Math Problem Statement

Using all of the following numbers: 3, 3, 7, 1. Rearrange them and use: +, -, ×, ÷, to get a sum of 10. You may also use "(" and ")" once.

Solution

To achieve a sum of 10 using the numbers 3, 3, 7, 1 and operations +, -, ×, ÷ with parentheses if necessary, one possible solution is:

(7+3)÷(31)=10(7 + 3) ÷ (3 - 1) = 10

Steps to verify:

  1. Calculate inside parentheses: (7+3)=10(7 + 3) = 10.
  2. Calculate inside the second parentheses: (31)=2(3 - 1) = 2.
  3. Perform the division: 10÷2=1010 ÷ 2 = 10.

This satisfies the requirement.


Would you like me to provide a detailed breakdown or explore alternative solutions?

Here are 5 related questions for you:

  1. Can you derive another solution using these numbers and operations?
  2. How do parentheses affect the outcome of expressions in general?
  3. Can the same approach be applied to find different target sums with these numbers?
  4. What other mathematical rules can help in solving such puzzles?
  5. Can you generalize a method to test all combinations systematically?

Tip: When solving puzzles like this, try operations systematically, starting with addition or subtraction before applying multiplication or division.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Order of Operations
Parentheses Usage

Formulas

Basic Arithmetic Operations: a + b, a - b, a × b, a ÷ b

Theorems

Order of Operations (PEMDAS/BODMAS)

Suitable Grade Level

Grades 6-8