Let's solve this step by step:
First, let's represent the unknown number as "x."
The problem states that the number was multiplied by 2 1/2, which can be written as 5/2. Multiplying the unknown number by 2 1/2 gives us (5/2) * x, which simplifies to (5/2)x.
Next, the result is divided by 1 1/5, which can be written as 6/5. Dividing (5/2)x by 6/5 gives us [(5/2)x] / (6/5). We can simplify this expression by multiplying by the reciprocal, so [(5/2)x] * (5/6), which becomes (25/12)x.
Now, 7/18 is subtracted from (25/12)x. Therefore, our equation becomes (25/12)x - 7/18 = 1 5/6.
Next, we need to convert 1 5/6 into a fraction. 1 can be rewritten as 6/6, so 1 5/6 becomes (6/6) + 5/6 = 11/6.
Now, we have the equation (25/12)x - 7/18 = 11/6.
To clear the fractions, we can multiply every term by the least common denominator (LCD) of 12, 18, and 6, which is 36. Multiplying both sides of the equation by 36 gives us:
36 * [(25/12)x - 7/18] = 36 * (11/6)
[(36 * 25/12)x] - [(36 * 7/18)] = 36 * 11/6
[(3 * 25/12)x] - [(2 * 7/18)] = 2 * 11/1
(75/12)x - (14/18) = 22
To simplify further, we can convert all fractions to have the same denominator of 36:
(75/12)x - (14/18) = 22
(75/12)x - (28/36) = 22
(75/12)x - (14/9) = 22
Next, to eliminate any decimals, we can multiply every term by 12:
12 * [(75/12)x - (14/9)] = 12 * 22
[(12 * 75/12)x] - [(12 * 14/9)] = 12 * 22
75x - (14 * 12/9) = 264
75x - (168/9) = 264
Now, we convert 264 to have a denominator of 9:
75x - (168/9) = (264 * 9/9)
75x - (168/9) = 2376/9
To simplify further, we multiply every term by 9:
9 * [75x - (168/9)] = 9 * (2376/9)
(9 * 75x) - (9 * 168/9) = 2376/1
675x - 168 = 264
Next, we isolate the term with x by moving the constant term to the other side of the equation:
675x - 168 = 264
675x = 264 + 168
675x = 432
Now, to find the value of x, we divide both sides of the equation by 675:
x = 432/675
After simplifying the fraction, we find that x = 16/25.
Hence, the number you thought of was 16/25.
I thought of a number and 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 number?
5 answers
Wrong.
Apologies for the mistake. Let's solve it again:
Let's represent the unknown number as "x."
The problem states that the number was multiplied by 2 1/2, which can be written as 5/2. Multiplying the unknown number by 2 1/2 gives us (5/2) * x, which simplifies to (5/2)x.
Next, the result is divided by 1 1/5, which can be written as 6/5. Dividing (5/2)x by 6/5 gives us [(5/2)x] / (6/5). We can simplify this expression by multiplying by the reciprocal, so [(5/2)x] * (5/6), which becomes (25/12)x.
Now, 7/18 is subtracted from (25/12)x. Therefore, our equation becomes (25/12)x - 7/18 = 1 5/6.
Next, we need to convert 1 5/6 into a fraction. 1 can be rewritten as 6/6, so 1 5/6 becomes (6/6) + 5/6 = 11/6.
Now, we have the equation (25/12)x - 7/18 = 11/6.
