What is [ggfrac]3/3[/ggfrac] equal to? What about [ggfrac]5/5[/ggfrac]? [ggfrac]12/12[/ggfrac]?

Any fraction that has the same numerator and denominator is equal to 1.

How do you multiply 3∙[ggfrac]4/7[/ggfrac]?

I can write any whole number as a fraction with a 1 in the denominator. When I multiply fractions, I multiply the numerators together and the denominators together. So I multiply 3 by 4 to get 12, and 1 by 7 to get 7. The answer is [ggfrac]1/2[/ggfrac]7, or 1[ggfrac]5/7[/ggfrac].

What is 3∙[ggfrac]4/3[/ggfrac]? 4∙[ggfrac]7/4[/ggfrac]? [ggfrac]8/9[/ggfrac]∙9? Explain how you found those numbers.

4, 7, and 8. In each case, I multiply by a number and divide by the same number. It’s like I do an operation, and then undo it. This is why my answer is the same as the number that the inverse operations are done to: it is like nothing happened to it!

Find the missing number: [ggfrac]5/?[/ggfrac]∙2=5

? = 2. Since 5 is multiplied by 2, I can do the inverse operation, division, to undo the multiplication.

Find the missing number: ? ∙[ggfrac]7/6[/ggfrac]=7

? = 6. Since 7 is divided by 6, I can multiply it by 6 to get back to 7.

What is a variable? What does it look like in an equation?

A variable represents an unknown quantity. In an equation, I can use an x to represent it, or any other letter of symbol I choose.

x – 8 = 7 What operation is done to x, and what operation should you use to solve for x?<br />

8 is subtracted from x, and since I want x to be alone on the left side, I should add 8 to it. I also have to add 8 on the right side to keep the equation balanced.

7x = 21 What operation is done to x, and what operation should you use to solve for x?<br />

x is multiplied by 7, so I should divide it by 7 to get 1x, which is the same as x. Then I also have to divide the other side by 7.

To solve [ggfrac]x/4[/ggfrac]=10, Joe’s first step was [ggfrac]4 ∙ x/4 ∙ 4[/ggfrac]=10∙4. What did Joe do wrong?

On the left side of the equation, Joe multiplied both the numerator and denominator by 4. That does not help him solve for x, since [ggfrac]4/4[/ggfrac] is equal to 1. To multiply x by 4, he should multiply only the numerator on both sides.

Morgan says that the solution to the equation 4x = 20 is x = 6. Can you check if she is right?

If I substitute 6 for x in the equation, I get 4∙6 on the left side, which is equal to 24. I have 20 on the right side. 24 is not equal to 20, therefore 6 is not the value of x.

Solve Algebraic Equations (1-Step)

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What you will learn from this videoWhat you will learn

That an algebraic equation is an equation with an unknown number.
How to solve algebraic equations using inverse operations.
That this knowledge can help us count our savings, sell cupcakes, and even take care of pets!

Discussion Questions
- Before Video
  What is [ggfrac]3/3[/ggfrac] equal to? What about [ggfrac]5/5[/ggfrac]? [ggfrac]12/12[/ggfrac]?ANSWER
  - Any fraction that has the same numerator and denominator is equal to 1.
  How do you multiply 3∙[ggfrac]4/7[/ggfrac]?ANSWER
  - I can write any whole number as a fraction with a 1 in the denominator. When I multiply fractions, I multiply the numerators together and the denominators together. So I multiply 3 by 4 to get 12, and 1 by 7 to get 7. The answer is [ggfrac]1/2[/ggfrac]7, or 1[ggfrac]5/7[/ggfrac].
  What is 3∙[ggfrac]4/3[/ggfrac]? 4∙[ggfrac]7/4[/ggfrac]? [ggfrac]8/9[/ggfrac]∙9? Explain how you found those numbers.ANSWER
  - 4, 7, and 8. In each case, I multiply by a number and divide by the same number. It’s like I do an operation, and then undo it. This is why my answer is the same as the number that the inverse operations are done to: it is like nothing happened to it!
  Find the missing number: [ggfrac]5/?[/ggfrac]∙2=5ANSWER
  - ? = 2. Since 5 is multiplied by 2, I can do the inverse operation, division, to undo the multiplication.
  Find the missing number: ? ∙[ggfrac]7/6[/ggfrac]=7ANSWER
  - ? = 6. Since 7 is divided by 6, I can multiply it by 6 to get back to 7.
- After Video
  What is a variable? What does it look like in an equation?ANSWER
  - A variable represents an unknown quantity. In an equation, I can use an x to represent it, or any other letter of symbol I choose.
  x – 8 = 7 What operation is done to x, and what operation should you use to solve for x?
  ANSWER
  - 8 is subtracted from x, and since I want x to be alone on the left side, I should add 8 to it. I also have to add 8 on the right side to keep the equation balanced.
  7x = 21 What operation is done to x, and what operation should you use to solve for x?
  ANSWER
  - x is multiplied by 7, so I should divide it by 7 to get 1x, which is the same as x. Then I also have to divide the other side by 7.
  To solve [ggfrac]x/4[/ggfrac]=10, Joe’s first step was [ggfrac]4 ∙ x/4 ∙ 4[/ggfrac]=10∙4. What did Joe do wrong?ANSWER
  - On the left side of the equation, Joe multiplied both the numerator and denominator by 4. That does not help him solve for x, since [ggfrac]4/4[/ggfrac] is equal to 1. To multiply x by 4, he should multiply only the numerator on both sides.
  Morgan says that the solution to the equation 4x = 20 is x = 6. Can you check if she is right?ANSWER
  - If I substitute 6 for x in the equation, I get 4∙6 on the left side, which is equal to 24. I have 20 on the right side. 24 is not equal to 20, therefore 6 is not the value of x.
Vocabulary
- Equation DEFINE
- Algebraic equation DEFINE
- Variable DEFINE
- Inverse Operations DEFINE
- Addition DEFINE
- Subtraction DEFINE
- Multiplication DEFINE
- Division DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket