"How many different equivalent expressions for a particular number can be found?"
Various constraints can be (and need to be) applied, such as the use of integers only, the number of expressions listed, a restricted choice of digits, or operations etc.
List ten mathematically different expressions equivalent to 46, using the digits 2, 4, 5, 7, and 9.
• You may use any or all digits in a single expression. You may not repeat any digits in any one expression. You may use any mathematical operation that is valid, and does not repeat the use of a digit IN ANY FORM!
•At least one expression should use all five digits.
•At least one expression should use all four arithmetic operators (+, - , ×, ÷) at least once.
•One expression might even use all five digits AND all four operators!
For example: If you have the digits 1, 3, 5, 8, and 2,and use them to write equivalent expressions for the number 24, you could write: 3 × 8, or 23 + 1, but you cannot write: 13 × 2 − 2, because the "2" is used twice in the one expression.
My solutions so far are:
(5 × 7) + (9 + 4) – 2 = 46
(9²) – (7 × 5) = 46
(√9 × 7 × 2) + 4 = 46
(9 × 5) + ( 7 – 2) – 4 = 46
(9 × 4) + (5 + 7) – 2 = 46
I'm having troubles with the other five..
Also what are the ESSENTIAL (BIG) mathematical ideas (concepts) that are IN the problem?
And how can i generalise these ideas that are particular to the problem, to a broader context that still focuses on the problem.
Cut-and-paste operations do not work so well on Jiskha posts. You may need to type out each of your current solutions.
(5 x 7) + 9 + 2 = 46
(7 + 5) x 4 – 2 = 46
5+67=
To find the remaining five different equivalent expressions for the number 46 using the digits 2, 4, 5, 7, and 9, let's consider the constraints set in the problem:
1. At least one expression should use all five digits: One way to achieve this is by using each digit once in a multiplication expression. For example:
(5 × 7 × 4) + 9 - 2 = 46
2. At least one expression should use all four arithmetic operators at least once: To satisfy this constraint, you can create an expression that involves all four operators. For example:
(9 + 5) ÷ (7 - 4) × 2 = 46
3. One expression might use all five digits and all four operators: To fulfill this requirement, you can create a more complex expression using all five digits and all four operators. One possibility is:
(7 ÷ 5) + (2 × 9) - 4 = 46
Now, let's find the remaining two expressions:
4. Using a combination of addition and subtraction:
(9 + 7) - (5 × 2) + 4 = 46
5. Using a combination of multiplication and addition:
(9 × 2) + (7 × 4) - 5 = 46
Essential (big) mathematical ideas in this problem include:
1. Operations: Addition, subtraction, multiplication, and division.
2. Order of operations: The necessity to follow the correct order of operations to evaluate the expressions.
3. Digit constraints: The restriction on repeating digits within an expression.
To generalize these ideas to a broader context focusing on the problem, you can look at different numbers and explore the various equivalent expressions that can be formed using specific constraints. You can vary the number of digits or the available operations to generate a broader set of problems and solutions. By doing so, you will deepen your understanding of operations and their interconnectedness while enhancing problem-solving skills.