🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2023 Math Kangaroo

Problem 1

Problem 1 · 2023 Math Kangaroo Easy
Arithmetic & Operations grouping

What is the simplified representation of the following fraction? \(\dfrac{7777^2}{5555 \cdot 2222}\)

Show answer
Answer: C — \(\dfrac{49}{10}\)
Show hints
Hint 1 of 2
Write 7777, 5555 and 2222 as a single digit times 1111.
Still stuck? Show hint 2 →
Hint 2 of 2
Once the 1111 factors cancel, only small numbers remain.
Show solution
Approach: factor out the common 1111 and cancel
  1. Note 7777 = 7·1111, 5555 = 5·1111, 2222 = 2·1111.
  2. The expression becomes (7·1111)2 over (5·1111)(2·1111) = 49·11112 over 10·11112.
  3. The 11112 cancels, leaving 49/10.
Mark: · log in to save
↑