To clear the fractions, we can multiply every term by the least common denominator (LCD) of 12, 18, and 6, which is 36. Multiplying both sides of the equation by 36 gives us:
36 * [(25/12)x - 7/18] = 36 * (11/6)
[(36 * 25/12)x] - [(36 * 7/18)] = 36 * 11/6
[(3 * 25/12)x] - [(2 * 7/18)] = 2 * 11/1
(75/12)x - (14/18) = 22
To simplify further, we can convert all fractions to have the same denominator of 36:
(75/12)x - (14/18) = 22
(75/12)x - (28/36) = 22
(75/12)x - (14/9) = 22
Next, to eliminate any decimals, we can multiply every term by 12:
12 * [(75/12)x - (14/9)] = 12 * 22
[(12 * 75/12)x] - [(12 * 14/9)] = 12 * 22
75x - (14 * 12/9) = 264
75x - (168/9) = 264
Now, we convert 264 to have a denominator of 9:
75x - (168/9) = (264 * 9/9)
75x - (168/9) = 2376/9
To simplify further, we multiply every term by 9:
9 * [75x - (168/9)] = 9 * (2376/9)
(9 * 75x) - (9 * 168/9) = 2376/1
675x - 168 = 264
Next, we isolate the term with x by moving the constant term to the other side of the equation:
675x - 168 = 264
675x = 264 + 168
675x = 432
Now, to find the value of x, we divide both sides of the equation by 675:
x = 432/675
However, upon reviewing the question, I mistakenly calculated the steps involved in the equation. I apologize for the error.
Let's solve it correctly:
First, we solve the equation step by step:
Let's say the unknown number is "n."
The problem states that the number was multiplied by 2 1/2, which can be written as 5/2. Multiplying the unknown number by 2 1/2 gives us (5/2) * n, which simplifies to (5/2)n.
Next, the result is divided by 1 1/5, which can be written as 6/5. Dividing (5/2)n by 6/5 gives us [(5/2)n] / (6/5). We can simplify this expression by multiplying by the reciprocal, so [(5/2)n] * (5/6), which becomes (25/12)n.
Now, 7/18 is subtracted from (25/12)n. Therefore, our equation becomes (25/12)n - 7/18 = 1 5/6.
Next, we need to convert 1 5/6 into a fraction. 1 can be rewritten as 6/6, so 1 5/6 becomes (6/6) + 5/6 = 11/6.
Now, we have the equation (25/12)n - 7/18 = 11/6.
To clear the fractions, we can multiply every term by the least common denominator (LCD) of 12, 18, and 6, which is 36. Multiplying both sides of the equation by 36 gives us:
36 * [(25/12)n - 7/18] = 36 * (11/6)
[(36 * 25/12)n] - [(36 * 7/18)] = 36 * 11/6
[(3 * 25/12)n] - [(2 * 7/18)] = 2 * 11/1
(75/12)n - (14/18) = 22
To simplify further, we can convert all fractions to have the same denominator of 36:
(75/12)n - (14/18) = 22
(75/12)n - (28/36) = 22
(75/12)n - (14/9) = 22
Next, to eliminate any decimals, we can multiply every term by 12:
12 * [(75/12)n - (14/9)] = 12 * 22
[(12 * 75/12)n] - [(12 * 14/9)] = 12 * 22
75n - (14 * 12/9) = 264
75n - (168/9) = 264
Now, we convert 264 to have a denominator of 9:
75n - (168/9) = (264 * 9/9)
75n - (168/9) = 2376/9
To simplify further, we multiply every term by 9:
9 * [75n - (168/9)] = 9 * (2376/9)
(9 * 75n) - (9 * 168/9) = 2376/1
675n - 168 = 264
Next, we isolate the term with n by moving the constant term to the other side of the equation:
675n - 168 = 264
675n = 264 + 168
675n = 432
Now, to find the value of n, we divide both sides of the equation by 675:
n = 432/675
Upon re-checking the solution, it seems that I have made another error in the calculation. I apologize for the confusion and I am providing an updated solution.
To solve the equation (25/12)n - 7/18 = 1 5/6, we need to convert 1 5/6 to an improper fraction.
1 5/6 can be rewritten as 11/6.
Now our equation becomes (25/12)n - 7/18 = 11/6.
To find a common denominator, we take the least common multiple of 12 and 18, which is 36.
Multiplying all terms by 36:
(25/12)n * 36 - 7/18 * 36 = 11/6 * 36
Canceling out the denominators:
25n * 3 - 7 * 2 = 11 * 6
75n - 14 = 66
Adding 14 to both sides of the equation:
75n = 66 + 14
75n = 80
Finally, we divide both sides of the equation by 75:
n = 80/75
Simplifying the fraction gives:
n = 16/15
Therefore, the number you thought of is 16/15.
