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When there is no article in front of the noun that we want to describe with an adjective, the adjective has to be declined according to the gender, number, and case of the noun as well, but in some cases (markmarked bold) the declension differs from the weak declension. This form is usually used with plural words and words that rarely or never appear in the plural (Singulariatantum), such as Wein (vine):

More information and word tables can be found here.

When there is no article in front of the noun that we want to describe with an adjective, the adjective has to be declined according to the gender, number, and case of the noun as well, but in some cases (mark bold) the declension differs from the weak declension. This form is usually used with plural words and words that rarely or never appear in the plural (Singulariatantum), such as Wein (vine):

More information and word tables can be found here

When there is no article in front of the noun that we want to describe with an adjective, the adjective has to be declined according to the gender, number, and case of the noun as well, but in some cases (marked bold) the declension differs from the weak declension. This form is usually used with plural words and words that rarely or never appear in the plural (Singulariatantum), such as Wein (vine):

More information and word tables can be found here.

5 Fixing some errors, throwing in some linguistic terms, restructuring.
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TL;DR: Adjectives have to be declined not only according to the noun'snoun’s gender, the casenumber, and the type of articlecase but also according to the type of article used. If a verb links the adjective to the subject, the adjective is not declined at all.

Definite and indefinite articles

Using the German language, we differentiate between definite articles (Ger.: bestimmtebestimmte Artikel) and indefinite articles (Ger.: unbestimmteunbestimmte Artikel)

Definite articles Definite articles include:

this, these, that, those

Ger.:

[dieser (English),
dieser, diese, dieses]dieses, [jenerjener, jene, jenes] etc..jenes (German)

Indefinite articles Indefinite articles (for our purposes) include: 

a, many, few

Ger.:

[ein (English)
ein, eine]eine, vielekeiner, wenigekeine (German)

Case 1 (weak declension):

When we use a definite article with a noun that we want to describe with an adjective, e.g.the adjective has to be declined according to the gender, number, and case of the noun:

Der rote Apfel liegt auf dem Tisch. (nominative, masculine, singular)

Ich sehe den roten Apfel. (accusative, masculine, singular)

Ich sehe die rote Tomate. (accusative, feminine, singular)

Ich sehe die roten Tomaten. (accusative, plural)

Ich sehe das rote Haus. (accusative, neutral)

the adjective has to be declined according to the noun being described(There is no distinction between genders in plural.)

Case 2 (mixedstrong declension):

When we use anthere is indefiniteno article with ain front of the noun that we want to describe with an adjective, e.g.:

Ein roter Apfel

the adjective also has to be declinedadjective has to be declined according to the gender, number, and case of the noun being described. Howeveras well, but in some cases (mark bold) the declension varies such that we might have to use a different form of our adjective ifdiffers from the gender of our noun changesweak declension.

Case 3:

When we use a This form of "ist" to link our noun to an adjective, e.g.:

Der Apfel ist rot

we exclusively useis usually used with plural words and words that rarely or never appear in the adjective's base.plural No declension is needed.

Case 4 (strong declension):

When there is(Singulariatantum), such as noWein (vine) article in front of the noun, the adjective also changes:

RoterRoter Käse liegt auf dem Tisch. (nominative, masculine, singular)

Ich sehe roten Wein gefällt mir nicht. (accusative, masculine, singular)

Examples:

Case 1 (weak):

definite article

 

DerIch sehe rote ApfelMilch. (accusative, feminine, singular)

Die rote TomateIch sehe rote Tomaten. (accusative, plural)

Das rote HausIch sehe rotes Gemüse. (accusative, neutral)

Our noun changes gender while the adjective stays the same. Our adjective can change only when our noun changes quantity or case (Kasus)The strong declension is called such because endings differ most often between genders, cases, and numbers.

