Solutions: Sec 3.8 Mental Math

Page 66: Figure It Out

Q1. Examples for scenarios

• 5-digit + 5-digit > 90,250
  • $50,000 + 50,000 = 100,000$.
• 5-digit - 5-digit < 56,503
  • $60,000 - 50,000 = 10,000$.
• 4-digit + 4-digit = 6-digit sum
  • Max 4-digit is 9999.
  • $9999 + 9999 = 19,998$.
  • This is a 5-digit number.
  • Answer: Impossible.

Page 67: Always, Sometimes, Never

a. 5-digit + 5-digit = 5-digit

• $10,000 + 10,000 = 20,000$ (True).
• $90,000 + 90,000 = 180,000$ (False, gives 6-digit).
• Answer: Sometimes.

b. 4-digit + 2-digit = 4-digit

• $1000 + 10 = 1010$ (True).
• $9999 + 10 = 10009$ (False, gives 5-digit).
• Answer: Sometimes (mostly true, except near boundary).

c. 4-digit + 2-digit = 6-digit

• Max: $9999 + 99 = 10098$ (5-digit).
• Answer: Never.

d. 5-digit - 5-digit = 5-digit

• $90,000 - 10,000 = 80,000$ (True).
• $10,001 - 10,000 = 1$ (False, gives 1-digit).
• Answer: Sometimes.