Kurikulum Merdeka Matematika Kelas 7 Bab 4 Bentuk Aljabar

Summary

This educational video script covers algebraic concepts for 7th graders, focusing on algebraic terms like coefficients, variables, and constants. It explains how to simplify expressions by combining like terms and demonstrates addition, subtraction, multiplication, and division of algebraic expressions. The script also clarifies the rules for multiplying and dividing terms with variables, including handling of exponents and expressions within parentheses. The aim is to make algebra more accessible and engaging for students.

Takeaways

• 🔢 Algebra involves understanding terms like coefficients, variables, and constants.
• 📐 A term in algebra is a mathematical expression separated by addition, subtraction, multiplication, or division.
• 🔄 Coefficients are the numbers preceding variables, while constants are standalone numbers.
• 🧩 Like terms in algebra can be combined by adding or subtracting their coefficients.
• ➕ To add algebraic expressions, combine like terms by adding their coefficients.
• ➖ When subtracting, only like terms with the same variables can be simplified.
• 🔄 Multiplication in algebra involves multiplying coefficients and variables separately.
• 📚 When multiplying a variable by a number, the result is a new term with the variable's exponent increased.
• 📉 Division in algebra requires dividing both the coefficients and the variables.
• 📘 Exponents in division are reduced by subtracting the exponents of like bases.
• 👉 Parentheses indicate that the expression inside must be multiplied by the expression outside.

Q & A

What are the basic components of an algebraic expression?

The basic components of an algebraic expression are terms, coefficients, variables, and constants. Terms are separated by addition, subtraction, multiplication, and division. Coefficients are the numbers preceding variables, variables are represented by letters, and constants are numbers not followed by letters.

How do you combine like terms in algebra?

Like terms are terms that have the same variables raised to the same power. To combine them, you add or subtract their coefficients while keeping the variable part unchanged.

What happens when you try to add terms with different variables?

Terms with different variables cannot be combined through addition or subtraction because they are not like terms.

Can you give an example of how to add algebraic expressions?

Yes, for example, to add 2A + 3A, you add the coefficients (2 + 3) to get 5A.

How do you subtract algebraic expressions with the same variable?

Subtraction of algebraic expressions with the same variable involves subtracting their coefficients. For instance, 5A - 3A results in 2A.

What is the rule for multiplying algebraic expressions?

When multiplying algebraic expressions, you multiply the coefficients and the variables separately. If a variable is multiplied by another variable of the same kind, you add their exponents.

What does it mean when there is no number written before a variable in an algebraic expression?

If there is no number written before a variable, it means the coefficient is 1. For example, in the expression 7A - A, the second term is equivalent to 1A, which simplifies to 6A.

How do you handle parentheses in algebraic expressions?

Parentheses indicate that the expression inside them should be treated as a single entity. When multiplying, every term inside the parentheses is multiplied by the term outside.

Can you explain the process of dividing algebraic expressions?

Division of algebraic expressions involves dividing the coefficients and the variables separately. If you divide a variable by itself, the result is 1, and any exponents are subtracted from one another.

What is the significance of exponents in algebraic division?

When dividing expressions with the same base, you subtract the exponents. For example, if you divide a^5 by a^3, the result is a^2.

How do you simplify an expression like 3(a + b)?

To simplify 3(a + b), you distribute the 3 to both a and b, resulting in 3a + 3b.

Outlines

00:00

📘 Algebra Basics in Mathematics

This paragraph introduces the fundamental concepts of algebra, specifically for 7th-grade students. It explains the components of algebraic expressions, including coefficients, variables, and constants. Coefficients are numbers preceding variables, variables are represented by letters, and constants are numbers without letters. The paragraph also discusses how algebraic terms are formed and separated by addition, subtraction, multiplication, and division. Examples are given to illustrate the concepts, such as '2x' consisting of one term with a coefficient of 2 and a variable x, and '2x + 4' consisting of two terms, '2x' and '4'. The paragraph further explains how to simplify algebraic expressions by combining like terms, emphasizing that only terms with the same variables can be combined.

