Question

2 2/3 : 1 7/9 + 55/84:( 43/63 - 23/36)

Answer 1

Ответ:

Пошаговое объяснение:

2 2/3:1 7/9

8/3*9/16=3/2= 1 1/2

43/63-23/36=172/252-161/252=11/252

55/84:11/252=55/84*252/11=15

15+1 1/2=16 1/2

Answer 2

To solve this expression, let's follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Step 1: Simplify the expressions inside the parentheses: 43/63 - 23/36

To add or subtract fractions, they need a common denominator. The common denominator for 63 and 36 is 252. So, let's convert both fractions:

(43/63) * (4/4) = 172/252 (23/36) * (7/7) = 161/252

Now, subtract the fractions: (172/252) - (161/252) = (172 - 161)/252 = 11/252

Step 2: Perform the division: 55/84 ÷ (11/252)

To divide fractions, we multiply by the reciprocal of the divisor:

(55/84) * (252/11) = (55 * 252) / (84 * 11) (55 * 252) = 13860 (84 * 11) = 924

So, (55/84) ÷ (11/252) = 13860/924 = 15

Step 3: Add the fractions: 2 2/3 + 1 7/9

To add mixed numbers, we first convert them to improper fractions: 2 2/3 = (3 * 2 + 2) / 3 = 8/3 1 7/9 = (9 * 1 + 7) / 9 = 16/9

Now, find the common denominator, which is 9:

(8/3) * (3/3) = 24/9 (16/9) * (1/1) = 16/9

Now, add the fractions: (24/9) + (16/9) = (24 + 16) / 9 = 40/9

Step 4: Divide the results: 40/9 ÷ 15

To divide fractions, we multiply by the reciprocal of the divisor:

(40/9) * (1/15) = 40/135

Step 5: Convert the result to a mixed number (if possible):

Divide 40 by 135: 40 ÷ 135 ≈ 0.2963

Now, we can express this as a mixed number: 0.2963 ≈ 0 + 2963/10000

To simplify the fraction, we can find the greatest common divisor (GCD) between 2963 and 10000:

GCD(2963, 10000) = 67

Divide both the numerator and denominator by the GCD: 2963 ÷ 67 = 44 10000 ÷ 67 = 149

So, 2963/10000 is simplified to 44/149.

Therefore, the final result is approximately:

0 + 44/149 or 44/149 as an improper fraction.