Solve the Division Equation: Finding the Number That Equals 19 When Divided By 1

Q: Why does any number divided by 1 equal itself?

Think of division as sharing equally. When you divide something into 1 group, you keep the whole amount! For example, if you have 19 cookies and put them in 1 box, you still have all 19 cookies.

Q: Is this the same as multiplying by 1?

Similar result, different operation! Both $ 19 \times 1 = 19 $ and $ 19 \div 1 = 19 $ give 19, but they represent different mathematical processes.

Q: How is this different from dividing by other numbers?

Division by 1 is special because 1 is the identity element. When you divide by any other number like 2 or 5, you get a smaller result, but dividing by 1 keeps the number unchanged.

Q: Can I use this property with fractions and decimals too?

Absolutely! $ \frac{3}{4} \div 1 = \frac{3}{4} $ and $ 2.5 \div 1 = 2.5 $. The identity property works with all real numbers!

Division Properties with Identity Element

$?:1=19$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Any number divided by 1 is always equal to itself

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?:1=19$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize the type of operation: division by 1.
Step 2: Apply the property of division which states that dividing any number by 1 results in the number itself.
Step 3: Identify the unknown value that satisfies the equation using this property.

Now, let's work through each step:
Step 1: The problem is represented as $?:1 = 19$ . We need to determine the missing number that satisfies this equation.
Step 2: Recall the fundamental property of division: for any number $x$ , $x \div 1 = x$ . Thus, the number divided by 1 is equal to the number itself.
Step 3: To satisfy the equation $?:1 = 19$ , the unknown value must be the number 19 itself because dividing 19 by 1 gives 19.

Therefore, the solution to the problem is 19.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Property: Any number divided by 1 equals the number itself
Technique: For $x \div 1 = 19$ , the answer is x = 19
Check: Substitute back: 19 ÷ 1 = 19 ✓

Common Mistakes

Avoid these frequent errors

Confusing division by 1 with multiplication by 1
Don't think you need to find 19 × 1 = 19! This makes students overthink a simple concept. The division by 1 property is direct: any number ÷ 1 equals that same number. Always recognize that ? ÷ 1 = 19 means ? must be 19.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does any number divided by 1 equal itself?

Think of division as sharing equally. When you divide something into 1 group, you keep the whole amount! For example, if you have 19 cookies and put them in 1 box, you still have all 19 cookies.

Is this the same as multiplying by 1?

Similar result, different operation! Both $19 \times 1 = 19$ and $19 \div 1 = 19$ give 19, but they represent different mathematical processes.

What if I see ? ÷ 1 = any other number?

The pattern stays the same! Whatever number appears after the equals sign is your answer. If $? \div 1 = 7$ , then ? = 7.

How is this different from dividing by other numbers?

Division by 1 is special because 1 is the identity element. When you divide by any other number like 2 or 5, you get a smaller result, but dividing by 1 keeps the number unchanged.

Can I use this property with fractions and decimals too?

Absolutely! $\frac{3}{4} \div 1 = \frac{3}{4}$ and $2.5 \div 1 = 2.5$ . The identity property works with all real numbers!

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