# Fractional Operation

Pro Problems > Math > Number and Quantity > Number Theory > Star Operations## Fractional Operation

The operation a » b is defined as follows: a » b = + . Find the value of a such that a » a = .

a

a + 1

b

b - 3

12

5

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Problem by Mr. Twitchell

## Solution

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Click here to assign this problem to your students.## Similar Problems

### Star and Pound Operations

If a * b = (a + b)^{2}, and a # b = (a - b)^{2}, find x such that (2 * x) # (x * 1) = 81

### Star Operation with Cubes

If the operation (*) is defined as follows: a * b = , find the value of (7 * 3) * 4.

a

^{3}+ b^{3}a

^{2}- ab + b^{2}### h and k

x * y = x^{2} - y^{2} + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).

### Hashtag Operation

The "hashtag operation" is defined as follows: a # b = + .
If x # 7 = , find all possible values of x.

a + b

a

a + b

b

16

3

### Guess the Star

There exists a star (*) operation for which the following equations are true:

2 * 3 = 10

5 * 2 = 35

3 * 6 = 27

8 * 7 = 120

Find a star operation rule which satisfies all of these equations, and then use your rule to calculate the following:

10 * 11 = ?

### Diamond Operation

If the operation ♦ is defined as follows: a ♦ b = a^{2} - b^{2} , and 18 ♦ (x ♦ 8) = 6 ♦ 1, find all possible values of x.

### Non-Commutative Operation

If the operation a ♦ b is defined as follows: a ♦ b = + a, find the value of x such that:

a

b

x ♦ 2x = 2x ♦ x.

Note that this operation is not commutative; the order of operands cannot be exchanged without altering the result of the operation.

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