05:03

🔢 Algebraic Operations: Addition and Subtraction

This section delves into the rules of addition and subtraction in algebra. It clarifies that these operations can only be performed on like terms, meaning terms with the same variables. The paragraph provides examples to demonstrate how to add and subtract coefficients while keeping the variable part unchanged. For instance, '2A + 3A' results in '5A', and '3B + 4B' results in '7B'. The concept of simplifying expressions by arranging like terms and then combining coefficients is also explained. The paragraph concludes with a discussion on how to handle subtraction when terms have different variables, emphasizing that such terms cannot be simplified.

10:03

📐 Multiplication and Division in Algebra

The final paragraph covers the rules for multiplication and division in algebra. It explains that when multiplying, coefficients and variables must be multiplied separately, and the same applies to division. The paragraph uses examples to illustrate these rules, such as multiplying '2A' by '4' resulting in '8A', and '3A' by '2B' resulting in '6AB'. It also addresses the multiplication of terms without coefficients, which are implicitly considered to have a coefficient of 1. The paragraph further explains how to handle expressions within parentheses, emphasizing the need to distribute the multiplication across all terms inside the parentheses. Lastly, it touches on the division of algebraic expressions, showing how to simplify by canceling out common factors, including variables and their powers.

Keywords

💡Algebra

Algebra is a branch of mathematics concerning the study of symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to studying abstractions such as groups, rings, and fields. In the video, algebra is the central theme, with a focus on teaching basic algebraic concepts to a seventh-grade audience.

💡Coefficient

A coefficient is a numerical factor multiplying a variable in an algebraic expression. It indicates the number of times the variable is used in the term. For example, in the term '3x', the coefficient is 3, indicating that the variable 'x' is used three times. The video explains coefficients as the numbers that precede variables in algebraic expressions.

💡Variable

In algebra, a variable is a symbol, usually a letter, that stands for an unknown number, or a value that can change. Variables are used to represent unknowns or general values in equations. The video mentions variables as letters in algebraic expressions, contrasting them with constants.

💡Constant

A constant is a value that does not change during a particular operation or calculation. In algebra, constants are numbers that stand alone without being associated with a variable. The script uses the term to illustrate the difference between numbers that are part of an algebraic expression and those that are not.

💡Term

In algebra, a term is a part of an expression that consists of a number and its associated variables raised to their respective powers. For example, '2x' and '4' are terms in the expression '2x + 4'. The video script explains terms as parts of algebraic expressions separated by signs of addition, subtraction, multiplication, and division.

💡Addition

Addition in algebra refers to the process of combining like terms. Like terms are terms that have the same variables raised to the same powers. The video provides examples of adding algebraic expressions, such as '2A + 3A' which results in '5A' after combining like terms.

💡Subtraction

Subtraction in algebra is similar to addition but involves taking away like terms. The video script gives examples of subtracting algebraic expressions, like '5A - 3A' which equals '2A' after subtracting the coefficients of like terms.

💡Multiplication

Multiplication in algebra involves the distributive property, where a number is multiplied by each term inside a parenthesis or by each part of an expression. The video explains how to multiply terms, including the multiplication of coefficients and variables, such as '2A * 4' resulting in '8A'.

💡Division

Division in algebra often involves simplifying expressions by dividing coefficients and reducing the powers of like bases. The script explains how to divide algebraic expressions, such as '6a / 2A' which simplifies to '3' after dividing the coefficients and canceling out the variable 'a'.

💡Exponentiation

Exponentiation is the operation of raising a number to a power. In algebra, it is often used to denote repeated multiplication of the same number. The video script explains exponent rules, such as 'a^2 / a' which simplifies to 'a', because the exponents are reduced by 1 when dividing like bases.

💡Like Terms

Like terms in algebra are terms that contain the same variables raised to the same powers. They can be combined through addition or subtraction. The video emphasizes the importance of recognizing like terms to perform algebraic operations correctly, such as adding '3A + 4A' to get '7A'.