Case 23 (mixed declension):

When we use an indefinite article

Ein roter Apfel

Eine rote Tomate

Ein rotes Haus

Our with a noun changes gender and so does ourthat we want to describe with an adjective. Changes, the adjective has to be declined in our noun's quantityyet another way. However, the declension always corresponds to either the weak or casethe strong declension (Kasushence “mixed”) can also effect our Adjective

Case 3:

using a form of "ist" to describe a noun:

DerEin roter Apfel ist rotliegt auf dem Tisch. (nominative, masculine, singular)

DieIch sehe einen roten Apfel. (accusative, masculine, singular)

Ich sehe eine rote Tomate ist rot. (accusative, feminine, singular)

Die Häuser sind rotIch sehe keine roten Tomaten. (accusative, plural)

Die Haare der Frau sind rotIch sehe ein rotes Haus. (accusative, neutral)

Our noun changes gender, quantity and case while our adjective stays the same. As in English, even the type of article we use can change without affecting our adjective.

Case 4 (strongpredicative):

When we use a not using any articleverb to introduce the nounlink the noun to the adjective, we exclusively use the adjective’s base. No declension is needed:

Guten Käse kann man hier nicht findenDer Apfel ist rot.

Ich habe gute Äpfel gegessenDer Apfel schmeckt gut.

Er malte das Haus rot an.

This form is usually used with plural words and words that don't usually appear in the plural (such as Käse/cheese).

 

TL;DR: Adjectives have to be declined according to the noun's gender, the case, and the type of article used

Using the German language we differentiate between definite articles (Ger.: bestimmte Artikel) and indefinite articles (Ger.: unbestimmte Artikel)

Definite articles include:

this, these, that, those

Ger.:

[dieser, diese, dieses], [jener, jene, jenes] etc..

Indefinite articles (for our purposes) include:

a, many, few

Ger.:

[ein, eine], viele, wenige

Case 1 (weak declension):

When we use a definite article with a noun that we want to describe with an adjective, e.g.:

Der rote Apfel

the adjective has to be declined according to the noun being described.

Case 2 (mixed declension):

When we use an indefinite article with a noun that we want to describe with an adjective, e.g.:

Ein roter Apfel

the adjective also has to be declined according to the noun being described. However the declension varies such that we might have to use a different form of our adjective if the gender of our noun changes.

Case 3:

When we use a form of "ist" to link our noun to an adjective, e.g.:

Der Apfel ist rot

we exclusively use the adjective's base. No declension is needed.

Case 4 (strong declension):

When there is no article in front of the noun, the adjective also changes:

Roter Wein gefällt mir nicht.

Examples:

Case 1 (weak):

definite article

Der rote Apfel

Die rote Tomate

Das rote Haus

Our noun changes gender while the adjective stays the same. Our adjective can change only when our noun changes quantity or case (Kasus).

Case 2 (mixed):

indefinite article

Ein roter Apfel

Eine rote Tomate

Ein rotes Haus

Our noun changes gender and so does our adjective. Changes in our noun's quantity or case (Kasus) can also effect our Adjective

Case 3:

using a form of "ist" to describe a noun

Der Apfel ist rot

Die Tomate ist rot

Die Häuser sind rot

Die Haare der Frau sind rot

Our noun changes gender, quantity and case while our adjective stays the same. As in English, even the type of article we use can change without affecting our adjective.

Case 4 (strong):

not using any article to introduce the noun

Guten Käse kann man hier nicht finden

Ich habe gute Äpfel gegessen

This form is usually used with plural words and words that don't usually appear in the plural (such as Käse/cheese).

TL;DR: Adjectives have to be declined not only according to the noun’s gender, number, and case but also according to the type of article used. If a verb links the adjective to the subject, the adjective is not declined at all.

Definite and indefinite articles

Using the German language, we differentiate between definite articles (bestimmte Artikel) and indefinite articles (unbestimmte Artikel)

Definite articles include:

this, these, that, those (English),
dieser, diese, dieses, jener, jene, jenes (German)

Indefinite articles (for our purposes) include: 

a, many, few (English)
ein, eine, keiner, keine (German)

Case 1 (weak declension)

When we use a definite article with a noun that we want to describe with an adjective, the adjective has to be declined according to the gender, number, and case of the noun:

Der rote Apfel liegt auf dem Tisch. (nominative, masculine, singular)

Ich sehe den roten Apfel. (accusative, masculine, singular)

Ich sehe die rote Tomate. (accusative, feminine, singular)

Ich sehe die roten Tomaten. (accusative, plural)

Ich sehe das rote Haus. (accusative, neutral)

(There is no distinction between genders in plural.)

Case 2 (strong declension)

When there is no article in front of the noun that we want to describe with an adjective, the adjective has to be declined according to the gender, number, and case of the noun as well, but in some cases (mark bold) the declension differs from the weak declension. This form is usually used with plural words and words that rarely or never appear in the plural (Singulariatantum), such as Wein (vine):

Roter Käse liegt auf dem Tisch. (nominative, masculine, singular)

Ich sehe roten Wein. (accusative, masculine, singular)

 

Ich sehe rote Milch. (accusative, feminine, singular)

Ich sehe rote Tomaten. (accusative, plural)

Ich sehe rotes Gemüse. (accusative, neutral)

The strong declension is called such because endings differ most often between genders, cases, and numbers.

Case 3 (mixed declension)

When we use an indefinite article with a noun that we want to describe with an adjective, the adjective has to be declined in yet another way. However, the declension always corresponds to either the weak or the strong declension (hence “mixed”):

Ein roter Apfel liegt auf dem Tisch. (nominative, masculine, singular)

Ich sehe einen roten Apfel. (accusative, masculine, singular)

Ich sehe eine rote Tomate. (accusative, feminine, singular)

Ich sehe keine roten Tomaten. (accusative, plural)

Ich sehe ein rotes Haus. (accusative, neutral)

Case 4 (predicative)

When we use a verb to link the noun to the adjective, we exclusively use the adjective’s base. No declension is needed:

Der Apfel ist rot.

Der Apfel schmeckt gut.

Er malte das Haus rot an.

 
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TL;DR: Adjectives have to be declined according to the noun's gender, the case, and the type of article used

Using the German language we differentiate between definite articles (gerGer.: bestimmte Artikel) and indefinite articles (gerGer.: unbestimmte Artikel)

Definite articles include:

this, these, that, those

gerGer.:

[dieser, diese, dieses], [jener, jene, jenes] etc..

Indefinite articles (for our purposes) include:

a, many, few

gerGer.:

[ein, eine], viele, wenige

I will presume the distinctions between these two groups and their respective usages are understood.

Case 1 (weak declension):

When we use a definite article with a noun that we want to describe with an adjective, ege.g.:

Der rote Apfel

the adjective has to be declined according to the noun being described.

Case 2 (mixed declension):

When we use an indefinite article with a noun that we want to describe with an adjective, ege.g.:

Ein roter Apfel

the adjective also has to be declined according to the noun being described. However the declension varies such that we might to have to use a different form of our adjective if the gender of our noun changes.

Case 3:

When we use a form of "ist" to link our noun to an adjective, ege.g.:

Der Apfel ist rot

we exclusively use the adjectivesadjective's base. No declension is needed.

Case 4 (strong declension):

When there is no article in front of the noun, itthe adjective also changes:

Roter Wein gefällt mir nicht.

Examples:

Case 1 (weak):

definite article

Der rote Apfel

Die rote Tomate

Das rote Haus

Our noun changes gender while the adjective stays the same. Our adjective can change only when our noun changes quantity or case (Kasus).

Case 2 (mixed):

indefinite article

Ein roter Apfel

Eine rote Tomate

Ein rotes Haus

Our noun changes gender and so does our adjective. Changes in in our nounsnoun's quantity or case (Kasus) can also effect our Adjective

Case 3:

using a form of "ist" to describe a noun

Der Apfel ist rot

Die Tomate ist rot

Die Häuser sind rot

Die Haare der Frau sind rot

Our noun changes gender, quantity and case while our adjective stays the same. As is the case in English, even the type of article we use can change without affecting our adjective.

Case 4 (strong):

not using any article to introduce the noun

Guten Käse kann man hier nicht finden

Ich habe gute Äpfel gegessen

This form is usually used with plural words and words that don't usually appear in the plural (such as Käse/cheese).

More information and word tables can be found here

TL;DR: Adjectives have to be declined according to the noun's gender, the case, and the type of article used

Using the German language we differentiate between definite articles (ger.: bestimmte Artikel) and indefinite articles (ger.: unbestimmte Artikel)

Definite articles include:

this, these, that, those

ger.:

[dieser, diese, dieses], [jener, jene, jenes] etc..

Indefinite articles (for our purposes) include:

a, many, few

ger.:

[ein, eine], viele, wenige

I will presume the distinctions between these two groups and their respective usages are understood.

Case 1 (weak declension):

When we use a definite article with a noun that we want to describe with an adjective, eg.:

Der rote Apfel

the adjective has to be declined according to the noun being described.

Case 2 (mixed declension):

When we use an indefinite article with a noun that we want to describe with an adjective, eg.:

Ein roter Apfel

the adjective also has to be declined according to the noun being described. However the declension varies such that we might to have to use a different form of our adjective if the gender of our noun changes.

Case 3:

When we use a form of "ist" to link our noun to an adjective, eg.:

Der Apfel ist rot

we exclusively use the adjectives base. No declension is needed.

Case 4 (strong declension):

When there is no article in front of the noun, it also changes:

Roter Wein gefällt mir nicht.

Examples:

Case 1 (weak):

definite article

Der rote Apfel

Die rote Tomate

Das rote Haus

Our noun changes gender while the adjective stays the same. Our adjective can change only when our noun changes quantity or case (Kasus).

Case 2 (mixed):

indefinite article

Ein roter Apfel

Eine rote Tomate

Ein rotes Haus

Our noun changes gender and so does our adjective. Changes in in our nouns quantity or case (Kasus) can also effect our Adjective

Case 3:

using a form of "ist" to describe a noun

Der Apfel ist rot

Die Tomate ist rot

Die Häuser sind rot

Die Haare der Frau sind rot

Our noun changes gender, quantity and case while our adjective stays the same. As is the case in English, even the type of article we use can change without affecting our adjective.

Case 4 (strong):

not using any article to introduce the noun

Guten Käse kann man hier nicht finden

Ich habe gute Äpfel gegessen

This form is usually used with plural words and words that don't usually appear in the plural (such as Käse/cheese).

More information and word tables can be found here

TL;DR: Adjectives have to be declined according to the noun's gender, the case, and the type of article used

Using the German language we differentiate between definite articles (Ger.: bestimmte Artikel) and indefinite articles (Ger.: unbestimmte Artikel)

Definite articles include:

this, these, that, those

Ger.:

[dieser, diese, dieses], [jener, jene, jenes] etc..

Indefinite articles (for our purposes) include:

a, many, few

Ger.:

[ein, eine], viele, wenige

I will presume the distinctions between these two groups and their respective usages are understood.

Case 1 (weak declension):

When we use a definite article with a noun that we want to describe with an adjective, e.g.:

Der rote Apfel

the adjective has to be declined according to the noun being described.

Case 2 (mixed declension):

When we use an indefinite article with a noun that we want to describe with an adjective, e.g.:

Ein roter Apfel

the adjective also has to be declined according to the noun being described. However the declension varies such that we might have to use a different form of our adjective if the gender of our noun changes.

Case 3:

When we use a form of "ist" to link our noun to an adjective, e.g.:

Der Apfel ist rot

we exclusively use the adjective's base. No declension is needed.

Case 4 (strong declension):

When there is no article in front of the noun, the adjective also changes:

Roter Wein gefällt mir nicht.

Examples:

Case 1 (weak):

definite article

Der rote Apfel

Die rote Tomate

Das rote Haus

Our noun changes gender while the adjective stays the same. Our adjective can change only when our noun changes quantity or case (Kasus).

Case 2 (mixed):

indefinite article

Ein roter Apfel

Eine rote Tomate

Ein rotes Haus

Our noun changes gender and so does our adjective. Changes in our noun's quantity or case (Kasus) can also effect our Adjective

Case 3:

using a form of "ist" to describe a noun

Der Apfel ist rot

Die Tomate ist rot

Die Häuser sind rot

Die Haare der Frau sind rot

Our noun changes gender, quantity and case while our adjective stays the same. As in English, even the type of article we use can change without affecting our adjective.

Case 4 (strong):

not using any article to introduce the noun

Guten Käse kann man hier nicht finden

Ich habe gute Äpfel gegessen

This form is usually used with plural words and words that don't usually appear in the plural (such as Käse/cheese).

More information and word tables can be found here

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