Write 0.16 as a fraction in simplest form and a percent. \frac{16}{100} What property is shown? -9 + 9 = 0
The Correct Answer and Explanation is:
Correct Answer:
- Write 0.16 as a fraction in simplest form and as a percent
- Start by writing it as a fraction: 16100\frac{16}{100}
- Simplify by dividing numerator and denominator by 4 (their greatest common divisor): 16÷4100÷4=425\frac{16 ÷ 4}{100 ÷ 4} = \frac{4}{25}
- So, 0.16 as a fraction in simplest form is 425\frac{4}{25}
- To convert to a percent: 0.16×100=16%0.16 × 100 = 16\%
- Therefore, 0.16 = 425\frac{4}{25} and 16%
- What property is shown in -9 + 9 = 0?
- This demonstrates the additive inverse property.
Explanation :
The number sentence −9 + 9 = 0 illustrates an essential concept in arithmetic called the additive inverse property. This property states that for any number a, there exists a number −a such that a + (−a) = 0. In this equation, −9 and 9 are additive inverses of each other. When they are added, the result is zero.
This property is foundational in mathematics because it introduces the idea of balance and opposites on the number line. If you imagine a number line, moving nine units to the left from zero lands you at −9. Moving nine units back to the right brings you back to zero. In other words, their effects cancel each other out.
The additive inverse property also plays a crucial role in solving equations. When you want to isolate a variable on one side of an equation, you often subtract or add the inverse of a number. For example, to cancel a positive 5 on one side, you would add −5. Understanding this relationship simplifies algebraic manipulation.
It also connects to other areas of mathematics, such as vector math and group theory, where additive inverses are used to define symmetrical operations. Additionally, this property reinforces the identity element for addition, which is zero. Zero acts as the “neutral” number because adding it to any number leaves the original number unchanged.
In summary, the equation −9 + 9 = 0 exemplifies the additive inverse property by showing how a number and its opposite combine to yield zero. Recognizing and applying this property is vital for building fluency in both basic and advanced mathematical operations.
