Solving Inequalities with Addition & Subtraction of Fractions

Instructor: Kathleen Laib

I have been a teacher for 10 years with eight of those years teaching 4th grade. I have a master's of Ed and an ELL Endorsement.

In this lesson we will break down inequalities into their basic steps to help make them easier to understand. We'll talk about what each symbol means and how basic math skills work together to make inequalities easy to work through.

Oh No, Inequalities!

The idea of inequalities sometimes makes students nervous. But these equations become less scary when you break them into individual math skills. In fact, you may have even learned some of these skills in kindergarten - do you remember using an alligator to understand the < and > signs? The alligator is always trying to eat the bigger number. Combine this idea with the basic math skills you already know and you will be well on your way to solving inequalities.

The Equal Sign

A lot of students think that the = symbol means now it's time to tell the answer. However, the equal sign isn't always asking that. The equal sign is like the middle point in a balance scale. What it means is that both sides are worth the same amount.

Both sides are equal, so the dishes are even.

If one side of the equal sign says 3 + 4, then the other side should say something that equals the same total as 3 + 4. Most of the time we would write 7 because that is the simplest answer, but we could also put 6 + 1 or 10 - 3 and the answer would still be correct because they are also equal to 7.

What If There's an Inequality Sign?

Inequalities are a little different. With an inequality, one side of the number sentence is going to equal a greater amount than the other side. Looking at our scale image, one side will be lower and one side will be higher because they are not equal.

The dish that is lower is heavier, or worth more.
Now the first dish is higher, which means it is ligher or worth less.

Solving Inequalities

Let's try to solve one. We'll use adding and subtracting fractions for these examples. When you are presented with a number sentence, you are usually supposed to determine one correct answer. 2/10 + 5/10 = ? gives you one correct answer to find, by adding 2/10 and 5/10. The answer is 7/10, and because it is the simplest answer, you would write it after the equal sign. Pretty simple, right?

But what if it comes in the form of an inequality? For example:

Inequality with Fractions

In order to solve this inequality, you are still going to add 2/10 and 5/10, which is still 7/10. But this time there is not an equal sign after the problem, so the other side of symbol (which is a greater-than symbol) shouldn't say 7/10.

Whatever number you put in where the question mark is needs to be smaller than 7/10 so that the number sentence stays true - which means there are several correct answers - you may not be used to solving math problems that have more than one answer! You could put 6/10, 4/10, or even 0/10. All of these would be true because they result in a number that is smaller than what you get when you add 2/10 + 5/10.

A little more challenging inequality might give you two math problems to solve, like this one:

A bit more challenging.

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