I thought of a number, multiplied it by 2 1/2, divided the result by 1 1/5, subtracted 7/18 from it, and got 1 5/6. What was my original number?
Let's represent the original number as x.
According to the given information, the steps are as follows:
1. Multiply by 2 1/2: 2 1/2 is equal to 5/2, so (x * 5/2).
2. Divide by 1 1/5: 1 1/5 is equal to 6/5, so [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6.
To simplify, we need to convert the mixed number 1 5/6 into an improper fraction, which is 11/6.
So, (x * 5/2) ÷ (6/5) - 7/18 = 11/6.
To get rid of the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators of the fractions, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further gives:
45x/6 - 35/2 = 165/3.
Multiplying both sides by 6 to eliminate the fraction:
45x - 105 = 330.
Adding 105 to both sides:
45x = 435.
Dividing both sides by 45:
x = 435/45.
Therefore, the original number is x = 9.
NO
Apologies for any confusion. Let's go through the steps again to find the correct answer.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 11/6).
To eliminate fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further:
45x - 35 = 165.
Adding 35 to both sides:
45x = 200.
Dividing both sides by 45:
x = 200/45.
Therefore, the original number is x = 40/9 or approximately 4.44 when rounded to two decimal places.
No.
Apologies for the earlier incorrect response. Let's try again to find the correct answer.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 16/6).
To eliminate fractions, we can convert the whole number and mixed number into improper fractions:
1 5/6 = (6 * 1 + 5) / 6 = 11/6.
Now our equation becomes:
[(x * 5/2) ÷ (6/5)] - 7/18 = 11/6.
Next, we simplify the expression:
(5x/2) ÷ (6/5) - 7/18 = 11/6.
To divide by a fraction, we can multiply by its reciprocal:
(5x/2) * (5/6) - 7/18 = 11/6.
Simplifying further:
(25x/12) - 7/18 = 11/6.
To eliminate the fractions, we can find the least common denominator, which is 36, and multiply both sides of the equation by it:
36 * [(25x/12) - 7/18] = 36 * (11/6).
Simplifying further:
(25x/12) * 36 - 7/18 * 36 = 11/6 * 36.
This gives us:
(6 * 25x) - (2 * 7) = 66.
Simplifying further:
150x - 14 = 66.
Adding 14 to both sides:
150x = 80.
Dividing both sides by 150:
x = 8/15.
Therefore, the original number is x = 8/15 or approximately 0.533 when rounded to three decimal places.
To find the original number, we can work backwards through the given operations.
1. First, we subtract 1 5/6 from 1 5/6 to get back to 0.
2. Then, we add 7/18 to 0 to get 7/18.
3. Next, we multiply 7/18 by 1 1/5 to get 7/18 * 5/6, which equals 35/108.
4. Finally, we divide 35/108 by 2 1/2 to get (35/108) / (5/2), which can be rewritten as (35/108) * (2/5), resulting in 70/540 or 7/54.
Therefore, the original number is 7/54.
To find the original number, we need to reverse the operations that were done and work backwards.
Let's break down the problem step by step:
1. Start with the unknown number.
2. Multiply it by 2 1/2 (or 5/2), which gives us (5/2) * x.
3. Divide the result by 1 1/5 (or 6/5), giving us ((5/2) * x) / (6/5).
4. Subtract 7/18 from the previous result, giving us ((5/2) * x) / (6/5) - 7/18.
5. The final result is equal to 1 5/6, or 11/6.
Now, let's solve for x:
((5/2) * x) / (6/5) - 7/18 = 11/6
To simplify the expression, we'll get rid of the fractions:
Multiply both sides of the equation by 6 to clear the fractions:
6 * ((5/2) * x) / (6/5) - 6 * (7/18) = 6 * (11/6)
After canceling out common factors, the equation becomes:
15x / (6/5) - 42/18 = 11
Or:
(15 * 5/6) * x - 42/18 = 11
Simplify further:
(25/2) * x - 7/3 = 11
Now, let's isolate x by moving the constant term to the other side:
(25/2) * x = 11 + 7/3
Combine the fractions on the right side:
(25/2) * x = 33/3 + 7/3
Convert 33/3 + 7/3 to a single fraction with a common denominator of 3:
(25/2) * x = 40/3
To get x alone, divide both sides of the equation by (25/2):
x = (40/3) / (25/2)
Dividing by a fraction is the same as multiplying by its reciprocal:
x = (40/3) * (2/25)
Now, multiply the numerators together and the denominators together:
x = (80/75)
Reducing the fraction, the original number is:
x = 16/15
Therefore, your original number was 16/15.