Number Toolkit

Adding and subtracting

• A subtracted negative reverses into an addition
  • 8 − (−5) = 8 + 5 = 13
• An added negative reverses into a subtraction
  • 6 + (−9) = 6 − 9 = −3
• Two signs written next to each other collapse to one: two like signs give a plus, two unlike signs give a minus

Multiplying and dividing

• Matching signs on the two values produce a positive result
  • (−7) × (−3) = 21 and (−24) ÷ (−6) = 4
• Opposing signs produce a negative result
  • (−7) × 3 = −21 and 24 ÷ (−6) = −4
• With a longer product, count the negative factors: an even count gives a positive, an odd count gives a negative

Negatives in context

• Temperature below zero is the most common context
  • A temperature of 2 °C falling by 9 °C gives 2 − 9 = −7 °C
• Money owed is written as a negative balance
  • A balance of −£150 that receives a £90 repayment becomes −150 + 90 = −£60
• Depth below sea level and floors below ground are also recorded as negatives