Question

1 8/9:3 4/7+5 3/8-2/8*5​

Answer 1

1 8/9 : 3 4/7 + 5 3/8 - 2/8 · 5 = 4 1177/1800

1) 1 8/9 : 3 4/7 = 17/9 : 25/7 = 17/9 · 7/25 = 119/225

2) 2/8 · 5 = 1/4 · 5 = 5/4 = 1 1/4

3) 119/225 + 5 3/8 = 952/1800 + 5 675/1800 = 5 1627/1800

4) 5 1627/1800 - 1 1/4 = 5 1627/1800 - 1 450/1800 = 4 1177/1800

Ответ: 4 целых 1177/1800.

Answer 2

To solve the expression 1 8/9 : 3 4/7 + 5 3/8 - 2/8 * 5, you can follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) to simplify it step by step.

1. Start by dealing with the addition and subtraction within each fraction:

• In the first fraction, 8/9, there's no addition or subtraction.
• In the second fraction, 4/7, there's no addition or subtraction.
• In the third fraction, 3/8, there's no addition or subtraction.

So, you can rewrite the expression as:

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

2. Now, let's deal with the multiplication and division from left to right:

• 2/8 * 5 = 10/8 = 5/4

So, the expression becomes:

1 8/9 : 3 4/7 + 5 3/8 - 5/4

3. Now, we can focus on the addition and subtraction of mixed numbers:

• For addition and subtraction, you need to have the same denominator. To find a common denominator for 9, 7, and 8, you can use the least common multiple (LCM), which is 504.

Now, let's rewrite the fractions with a common denominator of 504:

• 1 8/9 = (9/9) + 8/9 = 17/9
• 3 4/7 = (7/7) + 3 4/7 = 24/7
• 5 3/8 = (8/8) + 5 3/8 = 43/8

So, the expression becomes:

(17/9) : (24/7) + (43/8) - 5/4

4. Now, you can perform the division and addition:

• (17/9) ÷ (24/7) = (17/9) * (7/24) = (119/216)
• (119/216) + (43/8) - 5/4

5. Now, let's find a common denominator for the fractions:

The common denominator for 216, 8, and 4 is 216.

So, rewrite the fractions with a common denominator:

• (119/216) + (1458/216) - (270/216)

6. Now, you can add and subtract the fractions:

• (119/216) + (1458/216) - (270/216) = (119 + 1458 - 270) / 216 = 1307/216

7. Finally, simplify the fraction if possible:

• 1307/216 cannot be simplified further because there are no common factors other than 1.

So, the simplified result of the expression is:

1307/216