − 1/3 =
7/8 − 3/4 =
3/5 − 1/4 =
2 − 3/4 =
Multiplying Fractions — Area Model
Use the area model to multiply fractions. Draw a rectangle and shade the regions.
Draw a rectangle. Shade 3/4 of it horizontally (3 rows out of 4). Then shade 2/3 of it vertically. What fraction is shaded in both directions? This equals 3/4 × 2/3.
Use the area model or algorithm to find: 2/5 × 5/6. Simplify your answer fully.
Dividing Fractions — Flip and Multiply
Use ÷ b/c = × c/b. Circle the correct answer.
2/3 ÷ 1/4 =
3/5 ÷ 3/10 =
5 ÷ 2/3 =
1½ ÷ ¾ =
Operations on Fractions — Sort the Steps
Sort each step into the correct operation column.
Integer and Fraction Word Problems
Show all working. Include units.
The temperature drops 3°C each hour for 5 hours from 8°C. What is the final temperature?
A diver is at −18 m and ascends at 3 m per minute. How long until she reaches the surface?
A recipe needs ¾ cup of sugar. You want to make 2⅓ batches. How much sugar do you need?
BODMAS with Integers — Advanced
Apply BODMAS carefully including brackets, powers, and negative numbers.
−2 × (3 + (−5))
(−4)² − 3 × (−2)
−18 ÷ (−3) + (−4) × 2
5 − 2 × (−3) + (−1)
Working Backwards from an Answer
Find the missing number in each equation. Show full working.
□ × (−4) = 28. What is □?
□ ÷ (3/4) = 8. What is □?
−3 × □ + 7 = −8. What is □?
A rectangle has area 2¼ m². One side is ¾ m. Find the other side.
Which Operation?
Match each word clue to the correct operation.
Complex Word Problems
Show all working. Include units in your answers.
A submarine descends 15 m, then a further 23 m, then rises 8 m. If it started at the surface (0 m), what is its final depth?
A bank account has a balance of −$240. The owner deposits $75 each week for 4 weeks. What is the new balance?
A pipe fills a tank at 2½ litres per minute. A second pipe drains it at 1¾ litres per minute. How long to fill a 30-litre tank? Show working.
Absolute Value
|x| means the distance of x from zero on the number line. It is always non-negative.
|−7| =
|+3| =
|−12| =
|−4 + (−3)| =
|5 − 9| =
Integers and Fractions — Mixed Challenge
Show full working for each multi-step problem.
Evaluate: (−2)³ + 4 × (−3) ÷ (−2) − 5. Show every step in BODMAS order.
Simplify: (3/4 − 1/3) ÷ (1/2 + 1/6). Show working.
BODMAS with Integers
Evaluate each expression using the correct order of operations. Show all steps.
−3 + 4 × (−2) − (−1)
(−5)² − 2 × (−3) + 10 ÷ (−2)
3 − (−2)³ + 4 × (−1)⁵
Fraction Operations — Set A
Calculate each. Show all steps. Simplify your answer.
3/4 + 2/3
5/6 − 1/4
2 1/3 + 1 5/6
3 1/2 − 1 3/4
Fraction Operations — Set B
Calculate each. Show all steps. Simplify.
3/4 × 8/9
5/6 ÷ 10/3
2 1/2 × 1 3/5
3 1/3 ÷ 2 1/2
Rational Numbers on a Number Line
Sort these rational numbers from smallest to largest.
Temperatures — Integer Problem Set
Solve each temperature problem. Show working.
At midnight, the temperature is −8°C. By noon, it has risen 15°C. What is the noon temperature?
The temperature in Moscow is −12°C. The temperature in Sydney is 28°C. What is the difference?
The temperature drops 3°C every hour. Starting at 7°C, what is the temperature after 6 hours?
Mixed Fractions and Integers
Evaluate each expression. Show all steps.
−(2/3) + 5/6 − 1/2
−3 × 2/5 + 1/4
What fraction of 24 is 9? Express as a fraction in simplest form.
Rates with Rational Numbers
Solve each rate problem. Show working.
A car travels at −3/4 of a kilometre per minute (it is reversing). How far does it travel in 8 minutes?
A scuba diver descends at 2.5 m per minute. After 6 minutes, what is the diver's depth? Express as a signed number.
Order of Operations — Full Mixed Review
Evaluate each expression. Use BODMAS. Show all steps.
(3/4 + 1/2) × (−8) + 2²
−2 × [3 − (−1)]² ÷ 8
3/5 of (−15) − (−2)³
Creating a Number Puzzle
Design your own calculation chain.
Create a multi-step calculation chain using integers and fractions that has a final answer of exactly 0. Write each step and verify.
Create a problem using negative integers that has the answer −12. It must include at least three operations and use BODMAS. Show the solution.