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Answer :
To determine which expression is equivalent to [tex]\( pq \)[/tex], let's analyze the choices:
1. [tex]\( p+q \)[/tex]: This expression represents the sum of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]. It is not equivalent to multiplying [tex]\( p \)[/tex] by [tex]\( q \)[/tex].
2. [tex]\( p-q \)[/tex]: This expression represents the difference between [tex]\( p \)[/tex] and [tex]\( q \)[/tex], which is also not equivalent to multiplying the two values.
3. [tex]\( \frac{p}{q} \)[/tex]: This indicates division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex]. Multiplying [tex]\( p \)[/tex] and [tex]\( q \)[/tex] is not the same operation as dividing [tex]\( p \)[/tex] by [tex]\( q \)[/tex].
4. [tex]\( qp \)[/tex]: This is the product of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. Due to the commutative property of multiplication, [tex]\( pq \)[/tex] is the same as [tex]\( qp \)[/tex]. Therefore, this expression is equivalent to [tex]\( pq \)[/tex].
Hence, the equivalent expression 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 multiplying [tex]\( p \)[/tex] by [tex]\( q \)[/tex].
2. [tex]\( p-q \)[/tex]: This expression represents the difference between [tex]\( p \)[/tex] and [tex]\( q \)[/tex], which is also not equivalent to multiplying the two values.
3. [tex]\( \frac{p}{q} \)[/tex]: This indicates division of [tex]\( p \)[/tex] by [tex]\( q \)[/tex]. Multiplying [tex]\( p \)[/tex] and [tex]\( q \)[/tex] is not the same operation as dividing [tex]\( p \)[/tex] by [tex]\( q \)[/tex].
4. [tex]\( qp \)[/tex]: This is the product of [tex]\( q \)[/tex] and [tex]\( p \)[/tex]. Due to the commutative property of multiplication, [tex]\( pq \)[/tex] is the same as [tex]\( qp \)[/tex]. Therefore, this expression is equivalent to [tex]\( pq \)[/tex].
Hence, the equivalent expression to [tex]\( pq \)[/tex] is [tex]\( qp \)[/tex].
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