Balancing Equations with Mathematical Signs

The question asks us to find the correct combination of mathematical signs that, when placed sequentially in the asterisks, will balance the given equation: \(88 * 44 * 22 * 66 * 99 * 251\).

We are provided with several options, each containing a sequence of signs. We need to test these sequences to see which one makes the left side of the equation equal to the right side.

Testing the Correct Combination of Signs

According to the provided information, the correct combination of signs is \(\minus, \div, +, +, =\). Let's substitute these signs into the equation:

\(88 \minus 44 \div 22 + 66 + 99 = 251\)

Now, we must evaluate the left side of the equation following the order of operations (often remembered by acronyms like BODMAS or PEMDAS):

1. Brackets / Parentheses
2. Orders / Exponents
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Applying the order of operations to our equation:

\(88 \minus 44 \div 22 + 66 + 99 = 251\)

Step 1: Division

First, perform the division operation: \(44 \div 22\).

\(44 \div 22 = 2\)

The equation now becomes:

\(88 \minus 2 + 66 + 99 = 251\)

Step 2: Addition and Subtraction (from left to right)

Next, perform the subtraction and addition from left to right.

Perform the first operation from the left, which is subtraction: \(88 \minus 2\).

\(88 \minus 2 = 86\)

The equation now becomes:

\(86 + 66 + 99 = 251\)

Now, perform the addition from left to right: \(86 + 66\).

\(86 + 66 = 152\)

The equation now becomes:

\(152 + 99 = 251\)

Finally, perform the last addition: \(152 + 99\).

\(152 + 99 = 251\)

Step 3: Check the Equality

After performing all operations on the left side, we get \(251\). The equation is:

\(251 = 251\)

Since the left side equals the right side, the equation is balanced with the signs \(\minus, \div, +, +, =\).

This confirms that the sequence of mathematical signs \(\minus, \div, +, +, =\) is the correct combination to balance the given equation \(88 * 44 * 22 * 66 * 99 * 251\).

Therefore, the correct combination of mathematical signs is \(\minus, \div, +, +, =\).

Revision Table: Mathematical Operations and Balancing Equations

Additional Information: Solving Sign Puzzles

Questions like this are common in reasoning and quantitative aptitude tests. They assess your understanding of basic arithmetic operations and the order of operations. Here are a few tips for solving such problems:

• Always remember and apply the correct order of operations (BODMAS/PEMDAS). Division and Multiplication come before Addition and Subtraction.
• When testing options, start with those that seem most likely to yield the target number. For instance, if the target number is large, you might look for combinations involving multiplication or addition. If it's small, subtraction or division might be key.
• Sometimes, estimating the outcome of operations can help rule out options quickly. For example, if an option starts with a large division that makes the number very small, and the subsequent additions are not significant, it might not reach a large target number.
• Work through each step carefully to avoid calculation errors.

Practicing different variations of these problems will help you become faster and more accurate at solving them.