The question asks us to find the correct combination of mathematical symbols to replace the asterisks (*) in the equation $62 * 14 * 7 * 18 * 26$ so that the equation is balanced. This means we need to test each option provided and see which set of symbols makes the left side of the equation equal to the right side.

Testing Mathematical Symbols to Balance the Equation

We will substitute the symbols from each option into the given equation and check if the equality holds true. Remember to follow the order of operations (BODMAS/PEMDAS - Brackets, Orders/Exponents, Division/Multiplication, Addition/Subtraction) when evaluating the expressions.

Evaluating Option 1: +, $\times$, =, -

If we replace the asterisks with the symbols from Option 1, the equation becomes:

$\text{Equation:} \quad 62 + 14 \times 7 = 18 - 26$

Now, let's evaluate both sides of the equation:

• Left Side (LS): $62 + 14 \times 7$
• According to the order of operations, multiplication is done before addition.
• $14 \times 7 = 98$
• LS = $62 + 98 = 160$
• Right Side (RS): $18 - 26$
• RS = $-8$

Comparing the two sides: $160 \neq -8$.

So, Option 1 does not balance the equation.

Evaluating Option 2: =, $\div$, $\times$, +

If we replace the asterisks with the symbols from Option 2, the equation becomes:

$\text{Equation:} \quad 62 = 14 \div 7 \times 18 + 26$

Here, the equals sign is the first symbol, meaning the left side is simply 62. We need to evaluate the right side.

• Left Side (LS): $62$
• Right Side (RS): $14 \div 7 \times 18 + 26$
• According to the order of operations, division and multiplication are done before addition. They are performed from left to right.
• First, division: $14 \div 7 = 2$
• Next, multiplication: $2 \times 18 = 36$
• Finally, addition: $36 + 26 = 62$
• RS = $62$

Comparing the two sides: $62 = 62$.

So, Option 2 balances the equation.

Since we found the correct combination in Option 2, we can stop here. However, for completeness, let's quickly look at the other options.

Evaluating Option 3: =, $\times$, +, -

Equation: $62 = 14 \times 7 + 18 - 26$

• LS: $62$
• RS: $14 \times 7 + 18 - 26$
• $14 \times 7 = 98$
• $98 + 18 - 26$
• $116 - 26 = 90$
• RS = $90$

Comparing: $62 \neq 90$. Option 3 does not balance the equation.

Evaluating Option 4: -, +, =, $\times$

Equation: $62 - 14 + 7 = 18 \times 26$

• LS: $62 - 14 + 7$
• $48 + 7 = 55$
• LS = $55$
• RS: $18 \times 26$
• $18 \times 26 = 468$
• RS = $468$

Comparing: $55 \neq 468$. Option 4 does not balance the equation.

Summary of Evaluation

The evaluation confirms that only Option 2 provides the correct combination of mathematical symbols to balance the equation $62 * 14 * 7 * 18 * 26$.

Revision Table: Equation Balancing Symbols

This section reviews the process of balancing equations using different symbol combinations.

• Understand the Goal: Replace placeholder symbols (*) with mathematical operators and an equals sign to make the left and right sides of the equation equal.
• Use Options Provided: Each option gives a specific sequence of symbols to try.
• Apply Order of Operations: Follow BODMAS/PEMDAS strictly when calculating the value of each side of the equation.
• Evaluate Both Sides: Calculate the value of the expression on the left side of the equals sign and the value on the right side.
• Check for Equality: Compare the calculated values. If they are equal, the equation is balanced, and the symbol combination is correct.
• Test All Options: If the first option doesn't work, proceed to the next until the correct one is found.

Additional Information: Understanding Order of Operations

The order of operations is crucial when solving mathematical expressions involving multiple operations. The widely used acronyms BODMAS or PEMDAS help remember this order:

• BODMAS:
  • Brackets
  • Orders (powers, square roots)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)
• PEMDAS:
  • Parentheses
  • Exponents (powers, roots)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

In the given problem, we primarily used Division, Multiplication, and Addition, following the left-to-right rule for division and multiplication, and then performing addition.

Mastering the order of operations is essential for accurately evaluating mathematical expressions and balancing equations.