Translating Math Sentences into Equations

Video Lessons > Translating Math Sentences into Equations

Introduction and Video

In this video lesson, you will learn about translating math sentences into algebraic equations. This skill is really helpful for solving word problems and connecting math concepts to real-world scenarios. We'll also discuss the difference between expressions and equations and how to tell them apart.

Before you translate math equations, it's important that you know how to translate math words and math expressions.

Lesson Notes

As a student, you'll often encounter math expressions and equations in your coursework. Understanding the distinction between the two is essential for solving mathematical problems effectively. Let's look at the key differences and learn how to translate math equations step by step.

Expressions vs. Equations

• Expressions: When written in words, math expressions resemble sentence fragments. They lack a verb and do not contain an equal sign. For instance, "5 cars" is a phrase, akin to a math expression like 5x.
• Equations: On the other hand, math equations resemble complete sentences. When expressed in words, equations contain verbs, typically "is," and always feature an equal sign. For example, "the car is driving 60 miles an hour" represents a complete sentence, analogous to a math equation like x = 60.

Translating Math Sentences: Step by Step

Next, we'll explore the process of translating math equations using examples. When practicing on your own, remember to carefully read the instructions. Sometimes, you'll need to go beyond translation and solve the equations. But for now, we'll just focus on translating each sentence into an equation.

1. A number increased by eight is twelve.

• Identify the unknown number as a variable (let's use x).
• "Increased by" implies addition, and "is" corresponds to an equal sign.
• Translate the statement into the equation: x + 8 = 12.

2. The difference between fifteen and a number is ten.

• Recognize "difference between" as subtraction.
• Assign a variable (let's use x).
• Translate to the equation: 15 − x = 10.

3. The quotient of a number and six is negative seven.

• Understand that "quotient of" signifies division.
• Select a variable (let's use x).
• Equation translation: x/6 ​= −7.

4. Thirty-four is twice a number.

• Note that "twice" implies multiplication by two.
• Choose a variable (let's use x).
• Equation transformation: 34 = 2x.

Summary and Practice

In summary, translating math sentences involves representing them as algebraic equations using variables, operations, and equal signs. By understanding the language of math, we can represent real-world problems and mathematical concepts in equation form. Now that you've learned about translating math sentences, you can apply it to solving word problems.

Try this practice activity to see what you learned:

Related Standard: Common Core 6.EE.A.2