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Year 6 Number Cheatsheet

Year 6 · Number · Australian Curriculum v9

What You Need to Know

Prime numbers have exactly 2 factors (1 and itself); composite numbers have more than 2 factors
Square numbers are products of a whole number multiplied by itself (e.g. 5 × 5 = 25)
All four operations (addition, subtraction, multiplication, division) work with whole numbers to millions
Integers include positive numbers, negative numbers, and zero
Fractions represent equal parts; equivalent fractions show the same value with different numerators and denominators
Decimals and percentages are alternative ways to represent parts of a whole
Percentages are useful for discounts, mark-ups, and financial calculations like GST and profit/loss

Concept	Rule or Fact
Prime Numbers	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...
Square Numbers	1, 4, 9, 16, 25, 36, 49, 64, 81, 100 (products: 1², 2², 3², 4², 5²...)
Equivalent Fractions	Multiply or divide both numerator and denominator by the same number
Add/Subtract Fractions	Find a common denominator first, then add or subtract numerators
Multiply Decimals	Multiply as whole numbers, then count decimal places in both numbers and place the decimal in the answer
Divide Decimals	Convert to fractions or use long division; move decimal point same places in dividend and divisor
Decimal to Percentage	Multiply by 100 (e.g. 0.35 = 35%)
Percentage to Decimal	Divide by 100 (e.g. 45% = 0.45)
Percentage Discount	Discount = Price × (Discount % ÷ 100)
Percentage Mark-up	Mark-up = Cost × (Mark-up % ÷ 100)
GST Calculation	GST = Price × 0.1 (10% in Australia)
Profit/Loss	Profit = Selling Price − Cost Price \| Loss = Cost Price − Selling Price

Example 1: Adding Fractions with Unlike Denominators

Calculate 1/3 + 1/4

Example 2: Percentage Discount

A shirt costs $60. There is a 20% discount. What is the sale price?

Example 3: Multiplying Decimals

Calculate 2.5 × 3.2

Mistake: Adding fractions with unlike denominators by adding numerators and denominators (1/3 + 1/4 = 2/7). Fix: Find a common denominator first. Both fractions must have the same denominator before adding.
Mistake: Forgetting to include 1 when identifying prime factors. Fix: Prime numbers are only divisible by 1 and themselves. 1 is not prime; it's neither prime nor composite.
Mistake: In decimal multiplication, placing the decimal in the wrong position. Fix: Count the total number of decimal places in both original numbers and count that many places from the right in your answer.
Mistake: Calculating percentage discount as "original price × discount %" and adding to the price instead of subtracting. Fix: Discount reduces the price, so subtract the discount amount from the original price.

Question 1: Is 47 prime or composite?

47 is prime because it can only be divided evenly by 1 and 47.

Question 2: What is 3/5 + 1/4?

Common denominator is 20: 3/5 = 12/20 and 1/4 = 5/20. Answer: 17/20

Question 3: A book costs $25. It is on sale for 30% off. What is the sale price?

Discount: $25 × 0.3 = $7.50. Sale price: $25 − $7.50 = $17.50

Question 4: Calculate 4.2 × 2.1

42 × 21 = 882. Two decimal places total, so answer is 8.82

Question 5: Express 65% as a decimal and a fraction.

Decimal: 0.65 | Fraction: 13/20

Prime number: A whole number greater than 1 with exactly 2 factors (1 and itself)
Composite number: A whole number with more than 2 factors
Square number: A number that is the product of a whole number multiplied by itself (e.g. 3 × 3 = 9)
Factor: A whole number that divides evenly into another number
Multiple: A number produced by multiplying a number by a whole number
Numerator: The top number in a fraction
Denominator: The bottom number in a fraction
Equivalent fractions: Fractions that represent the same value
Decimal: A number using the base-10 system with a decimal point
Percentage: A number out of 100 (represented by the % symbol)
Integer: A whole number, including positive numbers, negative numbers, and zero
GST: Goods and Services Tax in Australia, currently 10%
Profit: The amount gained when selling price exceeds cost price
Loss: The amount lost when selling price is less than cost price

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