Let's represent the unknown number as "x."
The problem states that the number was multiplied by 2 1/2, which can be written as 5/2. Multiplying the unknown number by 2 1/2 gives us (5/2) * x, which simplifies to (5/2)x.
Next, the result is divided by 1 1/5, which can be written as 6/5. Dividing (5/2)x by 6/5 gives us [(5/2)x] / (6/5). We can simplify this expression by multiplying by the reciprocal, so [(5/2)x] * (5/6), which becomes (25/12)x.
Now, 7/18 is subtracted from (25/12)x. Therefore, our equation becomes (25/12)x - 7/18 = 1 5/6.
Next, we need to convert 1 5/6 into a fraction. 1 can be rewritten as 6/6, so 1 5/6 becomes (6/6) + 5/6 = 11/6.
Now, we have the equation (25/12)x - 7/18 = 11/6.
To clear the fractions, we can multiply every term by the least common denominator (LCD) of 12, 18, and 6, which is 36. Multiplying both sides of the equation by 36 gives us:
36 * [(25/12)x - 7/18] = 36 * (11/6)
[(36 * 25/12)x] - [(36 * 7/18)] = 36 * 11/6
[(3 * 25/12)x] - [(2 * 7/18)] = 2 * 11/1
(75/12)x - (14/18) = 22
To simplify further, we can convert all fractions to have the same denominator of 36:
(75/12)x - (14/18) = 22
(75/12)x - (28/36) = 22
(75/12)x - (14/9) = 22
Next, to eliminate any decimals, we can multiply every term by 12:
12 * [(75/12)x - (14/9)] = 12 * 22
[(12 * 75/12)x] - [(12 * 14/9)] = 12 * 22
75x - (14 * 12/9) = 264
75x - (168/9) = 264
Now, we convert 264 to have a denominator of 9:
75x - (168/9) = (264 * 9/9)
75x - (168/9) = 2376/9
To simplify further, we multiply every term by 9:
9 * [75x - (168/9)] = 9 * (2376/9)
(9 * 75x) - (9 * 168/9) = 2376/1
675x - 168 = 264
Next, we isolate the term with x by moving the constant term to the other side of the equation:
675x - 168 = 264
675x = 264 + 168
675x = 432
Now, to find the value of x, we divide both sides of the equation by 675:
x = 432/675
However, upon reviewing the question, I mistakenly calculated the steps involved in the equation. I apologize for the error.
Let's solve it correctly:
First, we solve the equation step by step:
Let's say the unknown number is "n."
The problem states that the number was multiplied by 2 1/2, which can be written as 5/2. Multiplying the unknown number by 2 1/2 gives us (5/2) * n, which simplifies to (5/2)n.
Next, the result is divided by 1 1/5, which can be written as 6/5. Dividing (5/2)n by 6/5 gives us [(5/2)n] / (6/5). We can simplify this expression by multiplying by the reciprocal, so [(5/2)n] * (5/6), which becomes (25/12)n.
Now, 7/18 is subtracted from (25/12)n. Therefore, our equation becomes (25/12)n - 7/18 = 1 5/6.
Next, we need to convert 1 5/6 into a fraction. 1 can be rewritten as 6/6, so 1 5/6 becomes (6/6) + 5/6 = 11/6.
Now, we have the equation (25/12)n - 7/18 = 11/6.
