Problem 47 - Prealgebra

Question

Add and subtract as indicated. $$9.7-(5.2-1.4)$$

Step-by-Step Solution

Answer

9.7 - (5.2 - 1.4) = 5.9

Step 1: Simplify the Inner Expression

First, look at the expression inside the parentheses: \(5.2 - 1.4\). Subtract 1.4 from 5.2.\[5.2 - 1.4 = 3.8\]

Step 2: Substitute and Simplify the Remaining Expression

Now that we know \((5.2 - 1.4) = 3.8\), substitute this back into the original expression. You have:\[9.7 - 3.8\]. Now subtract 3.8 from 9.7.\[9.7 - 3.8 = 5.9\]

Key Concepts

Understanding Addition and Subtraction

Addition and subtraction are among the basic operations of arithmetic. They are inverse operations, meaning one can undo the effect of the other. When you're adding, you're combined values together, resulting in a larger total.
In contrast, subtraction reduces the total by removing part of it. These operations have specific symbols — plus (+) for addition, and minus (−) for subtraction.

• To add numbers, simply combine their values.
• For subtraction, take the value you want to remove away from the total.

When dealing with several numbers, or a mix of operations, the order of operations becomes crucial. It's important to perform addition and subtraction correctly to arrive at the right answer. Sequence matters!

The Role of Parentheses in Math

Parentheses are powerful tools in math as they help organize expressions and dictate the order of operations. Whenever you see parentheses in an arithmetic expression, calculations inside must be done first.
No matter how many operations are outside the parentheses, what’s inside takes precedence.

• For example, in the expression \(9.7 - (5.2 - 1.4)\), solve what's inside the parentheses first.
• Inside parentheses, perform the operations as they come, respecting their precedence.

This ensures that the integrity of the original expression is maintained and lets complex expressions be easier to follow. Once the operations inside parentheses are solved, the rest of the expression can be simplified according to the standard order of operations.

Simplifying Arithmetic Expressions

Arithmetic expressions are combinations of numbers and operators that represent a specific value. Simplifying these expressions accurately is essential to solve math problems.

• Begin by identifying any operations inside parentheses and compute them first.
• Next, address multiplication and division operations.
• Finish with addition and subtraction.

For instance, the expression \(9.7 - (5.2 - 1.4)\) requires you to begin by finding \(5.2 - 1.4\), which simplifies to \(3.8\).
Then subtract \(3.8\) from \(9.7\), resulting in \(5.9\).
This systematic approach makes solving arithmetic expressions less daunting and far more manageable.