8 2/3-6 3/5- 2 2/5+1 7/9

Question 1

Задача Задача №46039

А

Аноним

15 ноября 2023 08:24 · публичный вопрос

А

Аноним 15 ноября 2023 08:24

8 2/3-6 3/5- 2 2/5+1 7/9

Answer

To solve the expression \(8 \frac{2}{3} - 6 \frac{3}{5} - 2 \frac{2}{5} + 1 \frac{7}{9}\), it's best to start by converting each mixed number into an improper fraction.

\(8 \frac{2}{3}\) can be converted by multiplying the whole number 8 by the denominator 3 and adding the numerator 2: \(8 \times 3 + 2 = 24 + 2 = 26\) So this becomes: \( \frac{26}{3} \)

\(6 \frac{3}{5}\) can be converted similarly: \(6 \times 5 + 3 = 30 + 3 = 33\) So this becomes: \( \frac{33}{5} \)

\(2 \frac{2}{5}\) is converted as: \(2 \times 5 + 2 = 10 + 2 = 12\) So this becomes: \( \frac{12}{5} \)

\(1 \frac{7}{9}\) becomes: \(1 \times 9 + 7 = 9 + 7 = 16\) So this becomes: \( \frac{16}{9} \)

Now we have:

\(\frac{26}{3} - \frac{33}{5} - \frac{12}{5} + \frac{16}{9}\)

These fractions need a common denominator to be combined. The least common multiple (LCM) of the denominators \(3, 5\), and \(9\) is \(45\), so we need to convert each fraction to have this common denominator.

\(\frac{26}{3} \times \frac{15}{15} = \frac{390}{45}\)

\(\frac{33}{5} \times \frac{9}{9} = \frac{297}{45}\)

\(\frac{12}{5} \times \frac{9}{9} = \frac{108}{45}\)

\(\frac{16}{9} \times \frac{5}{5} = \frac{80}{45}\)

Now all fractions have the same denominator, and we can perform the operations:

\(\frac{390}{45} - \frac{297}{45} - \frac{108}{45} + \frac{80}{45} = \frac{390 - 297 - 108 + 80}{45}\)

Adding and subtracting the numerators:

\(\frac{390 - 297 - 108 + 80}{45} = \frac{390 - 297}{45} + \frac{80 - 108}{45}\) \(\frac{93}{45} + \frac{-28}{45} = \frac{93 - 28}{45}\) \(\frac{65}{45}\)

The fraction can also be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

\(\frac{65}{45} \div \frac{5}{5} = \frac{13}{9}\)

Since \( \frac{13}{9} \) is an improper fraction, we can convert it back to a mixed number by dividing the numerator by the denominator:

\(13 \div 9 = 1\) with a remainder of \(4\)

So it becomes \(1 \frac{4}{9}\)

Therefore,

\(8 \frac{2}{3} - 6 \frac{3}{5} - 2 \frac{2}{5} + 1 \frac{7}{9} = 1 \frac{4}{9}\)

Question 2

8 2/3-6 3/5- 2 2/5+1 7/9

Answer

To solve the expression \(8 \frac{2}{3} - 6 \frac{3}{5} - 2 \frac{2}{5} + 1 \frac{7}{9}\), it's best to start by converting each mixed number into an improper fraction. \(8 \frac{2}{3}\) can be converted by multiplying the whole number 8 by the denominator 3 and adding the numerator 2: \(8 \times 3 + 2 = 24 + 2 = 26\) So this becomes: \( \frac{26}{3} \) \(6 \frac{3}{5}\) can be converted similarly: \(6 \times 5 + 3 = 30 + 3 = 33\) So this becomes: \( \frac{33}{5} \) \(2 \frac{2}{5}\) is converted as: \(2 \times 5 + 2 = 10 + 2 = 12\) So this becomes: \( \frac{12}{5} \) \(1 \frac{7}{9}\) becomes: \(1 \times 9 + 7 = 9 + 7 = 16\) So this becomes: \( \frac{16}{9} \) Now we have: \(\frac{26}{3} - \frac{33}{5} - \frac{12}{5} + \frac{16}{9}\) These fractions need a common denominator to be combined. The least common multiple (LCM) of the denominators \(3, 5\), and \(9\) is \(45\), so we need to convert each fraction to have this common denominator. \(\frac{26}{3} \times \frac{15}{15} = \frac{390}{45}\) \(\frac{33}{5} \times \frac{9}{9} = \frac{297}{45}\) \(\frac{12}{5} \times \frac{9}{9} = \frac{108}{45}\) \(\frac{16}{9} \times \frac{5}{5} = \frac{80}{45}\) Now all fractions have the same denominator, and we can perform the operations: \(\frac{390}{45} - \frac{297}{45} - \frac{108}{45} + \frac{80}{45} = \frac{390 - 297 - 108 + 80}{45}\) Adding and subtracting the numerators: \(\frac{390 - 297 - 108 + 80}{45} = \frac{390 - 297}{45} + \frac{80 - 108}{45}\) \(\frac{93}{45} + \frac{-28}{45} = \frac{93 - 28}{45}\) \(\frac{65}{45}\) The fraction can also be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5: \(\frac{65}{45} \div \frac{5}{5} = \frac{13}{9}\) Since \( \frac{13}{9} \) is an improper fraction, we can convert it back to a mixed number by dividing the numerator by the denominator: \(13 \div 9 = 1\) with a remainder of \(4\) So it becomes \(1 \frac{4}{9}\) Therefore, \(8 \frac{2}{3} - 6 \frac{3}{5} - 2 \frac{2}{5} + 1 \frac{7}{9} = 1 \frac{4}{9}\)