To clear the fractions, we can multiply every term by the least common denominator (LCD) of 12, 18, and 6, which is 36. Multiplying both sides of the equation by 36 gives us:
36 * [(25/12)n - 7/18] = 36 * (11/6)
[(36 * 25/12)n] - [(36 * 7/18)] = 36 * 11/6
[(3 * 25/12)n] - [(2 * 7/18)] = 2 * 11/1
(75/12)n - (14/18) = 22
To simplify further, we can convert all fractions to have the same denominator of 36:
(75/12)n - (14/18) = 22
(75/12)n - (28/36) = 22
(75/12)n - (14/9) = 22
Next, to eliminate any decimals, we can multiply every term by 12:
12 * [(75/12)n - (14/9)] = 12 * 22
[(12 * 75/12)n] - [(12 * 14/9)] = 12 * 22
75n - (14 * 12/9) = 264
75n - (168/9) = 264
Now, we convert 264 to have a denominator of 9:
75n - (168/9) = (264 * 9/9)
75n - (168/9) = 2376/9
To simplify further, we multiply every term by 9:
9 * [75n - (168/9)] = 9 * (2376/9)
(9 * 75n) - (9 * 168/9) = 2376/1
675n - 168 = 264
Next, we isolate the term with n by moving the constant term to the other side of the equation:
675n - 168 = 264
675n = 264 + 168
675n = 432
Now, to find the value of n, we divide both sides of the equation by 675:
n = 432/675
Upon re-checking the solution, it seems that I have made another error in the calculation. I apologize for the confusion and I am providing an updated solution.
To solve the equation (25/12)n - 7/18 = 1 5/6, we need to convert 1 5/6 to an improper fraction.
1 5/6 can be rewritten as 11/6.
Now our equation becomes (25/12)n - 7/18 = 11/6.
To find a common denominator, we take the least common multiple of 12 and 18, which is 36.
Multiplying all terms by 36:
(25/12)n * 36 - 7/18 * 36 = 11/6 * 36
Canceling out the denominators:
25n * 3 - 7 * 2 = 11 * 6
75n - 14 = 66
Adding 14 to both sides of the equation:
75n = 66 + 14
75n = 80
Finally, we divide both sides of the equation by 75:
n = 80/75
Simplifying the fraction gives:
n = 16/15
Therefore, the number you thought of is 16/15.
Anna bought 2 3/5 lb of grapes, and Sanika bought 1/2 lb less than Anna. How many pounds of grapes did they buy in all?
To find the total weight of grapes bought by Anna and Sanika, we need to add their weights together.
Anna bought 2 3/5 lb of grapes, which can be written as 13/5 lb.
Sanika bought 1/2 lb less than Anna's weight, so we subtract 1/2 lb from Anna's weight:
13/5 lb - 1/2 lb
To subtract fractions, we need a common denominator. The least common multiple of 5 and 2 is 10, so we convert both fractions to have a denominator of 10:
(13/5) * (2/2) - 1/2
This gives us:
26/10 - 1/2
To subtract fractions, we need a common denominator of 10:
(26/10 - 5/10) lb
This simplifies to:
21/10 lb
Now, to find the total weight of grapes bought, we add Anna's weight to Sanika's weight:
(13/5 lb) + (21/10 lb)
To add fractions, we need a common denominator of 10:
(26/10 lb) + (21/10 lb)
This gives us:
47/10 lb
Therefore, Anna and Sanika bought a total of 47/10 lb of grapes, which can be simplified to 4 7/10 lb.
Anna bought 2 3/5 lb of grapes, which can be written as 13/5 lb.
Sanika bought 1/2 lb less than Anna's weight, so we subtract 1/2 lb from Anna's weight:
13/5 lb - 1/2 lb
To subtract fractions, we need a common denominator. The least common multiple of 5 and 2 is 10, so we convert both fractions to have a denominator of 10:
(13/5) * (2/2) - 1/2
This gives us:
26/10 - 1/2
To subtract fractions, we need a common denominator of 10:
(26/10 - 5/10) lb
This simplifies to:
21/10 lb
Now, to find the total weight of grapes bought, we add Anna's weight to Sanika's weight:
(13/5 lb) + (21/10 lb)
To add fractions, we need a common denominator of 10:
(26/10 lb) + (21/10 lb)
This gives us:
47/10 lb
Therefore, Anna and Sanika bought a total of 47/10 lb of grapes, which can be simplified to 4 7/10 lb.
5 answers