Question

Write each statement using symbols. The product of 5 and 2 equals \(10 .\)

Short answer

5 × 2 = 10

Step-by-step solution

Identify the Elements

Examine the statement to find the key mathematical elements. Here, 'The product of 5 and 2' and 'equals 10'.

Translate Words to Symbols

Translate the phrase 'The product of' to multiplication (×) and 'equals' to the equal sign (=).

Write the Equation

Combine the elements identified in the previous steps to write the equation: 5 × 2 = 10.

Key concepts

Mathematical Translation

Mathematical translation involves converting statements given in words into mathematical symbols and expressions.
This is a crucial skill because it allows us to represent real-world problems using the language of mathematics.

Let's break down the example provided: 'The product of 5 and 2 equals 10.'

• 'The product of' is a hint to use multiplication.
• The numbers involved are '5' and '2'.
• 'Equals' is a cue to use the equal sign (=).

By understanding these clues, we can translate the statement into the equation 5 × 2 = 10.
Practicing this skill helps immensely when tackling more complex problems.

Number Operations

Number operations are the basic mathematical processes we use to manipulate numbers.
The main operations are addition, subtraction, multiplication, and division.

• Multiplication is the operation used in our example ('the product of 5 and 2').
• 'Product' always indicates multiplication.
• Familiarity with these operations is key to solving equations accurately.

In the given exercise, we use multiplication to combine the numbers 5 and 2. This multiplication is written as 5 × 2.
Understanding how to correctly apply these operations can help solve a range of mathematical problems efficiently.

Equation Writing

Equation writing is the process of representing a mathematical statement in the form of an equation.
Equations are used to show that two expressions are equal. They consist of variables, numbers, and operation symbols.

• In our example, the statement is 'The product of 5 and 2 equals 10.'
• To write the equation, translate 'product' to multiplication (×) and 'equals' to the equal sign (=).

Thus, the statement becomes the equation: 5 × 2 = 10.
Equations are essential in algebra to express relationships between quantities and to solve for unknowns.