The fractions (2/3), (4/6), (6/9), ... are all equivalent to the fraction (2/3). Explain how the concept of equivalent fractions is analogous to the concept of equivalent vectors.
I completely lost, I don't know the answer or how to answer the question.
Frankly, I do not think it is all that analogous.
The point in vectors is that all vectors with the same length and direction are equivalent. It does not matter where they start , only their magnitude and direction.
So in x,y coordinates we might have a vector of length sqrt(2) and direction 45 degrees counterclockwise from the x axis (like north east)
You could say this was the vector from the origin (0,0) to the point (1,1)
HOWEVER
it is also the vector from (1,0) to (2,1)
and it is also the vector from (5,5) to (6,6)
In other words if they have the same length and compass heading, they are equivalent.
I have trouble comparing this to having common factors in the numerator and denominator, but that is all I can say.
No worries! I'm here to help you understand the concept of equivalent fractions and how it relates to the concept of equivalent vectors.
Equivalent fractions are fractions that represent the same part of a whole. In other words, they have the same value even though they may have different numerators and denominators. For example, the fractions 2/3, 4/6, and 6/9 are all equivalent because they all represent the same portion of a whole. To prove this, we can simplify these fractions to their simplest form: 2/3, 2/3, and 2/3.
Similarly, vectors in mathematics represent both magnitude (length) and direction. Two vectors are considered equivalent or equal if they have the same magnitude and direction, even if they are represented differently. This concept of equivalent vectors is analogous to equivalent fractions because just as equivalent fractions represent the same value, equivalent vectors represent the same magnitude and direction.
To determine if two vectors are equivalent, we can compare their components, which are similar to the numerators and denominators of fractions. For example, let's consider the vectors A (2, 3) and B (4, 6). These vectors have different components but are still equivalent because we can scale vector B to vector A by dividing its components by 2: (4/2, 6/2) = (2, 3).
In summary, the concept of equivalent fractions is similar to the concept of equivalent vectors. Both involve comparing different mathematical entities to determine if they represent the same value, whether it's in terms of portions of a whole (fractions) or magnitude and direction (vectors).