Question

3 1/8* (5 1/3-3,2) + 4 2/3-2,5=

Answer 1

3 1/8•(5 1/3-3,2)+4 2/3-2,5=8 5/6
1)5 1/3-3,2=5 1/3-3 2/10=5 10/30-
3 6/30=2 4/30=2 2/15
2)3 1/8•2 2/15=25/8•32/15=20/3=
6 2/3
3) 6 2/3+4 2/3=11 1/3
4)11 1/3-2,5=11 1/3-2 5/10=11 10/30-
2 15/30=8 5/6

Answer 2

To solve the given expression, we'll follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Given expression: 3 1/8 * (5 1/3 - 3.2) + 4 2/3 - 2.5

Step 1: Evaluate inside the parentheses first. 5 1/3 - 3.2

To subtract mixed numbers, let's convert 5 1/3 into an improper fraction: 5 1/3 = 5 + 1/3 = (5 * 3 + 1)/3 = 16/3

Now we have: 16/3 - 3.2

To subtract, we need a common denominator, which is 3 in this case. So, let's convert 3.2 into a fraction with a denominator of 3: 3.2 = 3 + 0.2 = 3 + 2/10 = 3 + 1/5 = (3 * 5 + 1)/5 = 16/5

Now we have: 16/3 - 16/5

To subtract fractions, we need a common denominator, which is 15 in this case (the least common multiple of 3 and 5): (16/3) * (5/5) - (16/5) * (3/3) = (80/15) - (48/15) = (80 - 48)/15 = 32/15

Step 2: Now, we evaluate the expression outside the parentheses:

3 1/8 * (Result from Step 1) + 4 2/3 - 2.5 3 1/8 = 3 + 1/8 = (3 * 8 + 1)/8 = 25/8

Now we have: (25/8) * (32/15) + 4 2/3 - 2.5

Step 3: Perform the multiplication: (25/8) * (32/15) To multiply fractions, simply multiply the numerators and denominators: = (25 * 32)/(8 * 15) = 800/120 = 20/3

Now we have: 20/3 + 4 2/3 - 2.5

Step 4: Perform the addition: 20/3 + 4 2/3 To add mixed numbers, let's convert 4 2/3 into an improper fraction: 4 2/3 = 4 + 2/3 = (4 * 3 + 2)/3 = 14/3

Now we have: 20/3 + 14/3 = (20 + 14)/3 = 34/3

Now we have: 34/3 - 2.5

Step 5: Convert 2.5 into a fraction with a denominator of 3: 2.5 = 2 + 0.5 = 2 + 1/2 = (2 * 2 + 1)/2 = 5/2

Now we have: 34/3 - 5/2

To subtract fractions, we need a common denominator, which is 6 in this case (the least common multiple of 3 and 2): (34/3) * (2/2) - (5/2) * (3/3) = (68/6) - (15/6) = (68 - 15)/6 = 53/6

The final result is 53/6.