o dia/a mão/a foto

To become proficient in Portuguese, you need to recognize these common exceptions early on:

• o dia (the day): Despite ending in -a, it is masculine. This comes from the Latin word dies.
• o problema, o programa, o sistema, o tema, o idioma, o clima, o poema, o fantasma, o cinema, o telefonema: Many masculine words ending in -a are of Greek origin and often end in -ma.
• a tribo (the tribe) and a libido (the libido): These are feminine despite ending in -o.
• Words ending in -ão: This is a 'split' ending that can be either masculine (o pão, o coração) or feminine (a mão, a ação). In fact, thousands of words ending in -ção and -são are feminine.
• Words ending in -r: While usually masculine, a cor (the color), a dor (the pain), a flor (the flower), a mulher (the woman), and a colher (the spoon) are extremely common feminine exceptions.
• Words ending in -e and -z: The gender of these words is often unpredictable and must be memorized. For example, o leite (the milk) and o nariz (the nose) are masculine, while a chave (the key), a árvore (the tree), and a luz (the light) are feminine.
• a foto and a moto: These keep the gender of their original full words (a fotografia and a motocicleta).
• o mapa (the map), o planeta (the planet), o pijama (the pajamas), and o sofá (the sofa): These are also masculine despite the -a ending.
• Feminine endings without -a: Many feminine words don't end in -a. Common feminine suffixes include -ção / -são (a informação), -dade (a cidade), and -gem (a viagem, a mensagem - though note exceptions like o pajem and o personagem, which can also be a personagem).
• Compound words: Words formed by a verb and a feminine noun are usually masculine, such as o guarda-chuva (the umbrella).
• Words that change meaning with gender: O rádio is the physical device, while a rádio is the radio station (short for a estação de rádio or a radiodifusão). O capital is money/funds, while a capital is the capital city. O cabeça is the leader/brains of the operation, while a cabeça is the body part.
• Two-way words (comum de dois gêneros): Words ending in -ista and -ente often have the same form for both genders, as do some words ending in -a. You must look at the article to know the gender, such as o/a estudante (the student), o/a artista (the artist), or o/a colega (the colleague).

When using these words, all articles and adjectives must match the 'exception' gender, not the ending of the word. For example:

• O problema é muito sério. (The problem is very serious.)
• A minha mão esquerda. (My left hand.)
• O dia está lindo. (The day is beautiful.)
• Ela comprou uma moto nova. (She bought a new motorcycle.)