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.
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?
5 answers
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.
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.
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.
5 answers