Mixed Integers: Multiplication and Division

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Bagaimana cara mengalikan dua angka bulat pada integer campuran?

Kalikan kedua angka bulat terlebih dahulu.

Apa yang harus dilakukan setelah mengalikan bagian pecahan dari dua integer campuran?

Bagi hasil perkalian kedua pecahan tersebut.

Apa langkah terakhir dalam mengalikan dua integer campuran?

Mengelompokkan dan menyederhanakan hasil.

Apa yang dilakukan dalam pembagian integer campuran terkait dengan pembagi?

Dikalikan

Apakah langkah awal dalam menghitung hasil bagi dari dua integer campuran?

Mencari nilai kebalikan dari pembagi.

Apa yang terjadi ketika mengalikan decimal portion dari dua integer campuran?

Dikalikan

Apa yang tidak dapat dilakukan jika salah satu bagian dari dividen (pembagi) adalah nol?

Membagi dengan dividen

Apa langkah pertama yang harus dilakukan ketika melakukan pembagian seperti dijelaskan dalam teks?

Membagi pembilang dengan bilangan bulat dividen

Apa yang harus dilakukan setelah membagi pembilang dengan bagian bilangan bulat dari dividen?

Mengalikan hasil dengan pembilang dividen

Mengapa urutan operasi antara bagian bilangan bulat dan non-bulat penting saat melakukan perkalian dan pembagian?

Agar hasilnya benar dan akurat

Kenapa penting untuk memperlakukan bagian bilangan bulat dan non-bulat secara terpisah saat melakukan operasi matematika?

Agar tingkat kesalahan berkurang

"Perhatikan bahwa kunci utamanya adalah memperlakukan bagian bilangan bulat dan non-bulat secara terpisah hingga menggabungkannya kembali di akhir" - Apa yang ingin disampaikan oleh kalimat ini?

Penting untuk memisahkan bilangan bulat dan non-bulat selama proses matematika

Study Notes

Working With Mixed Integers: Multiplication and Division

In this exploration of operations involving mixed integers, we'll delve into the specifics of how they behave during multiplication and division. A mixed integer is written as a combination of an integer and a fractional part, such as (5\frac{1}{3}) or (-2\frac{1}{6}.) Let's begin by understanding these operations in terms of their individual actions before tackling combined processes.

Multiplying Mixed Integers

To multiply two mixed integers, you perform standard arithmetic on both the whole numbers and decimal parts separately. First, find the product of each pair of whole numbers, denoted by the whole number portion of the first mixed integer times the whole number portion of the second one. Next, calculate the product of each decimal portion, using the numerator from the first mixed integer divided by its denominator, and repeat for the second mixed integer. Finally, regroup and simplify. Here's a step-by-step example:

[ (8\frac{3}{5}) \times (-4\frac{1}{3}) = (\underbrace{8}{whole\ number} + \frac{3}{5})\times(\underbrace{-4}{whole\ number}+\frac{1}{3}) \ = -32 + \left(\frac{3}{5}\cdot -\frac{1}{3}\right) +\left(\frac{9}{5}+ \frac{1}{3}\right)\ =-32-\frac{1}{5}-\frac{1}{15} + \frac{27}{15}\ =-32+\frac{26}{15}=-\frac{78}{15}=-\frac{27}{5} ]

Dividing Mixed Integers

Dividing mixed integers involves reciprocating the divisor, just like when working with decimals. However, since the dividend has both integer and fractional components, we must consider which aspect to divide by which component of the divisor. If either the whole or fractional parts of the dividend are zero, you cannot divide by the divisor because it would produce zero. Otherwise, follow these steps:

  1. Divide the numerator of the dividend by the whole number portion of the divisor.
  2. Multiply the resulting quotient by the denominator of the dividend. This gives you the new fractional portion of the resultant mixed integer.

Here's an illustration:

[ \frac{10\frac{3}{5}}{(-2\frac{1}{4})} =\frac{\underbrace{10}{numerator} + \frac{3}{5}}{\underbrace{-2}{divisor\ whole\ number}+\frac{1}{4}}\ =\frac{10}{-2}- \left(\frac{3}{5}\cdot \frac{1}{4}\right)=-5+ \frac{3}{20}=\frac{-17+3}{20}=\frac{-14}{20} = \frac{-7}{10} ]

Both multiplication and division require careful attention and correct sequencing between the integer and non-integer portions. Using proper order of operations will ensure accurate results. Remember that the key lies in treating associated whole and fractional parts separately until bringing them back together at the end.

Explore the operations involving mixed integers, focusing on how they behave in multiplication and division processes. Learn how to multiply and divide mixed integers step-by-step, considering both the whole number and fractional components separately. Proper sequencing and attention to details are crucial for accurate results.

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