Open sentences

Open sentences 

Open sentences is about looking for an unknown number. The unknown can be represent by a letter or shape.  

The letter or symbol is just a "seat" waiting for a number to sit in it. When we find the correct number that makes the mathematical sentence correct, we have "solved" the open sentence.

The Power of the Equals Sign (=)

The most important part of an open sentence is the equals sign. You must view the equals sign as a balance scale. Everything on the left side of the "=" must have the exact same total value as everything on the right side.

How to Solve Open Sentences (Step-by-Step)

To find the missing value, we often use Inverse Operations. "Inverse" simply means "opposite."

• The opposite of Addition (+) is Subtraction (-).

• The opposite of Multiplication (×) is Division (÷).

   

Example 1: Solving Addition Sentence: 25+x=40

1. Identify the goal: We want to find what x is. Collect like term
2. Use the inverse: + change to -

3. Calculate: x = 40- 25

                        x = 15

4. Check: Does 25+15=40 Yes! So, x=15

    

Example 2: Solving Multiplication Sentence: □×5=30

1. Identify the goal: Find the missing factor. Make the shape the subject of the equation
2. Use the inverse: ÷ change to x

3. Calculate: □ = 30 ÷ 5

                       □ = 6

4. Check: Does 6×5=30  Yes! So, the box is 6.

    

• Example 3

   142 - c = 47

  Step 1

   When an equation as - (minus) unknown, move the unknown to the right side of the equation to eliminate the - (minus)

   142 - 47 = c

   95 = c 

  Check : 142 - 95 = 47

   

Step 2

142- c = 47

Make c the subject of the equation 

-c = 47 - 142

-c = -95

Minus cancel minus on both sides

c = 95

• Example 4

  3a - 4 = 11

  Make the unknown the subject of the equation 

  3a = 11+4

  3a = 15 

  Divide both sides by 3

  3a/3 = 15/3

  a = 5

• Example 5

  19-6x =1

  19- 1 = 6x

  18=6x

  Divide both sides by 6

  18/6 = 6x/6

  3=x

• Example 6

  If Fola increases six times a number by 5 and the answer is 47. Find the number .

  Solution 

  Let the number be x

  6x +5 = 47

  6x = 47- 5

  6x = 42

  Divide both sides by 6

  6x/6 = 42/6

  x = 7

  Check : (6x7) +5= 47

               42+5= 47

 Activities

MacMillan Champion Mathematics Bk 5