Solve Integer Multiplication: (-7) × 1 Step by Step

Q: Why does (-7) × 1 equal -7 and not +7?

The multiplicative identity property states that any number multiplied by 1 equals itself exactly. Since we started with negative 7, we keep the negative sign!

Q: Is multiplying by 1 the same as doing nothing?

Mathematically, yes! Multiplying by 1 is like the "do nothing" operation. The number stays completely unchanged, including its sign and value.

Q: Does this work with fractions and decimals too?

Absolutely! Whether it's $ \frac{3}{4} \times 1 = \frac{3}{4} $ or 2.5 × 1 = 2.5, the identity property applies to all real numbers.

Q: How is this different from multiplying by zero?

Very different! Multiplying by zero makes everything zero, but multiplying by 1 preserves the original number. Think: 1 = identity, 0 = destroyer!

Integer Multiplication with Identity Property

Complete the following exercise:
$(-7)\cdot(1)=$

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Step-by-step video solution

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00:00 Solve

00:08 Negative times positive is always negative

00:13 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

Complete the following exercise:
$(-7)\cdot(1)=$

Step-by-step solution

Let's recall the law:

$(+x)\times(-x)=-x$

Therefore, the sign of the exercise result will be negative:

$-7\times+1=-7$

Final Answer

$-7$

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Any number multiplied by 1 equals itself
Technique: Maintain the sign: (-7) × 1 = -7
Check: The multiplicative identity preserves both value and sign ✓

Common Mistakes

Avoid these frequent errors

Changing the sign when multiplying by 1
Don't think (-7) × 1 = +7 because you see multiplication! The identity property means the number stays exactly the same, including its negative sign. Always remember that multiplying by 1 preserves the original number completely.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why does (-7) × 1 equal -7 and not +7?

The multiplicative identity property states that any number multiplied by 1 equals itself exactly. Since we started with negative 7, we keep the negative sign!

Is multiplying by 1 the same as doing nothing?

Mathematically, yes! Multiplying by 1 is like the "do nothing" operation. The number stays completely unchanged, including its sign and value.

What if I had (+7) × 1 instead?

Then the answer would be +7 (or just 7). The identity property works the same way: positive numbers stay positive, negative numbers stay negative.

Does this work with fractions and decimals too?

Absolutely! Whether it's $\frac{3}{4} \times 1 = \frac{3}{4}$ or 2.5 × 1 = 2.5, the identity property applies to all real numbers.

How is this different from multiplying by zero?

Very different! Multiplying by zero makes everything zero, but multiplying by 1 preserves the original number. Think: 1 = identity, 0 = destroyer!

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