Highlights

Introduction to algebraic terms: coefficients, variables, and constants.

Explanation of terms in algebra: expressions separated by addition, subtraction, division, and multiplication.

Coefficients are numbers preceding variables in algebraic expressions.

Variables are represented by letters in algebraic expressions.

Constants are numbers in algebraic expressions that are not followed by letters.

Example of identifying terms: 2x consists of one term, and 2x + 4 consists of two terms.

Example of identifying terms: 2A + 2B + 5 consists of three terms.

Algebraic addition can only be performed on like variables.

Example of adding like variables: 2A + 3A results in 5A.

Example of adding unlike variables: 3B + 4B results in 7B.

Combining like terms by adding their coefficients.

Example of combining like terms: 3a² + 5B + 3B + 4a² results in 7a² + 8B.

Algebraic subtraction is similar to addition, only like variables can be subtracted.

Example of subtracting like variables: 5A - 3A results in 2A.

Example of subtracting unlike variables: 7c² - 5c² results in 2c².

Handling variables without coefficients, which are implicitly considered as having a coefficient of 1.

Example of multiplying variables: 2A * 4 results in 8A.

Multiplication in algebra involves multiplying coefficients and combining variables.

Example of multiplying variables with implicit coefficients: 3A * a results in 3a².

Handling multiplication with parentheses, where each term inside the parentheses is multiplied by the term outside.

Example of complex multiplication with parentheses: 3(a + b) results in 3A + 3B.

Division in algebra requires dividing both the coefficients and the variables.

Example of dividing algebraic expressions: 6a / 2A results in 3.

Understanding the rules of exponents in division, where the exponents are subtracted when the bases are the same.

Example of dividing expressions with exponents: 7a⁵ / a³ results in a².

Final thoughts and encouragement to like, comment, and subscribe.

Transcripts

[Musik]

