Help Solving Equations for 4th Grade Students

Solving Simple Equations

Equations are math statements that tell you two things are equal. For instance, 5 + 3 = 8 is an equation that tells you the values on both sides of the equals sign are the same. If you wrote this equation and left out any of the three numbers, your friend could figure out the missing number, since both sides are equal. For example, if you gave your friend the equation '5 + ? = 8,' he would know that the missing number is three, since 5 + 3 = 8. This missing number is called a variable, and instead of a question mark, it's usually written with a letter, like x or n. Solve the practice problems below by finding the missing variables.

1. 4 + x = 10

2. n - 3 = 2

3. 12 ÷ k = 4

Solutions

1. Since 4 + 6 = 10, the missing variable is six.

2. You know that 5 - 3 = 2, so five is the missing variable.

3. To get four, you can divide 12 by three (12 ÷ 3 = 4), so the missing variable is three.

Tip: Remember that missing variables can be represented by lots of letters and symbols. These problems use the letters x, n and k, but any other letter or symbol could be used to show the missing variable. Sometimes, you'll be asked to use a specific letter to represent a variable.

Writing Equations

Now that you can solve simple equations, it's time to write your own equations. Sometimes, teachers will describe an equation and ask you to write it. For example, if you're asked to write the equation, 'A number plus two equals six,' you would write 'n + 2 = 6.' If your teacher asked you to write, 'Four times a number equals eight,' you would write '4 x k = 8.' For practice, write each statement below as an equation. Use any variable that you want to represent the missing numbers.

1. Nine minus a number equals five.

2. A number times six equals 12.

3. Eight divided by a number equals four.

Solutions

1. The solution is 9 - x = 5.

2. The correct answer is m x 6 = 12.

3. The equation is written like this: 8 ÷ n = 4.

Tip: Keep in mind that you can use any variable you want to write these equations. It doesn't need to be the same as the variable in the answer, but it does need to be in the same place as the variable in the answer.

Solving Word Problems with Equations

Now that you know how to write and solve simple equations, you can use these skills to solve word problems. Imagine that Jackie has ten pieces of gum in the morning, but she gives some to her friends. By the end of the day, she only has two pieces of gum left. To find out how many pieces of gum she gave away, you'd first write this equation: 10 - g = 2. This equation states that Jackie started the day with ten pieces of gum. Then, she gave away an unknown number of pieces, and was left with two. Since you know that 10 - 8 = 2, eight is the missing variable.

Let's try another example with multiplication. Imagine that Tony has sold ten cookies at a bake sale. If he has earned $20 so far from selling the cookies, how much is each cookie? We can represent this with the equation '10 x t = 20,' since ten cookies times the price they were sold for should equal $20. Since 10 x 2 = 20, then t = 2. So,Tony sold each cookie for $2.

Now, try solving these practice problems by writing the equation with the missing variable and then solving it.

1. Ellen and her friend Jesse are making sandwiches for a picnic. Ellen has made five, but there will be ten people at the picnic. How many sandwiches does Jesse have to make so that there will be enough for everyone?

2. Antonio's mom asked him to go to the store and buy three pounds of meat. If the meat cost Antonio exactly $12, how much money did each pound of meat cost, assuming each pound cost the same amount?

Solutions

1. The equation for this word problem is 5 + s = 10. Since 5 + 5 = 10, then s = 5. This means that Jesse has to make five sandwiches.

2. This word problem can be represented by the equation 3 x c = 12. Since 3 x 4 = 12, the missing variable is four. Antonio paid $4 for each pound of meat that he bought.