Question

2 1/16 : 1 1/8-5 7/9•2 1/3+4 4/5

Answer 1

Ответ:

65389/17280

Пошаговое объяснение:

2 1/16*11/8-5 7/9*2*1/3+4 4/5=33/16*11/8-52/9*2*1/3+24/5=363/128-104/27+24/5=65389/17280 примерно 3,78409

Answer 2

To solve the expression, we follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction. The expression you provided is:

2 1/16 : 1 1/8 - 5 7/9 • 2 1/3 + 4 4/5

Let's break it down step by step:

1. Perform the division first: 2 1/16 : 1 1/8 To divide fractions, we take the reciprocal of the divisor and then multiply: 2 1/16 ÷ 1 1/8 = (33/16) ÷ (9/8) Now, multiply by the reciprocal: (33/16) * (8/9) = (33 * 8) / (16 * 9) = 264 / 144

2. Perform the multiplication: 5 7/9 • 2 1/3 To multiply mixed numbers, first convert them into improper fractions: 5 7/9 = (5 * 9 + 7) / 9 = 52 / 9 2 1/3 = (2 * 3 + 1) / 3 = 7 / 3 Now, multiply the fractions: (52/9) * (7/3) = (52 * 7) / (9 * 3) = 364 / 27

3. Add the results from step 1 and step 2: 264/144 + 364/27

Now, we need to find a common denominator for the fractions. The least common multiple (LCM) of 144 and 27 is 432. We'll rewrite the fractions with the common denominator:

(264/144) + (364/27) = (264 * 3) / (144 * 3) + (364 * 16) / (27 * 16) = 792 / 432 + 5824 / 432

4. Add the fractions with the same denominator: 792/432 + 5824/432 = (792 + 5824) / 432 = 6616 / 432

5. Now, add the whole numbers: 6616 / 432 + 4 4/5

To add a fraction to a whole number, convert the whole number to an improper fraction: 4 4/5 = (4 * 5 + 4) / 5 = 24 / 5

Now, add the fractions: (6616/432) + (24/5)

Again, find a common denominator, which is 432 * 5 = 2160:

(6616/432) + (24/5) = (6616 * 5) / (432 * 5) + (24 * 432) / (5 * 432) = 33080 / 2160 + 10368 / 2160

6. Add the fractions with the same denominator: 33080/2160 + 10368/2160 = (33080 + 10368) / 2160 = 43448 / 2160

Now, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator, which is 8:

43448 / 2160 = (43448 / 8) / (2160 / 8) = 5431 / 270

So, the final result is 5431/270.