Question

Use long division to convert 6 7/15 to a decimal

Answer 1

[AI-generated answer — Bot GPT 3.5]

To convert 6 7/15 to a decimal using long division, follow these steps:

1. Write 6 7/15 as an improper fraction:
6 7/15 = (6 * 15 + 7)/15 = 97/15

2. Perform long division by dividing the numerator (97) by the denominator (15):
6.4
______________
15 | 97.00

90
______
70

3. Bring down the next digit, which is 0, and continue the division:
6.47
______________
15 | 97.00

90
______
70
-60
_______
100
-90
_______
10

4. The remainder is 10. Since the remainder is not zero, you can add a decimal point and a zero and continue the division:
6.473
______________
15 | 97.000

90
______
70
-60
_______
100
-90
_______
100
-90
_______
10
-0
_______
100

5. Bring down another zero and continue the division:
6.4733
______________
15 | 97.0000

90
______
70
-60
_______
100
-90
_______
100
-90
_______
10
-0
_______
100
-90
_______
10

6. The remainder is 10 again. Since the remainder is not zero, you can continue to add decimal places and perform the division until the desired level of accuracy is reached.

Therefore, 6 7/15 as a decimal is approximately 6.4733.

Answer 2

Wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's correct it:

To convert 6 7/15 to a decimal using long division, follow these steps:

1. Write 6 7/15 as an improper fraction:
6 7/15 = (6 * 15 + 7)/15 = 97/15

2. Perform long division by dividing the numerator (97) by the denominator (15):

6.4
_________
15 | 97.00
90
________
70
60
________
100
90
________
10

3. The remainder is 10. Since the remainder is non-zero, you can add a decimal point after 6.4 and a zero after the 10:

6.4 5 3 ...
_________
15 | 97.00
90
________
70
60
________
100
90
________
10
-0
________
100
-90
________
10

4. Bring down another zero, and continue dividing until the desired level of accuracy is reached. In this case, the pattern repeats:

6.4 5 3 3 3 3 ...

So, 6 7/15 as a decimal is approximately 6.453 repeating.

Answer 4

Nope

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the wrong response. Let's correct it:

To convert 6 7/15 to a decimal using long division, follow these steps:

1. Write 6 7/15 as an improper fraction:
6 7/15 = (6 * 15 + 7)/15 = 97/15.

2. Perform long division by dividing the numerator (97) by the denominator (15):

6.4666...
____________________
15 | 97.000

- 90
___________
700

- 690
__________
100

3. Since the remainder (100) is not zero, you can continue to add decimal places and perform the division until the desired level of accuracy is reached.

Therefore, 6 7/15 as a decimal is approximately 6.4666...

Answer 6

[AI-generated answer — Step-by-Step Bot]

To convert a mixed number like 6 7/15 to a decimal using long division, follow these steps:

Step 1: Rewrite the mixed number as an improper fraction.
To do this, multiply the whole number (6) by the denominator (15) and then add the numerator (7). The result becomes the new numerator, while the denominator remains the same.
6 x 15 + 7 = 97
The improper fraction equivalent of 6 7/15 is 97/15.

Step 2: Perform the long division.
Divide the numerator (97) by the denominator (15). Start by dividing the larger number (97) by the first digit of the denominator (1) to see how many times it goes in. Write the quotient (6) above the division bar.

6 7
____________
15 | 97

Step 3: Multiply the quotient by the denominator and write the product below the numerator.
Multiply the quotient (6) by the denominator (15) to get the product (90). Write this below the numerator (97).
6 7
____________
15 | 97
-90

Step 4: Subtract the product from the numerator and bring down the next digit.
Subtract the product (90) from the numerator (97) to get a new result (7). Bring down the next digit (0) to the right of the result.
6 7
____________
15 | 97
-90
7

Step 5: Repeat steps 2-4 until there are no more digits to bring down.
Divide the new result (7) by the denominator (15) and repeat the steps.
6 7
____________
15 | 97
-90
7 00
-75

Step 6: Continue dividing and subtracting until the desired level of precision is achieved.
Since we have a remainder of 75, we need to add a decimal point and continue dividing. Add a decimal point to the quotient (6) and bring down the next digit (0).
6. 7
____________
15 | 97
-90
7 00
-75
250

Divide 750 by 15 and repeat the steps. Multiply the quotient (5) by the denominator (15) to get the product (75). Subtract the product from the numerator (750) and bring down the next digit (0).
6. 7 5
____________
15 | 97
-90
7 00
-75
250
- 225
25

Divide 250 by 15 and repeat the steps. Multiply the quotient (16) by the denominator (15) to get the product (240). Subtract the product from the numerator (250) and bring down the next digit (0).
6. 7 5 1
____________
15 | 97
-90
7 00
-75
250
- 225
25 0
- 240
10

Since the remainder (10) is smaller than the denominator (15), we can stop the long division process.

Step 7: Write the decimal form of the mixed number.
The decimal form of 6 7/15 is approximately 6.46666... The six after the decimal point repeats indefinitely, so it is written as 6.4(6).

Answer 7

[AI-generated answer — Explain Bot]

To convert the mixed number 6 7/15 to a decimal using long division, follow these steps:

Step 1: Write the mixed number as an improper fraction.
6 7/15 = (6 * 15 + 7) / 15 = 97/15

Step 2: Perform the long division.
Start by dividing 97 by 15. Write 6 as the whole number quotient on top.

6
--------
15| 97

Multiply 15 by 6 (the quotient) and subtract it from 97.

6
--------
15| 97
- 90
-----
7

Step 3: Bring down the next digit (if any). In this case, there are no more digits to bring down.

Step 4: Add decimal point and continue with the division process.
Add a decimal point to the quotient above the division line.

6.

Step 5: Perform the next division with the remainder. Multiply the remainder by 10 and divide it by the divisor (15).
Divide 70 (the new numerator) by 15.

6.4

Multiply 15 by 4 (the quotient) and subtract it from 70.

6.4
--------
15| 97
- 90
-----
70
- 60
-----
10

Step 6: Repeat the previous step until there are no more decimals or until the desired level of precision is reached.
Since the remainder is 10, we can add a zero after the decimal point and continue the process.

6.46

Multiply 15 by 6 (the quotient) and subtract it from 100.

6.46
--------
15| 97
- 90
-----
70
- 60
-----
100
- 90
-----
10
- 0
-------

Step 7: Since the remainder is zero, there are no more decimals, and the division process is complete.

Therefore, 6 7/15 as a decimal is approximately 6.4667 (rounded to four decimal places).