Questions & Answers about Дети режут бумагу ножницами.
Why does ножницы become ножницами here, and why is there no word for "with"?
Ножницами is in the Instrumental case, which is used to show the tool or instrument used to complete an action. In Russian, you do not use a preposition for "with" when it means "using a tool". Since ножницы (scissors) is a plural noun, it takes the plural Instrumental ending -ами.
Can I use a singular form of ножницы if I am only talking about one pair of scissors?
No, just like in English, the Russian word ножницы only exists in the plural form. Whether you mean one pair or five, you always treat it as plural, which is why it uses the plural Instrumental ending here.
Why is the verb conjugated as режут instead of резают?
The verb резать (to cut) has a slight spelling change in its present tense. The consonant з changes to ж, and the vowel а is dropped. So, for the "they" form, it becomes режут, not резают.
Why does the word for paper end in -у (бумагу)?
Because paper is the direct object of the verb (it is the thing being cut), it must be in the Accusative case. The dictionary form is the feminine noun бумага, and its -а ending changes to -у in the Accusative case.