Year 5 Number Cheatsheet

• Factors are numbers that divide evenly into another number (e.g. factors of 12 are 1, 2, 3, 4, 6, 12)
• Multiples are numbers made by multiplying (e.g. multiples of 5 are 5, 10, 15, 20, 25...)
• Estimation and rounding help with mental maths: round to nearest 10, 100, or 1000 before calculating
• Multiply 2-digit by 2-digit numbers using the standard algorithm or area model (break into tens and ones)
• Division with remainders can be expressed as whole number remainder or as a decimal/fraction
• Fractions on a number line help visualize fractional values between whole numbers
• Add and subtract fractions with the same denominator by adding/subtracting numerators
• Decimals to hundredths: 0.01 represents 1 hundredth; 0.25 = 25/100
• Percentage means "per cent" or "out of 100" — 50% = 50/100 = 0.5

Example 1: Finding Factors and Multiples

List all factors of 24.

Step 1: Find pairs of numbers that multiply to 24:

1 × 24 = 24, 2 × 12 = 24, 3 × 8 = 24, 4 × 6 = 24

Step 2: Factors are: 1, 2, 3, 4, 6, 8, 12, 24

Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

Example 2: Multiplying 2-Digit × 2-Digit Numbers

Calculate 18 × 25

Step 1: Break 18 into 10 + 8 and 25 into 20 + 5

Step 2: (18 × 20) + (18 × 5) = 360 + 90 = 450

Or using the standard algorithm:
25 × 18: 25 × 8 = 200, 25 × 10 = 250. Total: 200 + 250 = 450

Answer: 18 × 25 = 450

Example 3: Division with Remainders

Divide 37 ÷ 5. Express as a mixed number.

Step 1: 5 goes into 37 how many times? 5 × 7 = 35, 5 × 8 = 40 (too much)

Step 2: 5 goes into 37 seven times (7 × 5 = 35)

Step 3: Remainder: 37 - 35 = 2

Step 4: As a mixed number: 7 2/5

Answer: 37 ÷ 5 = 7 2/5 (or 7 remainder 2)

Example 4: Adding Fractions with Same Denominator

Calculate 2/8 + 5/8

Step 1: Add numerators: 2 + 5 = 7

Step 2: Keep denominator: 8

Step 3: Simplify if possible: 7/8 is already in simplest form

Answer: 2/8 + 5/8 = 7/8

Example 5: Converting to Percentage

What is 30/100 as a percentage?

Step 1: Percentage means "out of 100"

Step 2: 30/100 = 30%

Answer: 30/100 = 30%

• Mistake: Confusing factors and multiples. Saying "2 is a multiple of 10" (wrong; 10 is a multiple of 2).
  Fix: Factors divide into a number; multiples are made by multiplying. 2 is a factor of 10.
• Mistake: In 2-digit multiplication, forgetting to line up place values or add partial products incorrectly.
  Fix: Use the area model or standard algorithm carefully. Line up tens and ones separately.
• Mistake: Adding fractions incorrectly: 1/4 + 1/4 = 2/8 (wrong!). Adding numerators AND denominators.
  Fix: Only add numerators if denominators are the same. 1/4 + 1/4 = 2/4 = 1/2
• Mistake: Not recognizing that 0.5 = 50% = 1/2. Treating them as different values.
  Fix: They are equivalent: 0.5 = 5/10 = 50/100 = 50% = 1/2
• Mistake: Rounding incorrectly. Rounding 47 to 40 instead of 50 (47 is closer to 50).
  Fix: If the last digit is 5 or more, round up. If 4 or less, round down.

• Factor: A number that divides evenly into another number
• Multiple: A number made by multiplying another number by a whole number
• Estimation: Making an educated guess by rounding to a nearby number
• Rounding: Changing a number to the nearest 10, 100, 1000, etc.
• Remainder: The amount left over after division
• Numerator: The top number in a fraction (how many parts you have)
• Denominator: The bottom number in a fraction (how many equal parts the whole is divided into)
• Mixed Number: A whole number combined with a fraction (e.g. 2 3/4)
• Decimal: A number with a decimal point showing tenths, hundredths, etc.
• Percentage: A number out of 100, shown with the % symbol