Question

Simplify. $$|-35|$$

Short answer

Answer: The simplified value of \(|-35|\) is \(35\).

Step-by-step solution

Calculate the absolute value of the number

To find the absolute value of \(|-35|\), think about how far away it is from zero. A negative number becomes positive when its absolute value is calculated. So, we just need to remove the negative sign and keep the number as it is.

Simplify the expression

The absolute value of \(|-35|\) is equal to \(35\). Therefore, the simplified expression is: $$|-35|=35$$

Key concepts

Integer Operations

Integer operations are a fundamental part of math that involves performing actions like addition, subtraction, multiplication, and division with whole numbers. Integers include both negative and positive numbers along with zero.
When you add or subtract integers, it's important to pay attention to their signs. For instance, adding two positive integers results in a positive sum, whereas adding two negative integers results in a more negative number. If you add a positive integer and a negative integer, their absolute values are subtracted.

• Addition: Positive plus positive equals positive. Negative plus negative equals more of a negative.
• Subtraction: Subtracting is the same as adding the opposite.
• Multiplication and Division: Positive times positive or negative times negative gives a positive product. Positive times negative gives a negative product.

Understanding these operations well will help you confidently handle problems involving integers.

Negative Numbers

Negative numbers are numbers less than zero, and they are used to represent values below a defined origin point. In real-life, negative numbers can represent losses, decreases, or opposites, like temperatures below zero or depths below sea level.
When you perform operations with negative numbers, the rules can change from how you normally calculate with positives. For example, subtracting a negative number is the same as adding its absolute value. Knowing how negative numbers work helps you solve many math problems with ease.

• Number Line: Negative numbers are typically represented on a number line to the left of zero.
• Opposite Values: A negative number paired with its positive counterpart results in zero. This displays the concept of opposites in mathematics.
• Visual Clarity: Using negative numbers makes subtraction and showing debt or deficits more logical and visual.

Negative numbers can often trip up students, but remember they follow consistent rules that help make math problems solvable.

Simplification in Mathematics

Simplification in math involves making an expression easier to understand or compute without changing its value. It's like untangling a knot— you work through the mess to find a clear answer. Simplification typically involves combining like terms, removing parentheses, or reducing fractions.
Working with the absolute value, like in our example with \(|-35|\), is an essential part of simplification. The absolute value removes any negative signs, making the number straightforward.

• Absolute Value: Always non-negative, it shows how far a number is from zero. Simplifying \(|-35|\) gave us \35\.
• Combining Like Terms: Helps reduce expressions to their simplest form, making them more readable.
• Reduction: Cuts down complicated fractions or numbers to their smallest, simplest quantity.

By simplifying expressions, you break down complex problems into manageable pieces, making it easier to find the solution.