Is this sentence correct?

[wang.cupid]

Dear friends,

I saw these 2 sentences in an essay, but I am not quite sure if there are correct.

1. (The percentage of)Households with vacuum-cleaners increased by 8%.

Do I need The percentage of in the above sentence?

2. The percentage of households with a fridge rose (by)21% and (that) of those with a washing machine by 14%.

Do we need by and that in the above one?

Thanks.

[wang.cupid]

Could anyone help me! Please!

[2006]

Dear friends,

I saw these 2 sentences in an essay, but I am not quite sure if there are correct.

1. (The percentage of)Households with vacuum-cleaners increased by 8%.

Do I need The percentage of in the above sentence?

2. The percentage of households with a fridge rose (by)21% and (that) of those with a washing machine by 14%.

Do we need by and that in the above one?

Thanks.

Those sentences are not good, because a sentence like 'The percentage of...........increased by 8%.' is not clear.
If previously 50% of households had vacuum cleaners, what percent have them now, 54% or 58%? (50% + 8% of 50 or 50% + 8%)

You have two clear choices. (which are not exactly the same because the total number of households would have changed)

1. The number of households with vacuum cleaners increased by 8%.
2. The percentage of households with vacuum cleaners increased from X% to Y%. (a percentage difference of 8)

[Offroad]

The percentage of households with vacuum cleaners increased by 8%.

In my opinion, if it is 8% of 50% or 100%, it does not matter, it does not affect the grammar of the sentence.

[2006]

The percentage of households with vacuum cleaners increased by 8%.

In my opinion, if it is 8% of 50% or 100%, it does not matter, it does not affect the grammar of the sentence.

But meaning is much more important than grammar. The purpose of any communication is to impart information or sentiment of some kind. If the meaning of a sentence is unclear it is a bad sentence, and nothing else matters.