Insert +, -, x, or + symbols to make each statement true
17?2?3?8=3
33?3?2?5=1
17 - 2 * 3 - 8 = 3
17 - 6 - 8 =
11 - 8 = 3
33 / 3 - 2 * 5 = 1
11 - 10 = 1
3/4 1/4
3/4 - 1/4
To solve these equations, we need to determine the missing symbols (+, -, x, or ÷) that will make each statement true. Let's go step by step:
1) 17 ? 2 ? 3 ? 8 = 3
First, let's consider the order of operations (PEMDAS/BODMAS): parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
We are given the equation: 17 ? 2 ? 3 ? 8 = 3
To make sense of the equation, let's start with the multiplication or division operation first. Since multiplication and division have the same priority, we need to determine which operation to use first. Let's try multiplication (x):
17 ? (2 x 3) ? 8 = 3
Now we have: 17 ? 6 ? 8 = 3
Next, let's perform the remaining multiplication operation:
(17 x 6) ? 8 =3
Now we have: 102 ? 8 = 3
Finally, we have only addition and subtraction left. To make the equation true, we need to subtract (–).
102 - 8 = 3
Therefore, the missing symbols for the first equation are:
17 - 2 x 3 - 8 = 3
2) 33 ? 3 ? 2 ? 5 = 1
Applying the same logic to the second equation:
33 ? 3 ? 2 ? 5 = 1
To avoid ambiguity, let's start with multiplication again (x):
33 ? (3 x 2) ? 5 = 1
Now we have: 33 ? 6 ? 5 = 1
Next, we have only addition and subtraction left. To make the equation true, we need to add (+).
33 + 6 + 5 = 1
However, this equation does not give us the desired result. It means that there might be an error in the problem. It is not possible to solve the equation by inserting the given symbols.
Therefore, the second equation has no solution using the provided symbols.
In summary:
1) 17 - 2 x 3 - 8 = 3
2) The second equation has no solution using the given symbols.