Question

Evaluate each expression. $$ (5+4) \frac{1}{3} $$

Short answer

3

Step-by-step solution

Simplify inside the parentheses

First, add the numbers inside the parentheses. i.e., \((5 + 4) = 9\).

Multiply the result by \(\frac{1}{3}\)

Next, multiply the result of the addition by \(\frac{1}{3}\). i.e., \(9 \times \frac{1}{3} = 3\).

Key concepts

Arithmetic Operations

Arithmetic operations are the basic calculations we do with numbers. They include addition, subtraction, multiplication, and division. Here’s a quick recap to make it clear:

• Addition (+): Combining two numbers to get a larger one, like in \(5+4\).
• Subtraction (-): Taking one number away from another, like \(9-5\).
• Multiplication (×): Repeated addition of a number, such as \(5×3=15\).
• Division (÷): Splitting a number into equal parts, like \(10÷2=5\).

Understanding these operations is key to solving expressions. In the given exercise, you performed both addition (inside the parentheses) and multiplication (by \(\frac{1}{3}\)). Let’s break it further.

Parentheses in Math

Parentheses are symbols used in math to group parts of an expression. They tell us which part to solve first. Imagine them like instructions in a recipe, guiding you step by step.

For example, in \((5+4) \frac{1}{3}\), parentheses around \(5+4\) indicate that addition should be done before multiplying by \(\frac{1}{3}\).

Remember, the general rule of operations, also known as PEMDAS/BODMAS:

• P/B: Parentheses/Brackets first
• E/O: Exponents/Orders (like squares)
• M: Multiplication
• D/A: Division next
• A/S: Addition and Subtraction last

This order helps to solve expressions correctly.

Multiplying Fractions

Multiplying fractions can seem tricky at first but is easy once you get the hang of it. Here’s how it works:

• Multiply the numerators (top numbers).
• Multiply the denominators (bottom numbers).
• Simplify the fraction if possible.

Let's look at our example:
\(9 \times \frac{1}{3} = \frac{9}{3}\)
1. Numerator: 9 (from 9) × 1 = 9
2. Denominator: 1 (implied) × 3 = 3

Result: \(\frac{9}{3} = 3\)
Multiplying by fractions often involves turning whole numbers into fractions by placing them over 1—like \(9 = \frac{9}{1}\). This example shows how straightforward it can be to multiply a fraction and a whole number.