Problem 1 - Prealgebra

Question

Write each of the following in words. $$4<7$$

Step-by-Step Solution

Answer

Four is less than seven.

Step 1: Understand the Inequality Symbols

In the inequality expression given, the symbol "<" means "less than." It's important to recognize that the number on the left is smaller than the number on the right.

Step 2: Identify the Numbers

The inequality presented is "4 < 7." The number on the left is 4, and the number on the right is 7. These are the two numbers being compared.

Step 3: Construct the Sentence

Based on Steps 1 and 2, we translate the inequality into words. The number 4 is less than the number 7. Therefore, the inequality "4 < 7" is written as "four is less than seven."

Key Concepts

Inequality Symbols

Inequality symbols are like little arrows in math that show us the relationship between two numbers or variables. One common inequality symbol is "<", which we read as "less than."

Imagine two numbers placed on a number line. If one number is to the left and smaller, we use "<" to show this. Other important symbols include ">" (which means "greater than"), "≤" ("less than or equal to"), and "≥" ("greater than or equal to"). Each helps us describe if one number is smaller, bigger, or possibly the same as another number.

• "<" indicates that the number on the left is smaller than the number on the right.
• "=" means the two numbers are equal.
• ">" indicates the number on the left is larger.

Understanding these symbols is like learning a new language that tells us more about numbers in math.

Writing Inequalities in Words

Transforming an inequality into a written sentence involves translating math symbols into English words. Let's take the example of "4 < 7." The symbol "<" becomes "is less than," while the numbers stay as they are.

So, if you encounter "4 < 7" in math, you write it in words as "four is less than seven." Thinking of it like a sentence helps students make sense of what the numbers mean in comparison to each other.

Here are some things to remember:

• Start by identifying the numbers and the inequality symbol.
• Replace the symbol with the corresponding phrase (like "is less than").
• Order the words in the same order as they appear in the inequality.

This simple method is your tool for turning mathematical expressions into understandable language.

Understanding Inequalities

Understanding inequalities means grasping how numbers relate to each other in different contexts. It’s more than just memorizing symbols—it's about knowing what they represent in real life situations.

Inequalities help us compare ages, sizes, amounts, distances, and more. They tell us how one thing measures up against another, offering insight into mathematical relationships.

• With "4 < 7", we know exactly how much smaller four is than seven—not just that it is smaller, but by how much when using a number line.
• Inequalities can involve not just whole numbers, but fractions and decimals too.
• We often use inequalities in everyday situations, like seeing what times are available for a meeting ("9:00 is earlier than 10:00") or even to compare temperatures ("45°F is colder than 60°F").

By understanding inequalities, students can better navigate the world of numbers and apply these concepts in everyday life. They provide a framework for problem-solving where comparison and order are important.