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Definite Article - The

1. Use "the" for specific or particular nouns (both the speaker and the listener know which specific noun is being referenced.)

2. Use "the" for singular and plural count nouns.

• Ex: The English book is on the table./The English books are on the table

3. "The" can be used with non-count nouns or you can omit the article.

• Ex: Juan loves to sail over the water. (Juan loves to sail over water.)
• Ex: The fresh fruit is in the kitchen. (Fresh fruit is in the kitchen.)

4. Use "the" b4 name of rivers, oceans: the Nile, the Atlantic Ocean
                                       points on the globe: the South Pole                           
                                       geographical areas: the Middle East
                                      deserts: the Sahara Desert
                                      forests: the Black Forest
                                      gulfs: the Gulf of Mexico
                                      peninsulas: the Iberian peninsula
 5. Don't use "the" b4 most countries and cities, except collections of places

• Ex: France, Asia, Lake Erie, Mount Fuji

    but
          the United States, the Philippines, the Netherlands, the Great Lakes, the Andes
6. Don't use "the" b4 the names of languages and nationalities: Russian, Chinese
                                                       sports: basketball
                                                       academic subjects: science, English

Indefinite Article - A, an

1. Use "a" or "an" for non-specific or non-particular nouns (Neither the speaker nor the listener knows which specific noun is being referenced.)
2. Use "a" b4 a  or an adjective plus a singular count nouns

• Ex: We want to buy a desk (any desk)
• Ex: We want to buy a new desk (any new desk)

3. Don't use "a" or "an" b4 plural count noun and non-count nouns. 
"Some" is often used like an indefinite article b4 plural count nouns and non-count nouns.

• Ex: Ken wants some potatoes.
• Ex: Would you like some water?
• Ex: Michiko needs to get some milk at the market

4. Use "a" b4 nouns or adjectives plus nouns beginning with a consonant sound.
Use "an" b4 nouns or adjectives plus nouns beginning with a vowel sound.

• Ex: a glass, a new computer
• Ex: an egg, an old computer

(Adopted from VOA)