Hai semuanya kembali lagi di channel

portal edukasi Pada kesempatan kali ini

kita akan membahas materi matematika

kelas 7 bab 4 yaitu tentang bentuk

aljabar materi ini sudah kurikulum

Merdeka ya

mari kita mulai dengan unsur-unsur

aljabar

pada aljabar kita akan mengenal beberapa

unsur yaitu ada suku koefisien variabel

dan konstanta

suku pada aljabar adalah bentuk-bentuk

yang dipisahkan oleh tanda penjumlahan

pengurangan pembagian dan perkalian

contohnya 2x itu terdiri dari satu suku

dua x tambah 4 terdiri dari dua suku

yaitu 2x dan 4

2A + 2B + 5 itu terdiri dari 3 suku

yaitu 2A 2B dan 5

koefisien adalah angka yang ada sebelum

sebuah variabel variabel adalah huruf

pada suatu aljabar sedangkan konstanta

adalah angka yang tidak diikuti huruf

biar lebih jelas lihat gambar ini ya 2x

itu adalah sebagai suku 4 juga sebagai

suku kalau kita nyebutin dua aja itu

adalah koefisien x nya itu adalah

variabel dan empatnya itu adalah

konstanta

selanjutnya kita masuk ke penjumlahan

aljabar

penjumlahan dalam aljabar hanya bisa

diselesaikan apabila memiliki variabel

yang sama ingat hanya variabel yang sama

yang dijumlahkan itu koefisiennya aja

apabila berbeda

variabelnya itu tidak dapat

disederhanakan

contohnya nih

misalkan ada dua a ditambah 3A cara

menambahkannya adalah tambahkan dulu

angkanya 2 ditambah 3 yaitu 5 nah ini

nggak perlu ditambahkan kita tulis lagi

jadinya a 2a + 3a jadinya 5A contoh lain

3B ditambah 4b jawabannya berapa jelas

7B dari mana 3 ditambah 4 ya 7 contoh

lainnya lagi misalkan ada 3 a² + 5B + 3B

+ 4 a² = lihat di sini di sini ada a²

dan ada B variabelnya cara yang paling

mudah adalah mengurutkan dulu dengan

variabel yang sejenis di sini ada a

kuadrat kita Urutkan juga dengan

kuadratnya jadinya

3a² + 4a² + 5B + 3B setelah kayak gini

baru kita Sederhanakan

a² dengan a² kita bisa tambahkan 3 + 4

jadinya 7 a² di sini kita nggak bisa

nambahin dengan yang di sini nggak bisa

tambah 5 tambah 3 Kenapa lihat

variabelnya berbeda ini a kuadrat ini B

jadinya gimana ya tulis aja lagi tambah

5 tambah 3 8 B beres cukup kayak gitu

aja bentuknya 7 a kuadrat ditambah 8 B

selanjutnya pengurangan aljabar sama

seperti penjumlahan pengurangan pada

aljabar Hanya apabila variabelnya sama

contohnya

5A dikurang 3A = ya tinggal 5 - 3 berapa

2 ya udah 2A contoh lain

7c² -

5c² = ya tinggal 7 kurangi 5 yaitu 2 2 C

kuadrat

kemudian misalkan dari contoh soal lagi

4b - 3B = Nah lihat di sini 4 - 3 itu

adalah 1 kalau 1 itu nggak perlu ditulis

jadi kita bisa langsung tulis

variabelnya aja yaitu B nah jadi ketika

kalian menemukan soal ketika di sini

cuman ada variabel doang tanpa angka di

sini angkanya itu artinya adalah 1

contoh takutnya kalian terjebak misalkan

7A - a = ini bukan hanya yang hilang ya

hati-hati variabel itu akan selalu tetap

ada Jadi gimana

7A - a Ingat nggak ada angka di sini

artinya angkanya adalah 1 jadinya 7

dikurangi 1 yaitu 6 hanya tetap A

seperti itu berbeda kasus kalau misalkan

a - a di sini ini kan berarti artinya 1

dan juga 1 1 - 1 0 0 A nggak perlu

ditulis a-nya jadinya ya 0 seperti itu

gampang ya

selanjutnya perkalian Aljabar

pada perkalian Aljabar kita harus

mengkalikan koefisien dan variabel pada

aljabar itu nah pemahaman dasarnya kayak

gini nih apabila a dikali B itu hasilnya

tinggal digabung jadinya AB kalau 2

dikali a hasilnya jadi 2A tinggal

digabung juga

jadi bila sebuah angka dikalikan dengan

variabel tinggal digabungkan aja nih

angka dahulu yang ditulis ya baru

diikuti variabel

contohnya nih

misalkan

2A

dikali 4 = ya tinggal dikalikan aja dulu

nih angka dengan angka 2 * 4 ya 8 di

sini A nggak ada kali lagi kan nggak ada

variabel lagi jika kita tunggu lagi ya A

contoh lain

3A dikali 2B = kalikan dulu angkanya 3 *

2 6 a * b ab jadi jawabannya adalah 6

