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Answer :
To determine which expression is equivalent to [tex]\( p q \)[/tex], let's analyze each option:
1. [tex]\( p+q \)[/tex]: This expression represents the sum of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to the multiplication of [tex]\( p \)[/tex] and [tex]\( q \)[/tex].
2. [tex]\( p-q \)[/tex]: This expression represents the difference between [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is also not equivalent to the multiplication of [tex]\( p \)[/tex] and [tex]\( q \)[/tex].
3. [tex]\( \frac{p}{q} \)[/tex]: This is the division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex], which is not the same as multiplying them.
4. [tex]\( qp \)[/tex]: Multiplying two values [tex]\( p \)[/tex] and [tex]\( q \)[/tex] can be written as [tex]\( pq \)[/tex] or [tex]\( qp \)[/tex]. Multiplication is commutative, meaning the order of the factors does not change the product. Therefore, [tex]\( pq \)[/tex] and [tex]\( qp \)[/tex] are equivalent.
Based on this analysis, the expression equivalent to [tex]\( pq \)[/tex] is [tex]\( qp \)[/tex].
1. [tex]\( p+q \)[/tex]: This expression represents the sum of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to the multiplication of [tex]\( p \)[/tex] and [tex]\( q \)[/tex].
2. [tex]\( p-q \)[/tex]: This expression represents the difference between [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is also not equivalent to the multiplication of [tex]\( p \)[/tex] and [tex]\( q \)[/tex].
3. [tex]\( \frac{p}{q} \)[/tex]: This is the division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex], which is not the same as multiplying them.
4. [tex]\( qp \)[/tex]: Multiplying two values [tex]\( p \)[/tex] and [tex]\( q \)[/tex] can be written as [tex]\( pq \)[/tex] or [tex]\( qp \)[/tex]. Multiplication is commutative, meaning the order of the factors does not change the product. Therefore, [tex]\( pq \)[/tex] and [tex]\( qp \)[/tex] are equivalent.
Based on this analysis, the expression equivalent to [tex]\( pq \)[/tex] is [tex]\( qp \)[/tex].
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