MathToSuccess
Where Practice Brings Success
X
IntroductionGT package Math Olympiad
Math Olympiad 1
Math Olympiad 2
Math Olympiad 3
Week 1: Logical MatchingWeek 2: Reverse ThinkingWeek 3: Addition & Subtraction ShortcutsWeek 4: ComparisonWeek 5: Quiz 1Week 6: Number Sequence (1) Week 7: Multiplication & Division Word ProblemsWeek 8: Counting ProblemsWeek 9: Average ProblemsWeek 10: Quiz 2Week 11: Fractions & Decimals (1)Week 12: Word Problem 1Week 13: Shape CountingWeek 14: MeasurementsWeek 15: Quiz 3Week 16: Number Sequence (2)Week 17: 2-Digit Number SenseWeek 18: Sum & DifferenceWeek 19: Pattern ProblemsWeek 20: Quiz 4Week 21: Money ProblemsWeek 22: Age ProblemsWeek 23: Divisibility Problems (1)Week 24: 3-Digit Number SenseWeek 25: Quiz 5Week 26: Mid-Term ExamWeek 27: Calendar ProblemsWeek 28: Proportion & CorrelationWeek 29: Multiplication & Division ShortcutsWeek 30: Make an EquationWeek 31: Quiz 6Week 32: Distribution & Substitution ProblemsWeek 33: Sum,Difference and MultipleWeek 34: Factors & PrimesWeek 35: Roman NumeralsWeek 36: Quiz 7Week 37: Least & MostWeek 38: GeometryWeek 39: CombinationWeek 40: Word Problem 2Week 41: Quiz 8Week 42: Divisibility Problems (2)Week 43: Fractions & Decimals (2)Week 44: Word Problems 3Week 45: Number ThinkingWeek 46: Quiz 9Week 47: Mixed Integer OperationsWeek 48: More Calulation ShortcutsWeek 49: Multiples & LCMWeek 50: Challenging QuestionsWeek 51: Quiz 10Week 52: Final Exam
Math Olympiad 4
Math Olympiad 5
COUNTS MORE
SHSAT MathSAT MathPrintable Booklet
Math Game My ArchiveFeedbackFAQContact Info
WeekTopic and action
Week 3
Addition & Subtraction Shortcuts

Example 1.

66 + 198 = 66 + 200 − 2 = 266 − 2 = 264.

Analyze: 198 → 200. The key is to think of 198 as 200, which is 2 more than 198. This is why you must subtract 2 from the sum to get the correct answer.

Example 2.

22 + 202 = 22 + 200 + 2 = 222 + 2 = 224.

Example 3.

683 − 397 = 683 − 400 + 3 = 283 + 3 = 286.

Analyze: 397 → 400. The key is to think of 397 as 400, which is 3 more than 397. This is why you must add 3 to the sum to get the correct answer.

Example 4.

363 − 302 = 363 − 300 − 2 = 63 − 2 = 61.


  • Commutative property: For any numbers a, and b (which can be any numbers):

    a + b = b + a

  • Associative property: For the numbers a, b, and c (which can be any numbers):

    (a + b) + c = a + (b + c)


Example 5.

45 + 68 + 55 = (45 + 55) + 68 = 100 + 68 = 168.

Analyze: by using commutative property and associative property, group 45 and 55 together.

Example 6

22 + 63 + 78 + 37 + 56 = (22 + 78) + (63 + 37) + 56 = 100 + 100 + 56 = 256.

Example 7.

237 − 26 − 137 = (237 − 137) − 26 = 100 − 26 = 74.

Analyze: The key is to switch the positions of the two numbers 26 and 137.

Example 8.

567 + 123 − 367 = (567 − 367) + 123 = 200 + 123 = 323.

Analyze: The key is to switch the positions of the two numbers 123 and 367.

Example 9.

123498 − 123466 = 98 − 66 = 32.

Analyze: Observing the two numbers. Only the last two digits are different.


Example 10.

2 + 92 + 992 + 9992 + 99992

= (10 − 8) + (100 − 8) + (1000 − 8) + (10000 − 8) + (100000 − 8)

= 111110 − 5 × 8

= 111070

Example 11.

24 − 22 + 20 − 18 + 16 − 14 + 12 − 10 + 8 − 6

= (24 − 22) + (20 − 18) + (16 − 14) + (12 − 10) + (8 − 6)

= 2 × 5 = 10.

Example 12.

69 + 70 + 71 + 72 + 73 + 74

= (70 − 1) + 70 + (70 + 1) + (70 + 2) + (70 + 3) + (70 + 4)

= 70 × 5 − 1 + 1 + 2 + 3 + 4 = 350 + 9 = 359