Question

Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.

Answer 1

Hint: In this question three numbers are given and by using these three numbers and applying addition, subtraction and multiplication between them we have to create the possible mathematical expressions with every number used only once. Since there are 3 numbers so the total number of possible combinations would be $3! = 6$ but there are also 3 operation signs that need to be filled between numbers so by alternating the position of the operation signs as well as the position of the numbers there are so many possible combinations.

Complete step-by-step answer:
Given:
The numbers given are – 5, 7 and 8
Now some of the expressions that can be formed by just alternating the operation signs without changing the position of the numbers are given below –
$
5 + 7 - 8\\
5 + 7 \times 8\\
5 - 7 + 8\\
5 - 7 \times 8
$
$
5 \times 7 + 8\\
5 \times 7 - 8\\
- 5 + 7 \times 8
$
And the expressions formed by alternating the operation signs as well as the position of the number are given below –
$
7 + 5 - 8\\
7 + 5 \times 8\\
7 - 5 + 8\\
7 - 5 \times 8
$
$
8 + 5 - 7\\
8 + 5 \times 7\\
8 - 5 + 7\\
8 - 5 \times 7
$
Therefore, the expressions given above are some of the possible expressions by using three numbers 5, 7 and 8 with operations used as addition, subtraction and multiplication.

Note: It should be noted that the expressions that have the same value but have the difference in the operation sign position and the position of the number are not considered as the different expressions. For example, the value of the expression $5 + 7 + 8$ has the same value as the expression $8 + 5 + 7$ but the position of the numbers is different, therefore these expressions are not considered different expressions and they are counted as one.