AMC 8 Daily Practice - Calculation Tricks by Grouping

Complete problem set with solutions and individual problem pages

Problem 7 Easy

What is the value of 211\times 555+445\times 789+555\times 789+211\times 445?

  • A.

    999999

  • B.

    1000000

  • C.

    936840

  • D.

    1111111

  • E.

    100000

Answer:B

Method 1:

By observation, we notice that the expression contains common factors 211 and 789.

Applying the associative property of multiplication, the original expression can be rewritten as: 211 \times 555 + 445 \times 789 + 555 \times 789 + 211 \times 445 = 211 \times (555 + 445) + 789 \times (445 + 555) = 211 \times 1000 + 789 \times 1000 = (211 + 789) \times 1000 = 1000 \times 1000 = 1,000,000

Thus, the result is \boxed{1000000}.

Method 2:

By observation, we notice that the expression contains common factors 555 and 445.

Applying the associative property of multiplication, the original expression can be rewritten as: 211 \times 555 + 445 \times 789 + 555 \times 789 + 211 \times 445 = 555 \times (211 + 789) + 445 \times (789 + 211) = (555 + 445) \times (211 + 789) = 1000 \times 1000 = 1,000,000

Thus, the result is \boxed{1000000}.

Related Problems
Problem 4 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 5 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 6 AMC 8 Daily Practice - Calculation Tricks by Grouping
Problem 8 AMC 8 Daily Practice - Calculation Tricks by Grouping
Think Academy Powered by ChatGPT