(3/4 divided by 3/100 - 47/2) divided by 3/2 times 1/2 +7/6 =
man, use your calculator. But first, change all those words to symbols:
(3/4 ÷ 3/100 - 47/2) ÷ 3/2 * 1/2 +7/6
I suspect there may be more parentheses needed, since otherwise you do all the multiplies and divides before any of the adds and subtracts.
To simplify the given expression step by step, let's break it down and solve it in parts.
Step 1: Simplify the expression inside the parentheses first.
The expression inside the parentheses is (3/4 / 3/100 - 47/2). We can simplify this by performing the division and subtraction.
3/4 divided by 3/100 can be rewritten as (3/4) * (100/3), by taking the reciprocal of the divisor.
This simplifies to (3/4) * (100/3) = 25/1 = 25.
Now we have 25 - 47/2. To subtract 47/2 from 25, we need to find a common denominator.
The common denominator is 2, so we multiply both the numerator and denominator of 25 by 2.
25 * 2 = 50.
Now the expression inside the parentheses simplifies to 50 - 47/2.
Step 2: Simplify the multiplication and addition outside the parentheses.
We have (50 - 47/2) divided by (3/2 * 1/2 + 7/6).
First, let's simplify the multiplication: 3/2 * 1/2 = (3 * 1) / (2 * 2) = 3/4.
Now we can simplify the addition: 3/4 + 7/6.
To find a common denominator, we multiply 4 and 6 to get 24.
3/4 rewritten with a denominator of 24 is (3*6) / (4*6) = 18/24.
7/6 rewritten with a denominator of 24 is (7*4) / (6*4) = 28/24.
Now we can add the fractions: 18/24 + 28/24 = 46/24.
So the expression becomes (50 - 47/2) / (46/24).
Step 3: Simplify the division.
To divide (50 - 47/2) by (46/24), we can rewrite it as a multiplication by taking the reciprocal of the divisor.
(50 - 47/2) / (46/24) is the same as (50 - 47/2) * (24/46).
Step 4: Simplify the multiplication.
Multiply the numerators together and the denominators together:
(50 - 47/2) * (24/46) = [(50*2 - 47)/2] * (24/46) = [100 - 47/2] * (24/46).
Step 5: Simplify the subtraction and multiplication.
Subtract 47/2 from 100, which is 100 - 47/2 = (100*2/2 - 47/2) = (200/2 - 47/2) = (153/2).
Now multiply (153/2) by (24/46):
(153/2) * (24/46) = (153*24) / (2*46) = 3672/92 = 1836/46 = 918/23.
Hence, the simplified expression is 918/23.
To solve this expression, let's break it down step by step:
Step 1: Simplify the expression.
To simplify the expression, we need to work from left to right, following the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
Step 2: Evaluate the expression inside the parentheses.
The expression inside the parentheses is (3/4 ÷ 3/100 - 47/2). To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction:
3/4 ÷ 3/100 = (3/4) * (100/3) = (3 * 100) / (4 * 3) = 300/12 = 25.
So, the expression becomes:
25 - 47/2 divided by 3/2 times 1/2 + 7/6.
Step 3: Evaluate any multiplication or division.
In this case, we have the division 47/2 ÷ 3/2. Similar to the previous step, we multiply the numerator of the first fraction by the reciprocal of the second fraction:
47/2 ÷ 3/2 = (47/2) * (2/3) = (47 * 2) / (2 * 3) = 94/6 = 47/3.
So, the expression becomes:
25 - 47/3 divided by 3/2 times 1/2 + 7/6.
Step 4: Evaluate any additional multiplication or division.
Now, we have the multiplication 3/2 times 1/2. To multiply fractions, we multiply the numerators and denominators:
(3/2) * (1/2) = (3 * 1) / (2 * 2) = 3/4.
So, the expression becomes:
25 - 47/3 divided by 3/4 + 7/6.
Step 5: Evaluate any addition or subtraction.
Now, we have the addition 3/4 + 7/6. To add fractions, we need to have a common denominator (the same number at the bottom). In this case, the least common denominator is 12. We multiply the fraction 3/4 by 3/3 and the fraction 7/6 by 2/2 to make the denominators the same:
(3/4) * (3/3) + (7/6) * (2/2) = 9/12 + 14/12 = 23/12.
Plugging this back into the original expression:
25 - 47/3 divided by 3/4 + 23/12.
Step 6: Evaluate any remaining addition or subtraction.
Now, we have subtraction and division left. Again, we need a common denominator for the subtraction. The least common denominator is 12. We multiply the fraction 23/12 by 3/3 to make the denominators the same:
25 - 47/3 divided by 3/4 + (23/12) * (3/3) = 25 - 47/3 divided by 3/4 + 69/36.
Now we simplify the subtraction and division separately:
25 - (47/3 ÷ 3/4) + 69/36 = 25 - (47/3) * (4/3) + 69/36 = 25 - (47 * 4) / (3 * 3) + 69/36 = 25 - 188/9 + 69/36.
Step 7: Evaluate the final expression.
To add or subtract fractions, we need a common denominator. The least common denominator between 9 and 36 is 36. We multiply the fraction 188/9 by 4/4 to get the common denominator and simplify:
25 - 188/9 + (69/36) * (1/1) = 25 - 188/9 + 69/36 = 25 - (188 * 4) / (9 * 4) + 69/36 = 25 - 752/36 + 69/36.
Now that we have a common denominator, we can subtract the fractions and simplify further:
25 - 752/36 + 69/36 = (25 * 36 - 752 + 69) / 36 = (900 - 752 + 69) / 36 = 217/36.
So, the final simplified answer is 217/36.