gimana Kok contohnya misalkan 3A dikali

a = lihat di sini

ketika nggak ada angka artinya adalah 1

3 * 1 3 a dikali a bukan jadi 2A ya A *

A itu menjadi a² contoh lainnya

3A dikali 4A dikali 5A =

kalikan dulu semuanya 3 * 4 12 12 * 5 60

a * a * a-nya jadi pangkat 3 pangkat di

sini adalah Jumlah si a-nya ada berapa

di sini a-nya ada 3 jadinya a ^ 3 gimana

gampang kan

nah sebelum Terlupakan dalam perkalian

apa namanya

aljabar ada juga kadang-kadang soal

seperti ini nih kalau ini kan

perkaliannya langsung berurutan kayak

gini tapi kalau ada dalam kurung kayak

gini 3 dalam kurung a ditambah B

misalkan nih kayak gini 3 dalam kurung a

+ b itu kalau dalam kurung itu itu

artinya adalah dikali jadinya semua yang

di luar sini harus dikalikan dengan

dalam di sini 3 dikali a yaitu 3A 3

dikali positif b jadinya 3B jadi

jawabannya 3 dalam kurung a + b itu

adalah 3A + 3B

nah kadang-kadang soal itu ada yang

lebih rumit lagi nih misalkan

ada dalam kurung a + 3 dalam kurung a

dikurang 4 nah kalau kayak gini dalam

kurung itu artinya dikali ingat setiap

dalam kurung itu pasti dikali caranya

gimana kita harus mengkalikan semua

anggota yang dalam kurung ini dengan

semua anggota yang dalam kurung di sini

caranya adalah kita lihat dulu yang A

yang pertama a dikalikan dulu dengan

yang di sini dikalikan dengan a * a

jadinya adalah a kuadrat kemudian a-nya

dikalikan dengan negatif 4 ingat

tandanya di bawah jadinya a * -4 jadinya

negatif 4A kemudian a beres nih sekarang

tinggal 3 positif 3 dikali a jadinya

adalah positif 3A kemudian positif 3

dikali juga ini dengan negatif 4 positif

kali negatif hasilnya adalah negatif 3

dikali 4 hasilnya adalah 12 Nah kita

tinggal Sederhanakan jadinya a² - 4A +

3A jawabannya adalah negatif a dikurang

12 udah bentuk kayak gini nggak bisa

disederhanakan lagi udah beres jadi a +

3 * A - 4 itu hasilnya adalah a kuadrat

dikurangi a dikurangi 12

selanjutnya pembagian aljabar

sama seperti pada perkalian pembagian

juga kita harus membagi koefisien dan

variabel pada aljabar tersebut contohnya

misalkan ada

6a dibagi 2A =

6 dibagi 2 itu adalah

3A dibagi A itu a-nya habis artinya

adalah A dibagi A itu adalah 1 kan 1

dibagi 1 ya 1 hanya kita bisa coret

jadinya 6a dibagi 2A itu hasilnya adalah

3 contoh lain misalkan ada tujuh a

pangkat 2 dibagi

7A = 7 dibagi 7 1 di depan nggak perlu

ditulis a kuadrat dibagi a hasilnya

adalah a

dari mana Di sini kita sekalian belajar

ya aturan perpangkatan ketika a kuadrat

dibagi a a di sini walaupun gak ada

pangkatnya itu artinya pangkatnya adalah

1 dalam perpangkatan kalau angka yang

besar angka yang utamanya adalah sama

kalau di sini kasusnya variabel

variabelnya sama maka pangkatnya tinggal

dikurang kalau dalam pembagian jadinya a

pangkat 2 dikurangi 1 yaitu adalah A ^ 1

atau bisa ditulis a aja karena pangkat 1

nggak perlu ditulis kayak gitu

contoh lain misalkan

[Musik]

6ab²/3a = nah dia di sini kita bisa

langsung bagi nih 6 dibagi 3 ingat

seperti itu adalah bagi 6 / 3 hasilnya

adalah 2 di sini ada a kita bisa coret

hanya artinya dihilangkan jadinya

tinggal b kuadrat Ya udah jadi

jawabannya adalah

2b² enggak pusing kan contoh lain

misalkan

di sini ada gimana ya contohnya misalkan

Oke 12 a pangkat 5 B pangkat 4 c pangkat

3 per

misalkan di sini adalah

6a ^ 3 b pangkat 2 C = 12

/ 6 yaitu adalah 2 a pangkat 5 dibagi a

pangkat 3 ingat seperti aturan di sini

kalau bagi artinya pangkatnya tinggal

dikurang 5 dikurangi 3 jadinya adalah a

pangkat 2 B pangkat 4 dibagi B pangkat 2

pasti hasilnya adalah B pangkat 2 c

pangkat 3 dibagi C berarti tinggal c

pangkat 2 jadi bentuk sederhananya

adalah 2² b² C kuadrat gimana gampang ya

Nah ya mungkin Cukup sekian terima kasih

telah menyimak video pembelajaran hingga

selesai semoga bermanfaat kita semua

jangan lupa like Comment and subscribe