Improper to Mixed Fractions Notes
This Improper to Mixed Fractions Calculator helps you turn an improper fraction into a whole number and a fraction, and shows the working clearly at every step. Divide the numerator by the denominator to see how many whole ones fit inside. That answer becomes the whole number, and whatever is left over becomes the numerator over the same denominator. Following the same pattern every time is what makes converting fractions easy to picture, check, and repeat on your own with any fraction.
Step-by-step method
- Set up the problem.
- Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
- The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
- Simplify the fraction part if you can. This step is Simplifying of Fractions.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
- The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
- Simplify the fraction part if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: We convert \(\frac{17}{4}\) into a mixed fraction.
Step 2
Step 2 - Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
In this problem: We divide the numerator by the denominator. \(17 \div 4 = 4 \;\text{remainder}\; 1\).
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(1\). \(4\) does not fit yet, so we include the next digit \(7\) to make \(17\).
| 4 | 1 | 7 |
Step 2
Step 2 - Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(17\). \(4\) fits \(4\) times. Multiply: \(4 \times 4 = 16\). Subtract: \(17 - 16 = 1\).
| 4 | ||
| 4 | 1 | 7 |
| - | 1 | 6 |
| 1 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(7 - 6 = 1\) → write \(1\) under the ones column.
| 1 | 7 | |
| − | 1 | 6 |
| 1 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(1 - 1 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 1 | 7 | |
| − | 1 | 6 |
| 1 | ||
Final Answer
Final Answer
Step 3
Step 3 - The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
In this problem: \(4\) goes in front as the whole number, and the \(1\) left over becomes the numerator over \(4\).
Step 4
Step 4 - Simplify the fraction part if you can. This step is Simplifying of Fractions.
In this problem: The only number that divides both \(1\) and \(4\) is \(1\), so the fraction part stays as it is.
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the problem.
- Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
- The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
- Simplify the fraction part if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: We convert \(\frac{14}{6}\) into a mixed fraction.
Step 2
Step 2 - Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
In this problem: We divide the numerator by the denominator. \(14 \div 6 = 2 \;\text{remainder}\; 2\).
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(1\). \(6\) does not fit yet, so we include the next digit \(4\) to make \(14\).
| 6 | 1 | 4 |
Step 2
Step 2 - Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(14\). \(6\) fits \(2\) times. Multiply: \(6 \times 2 = 12\). Subtract: \(14 - 12 = 2\).
| 2 | ||
| 6 | 1 | 4 |
| - | 1 | 2 |
| 2 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(4 - 2 = 2\) → write \(2\) under the ones column.
| 1 | 4 | |
| − | 1 | 2 |
| 2 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(1 - 1 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 1 | 4 | |
| − | 1 | 2 |
| 2 | ||
Final Answer
Final Answer
Step 3
Step 3 - The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
In this problem: \(2\) goes in front as the whole number, and the \(2\) left over becomes the numerator over \(6\).
Step 4
Step 4 - Simplify the fraction part if you can. This step is Simplifying of Fractions.
In this problem: The biggest number that divides both \(2\) and \(6\) is \(2\). Dividing each by it gives \(2 \div 2 = 1\) and \(6 \div 2 = 3\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{2}{6}\).
Step 2
Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 2\). The biggest of those is \(2\), so \(2\) is the number to divide by.
Step 3
Step 3 - Divide the numerator and the denominator by that number.
In this problem: Divide both by \(2\): \(2 \div 2 = 1\) and \(6 \div 2 = 3\).
Final Answer
Final Answer
See Example 3 Hide Example 3
Problem
Approach
Step-by-step method
- Set up the problem.
- Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
- The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
- Simplify the fraction part if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: We convert \(\frac{11}{3}\) into a mixed fraction.
Step 2
Step 2 - Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
In this problem: We divide the numerator by the denominator. \(11 \div 3 = 3 \;\text{remainder}\; 2\).
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(1\). \(3\) does not fit yet, so we include the next digit \(1\) to make \(11\).
| 3 | 1 | 1 |
Step 2
Step 2 - Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(11\). \(3\) fits \(3\) times. Multiply: \(3 \times 3 = 9\). Subtract: \(11 - 9 = 2\).
| 3 | ||
| 3 | 1 | 1 |
| - | 9 | |
| 2 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - When the top digit in a column is too small to subtract from, borrow from the nearest column to its left that is not zero. Take one away from that digit and add ten to the column on its right, passing the borrow along one column at a time until it reaches the column you are working on.
In this problem: We need to <span class="borrow-text">borrow</span> because \(1\) in the ones column is smaller than \(9\).<br>Take 1 from the tens column, so \(1\) becomes \(0\), and add 10 to the ones column, so \(1\) becomes \(11\).
| 0 | 11 | |
| − | 9 | |
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(11 - 9 = 2\) → write \(2\) under the ones column.
| 0 | 11 | |
| − | 9 | |
| 2 | ||
Step 3
Step 3 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(0 - 0 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 0 | 11 | |
| − | 9 | |
| 2 | ||
Final Answer
Final Answer
Step 3
Step 3 - The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
In this problem: \(3\) goes in front as the whole number, and the \(2\) left over becomes the numerator over \(3\).
Step 4
Step 4 - Simplify the fraction part if you can. This step is Simplifying of Fractions.
In this problem: The only number that divides both \(2\) and \(3\) is \(1\), so the fraction part stays as it is.
Final Answer
See Example 4 Hide Example 4
Problem
Approach
Step-by-step method
- Set up the problem.
- Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
- The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
- Simplify the fraction part if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: We convert \(\frac{29}{8}\) into a mixed fraction.
Step 2
Step 2 - Divide the numerator by the denominator, and note how many are left over. This step is Division of Large Numbers.
In this problem: We divide the numerator by the denominator. \(29 \div 8 = 3 \;\text{remainder}\; 5\).
Problem
Approach
Step-by-step method
- Set up the long-division box: the divisor goes outside, the dividend goes inside, and the quotient will be written on top.
- Look at the first digit of the number being divided. If the divisor is too big to fit into it, take one more digit, and keep taking digits until it does fit. Ask how many times the divisor fits, and write that number on top, above the last digit you used. If it will not fit once you have started, write 0 on top for that place. Multiply the divisor by the number you wrote, then take the result away. That part is Subtraction of Large Numbers. Bring down the next digit and start again. Keep going until no digits are left. The number on top is the answer, and anything left over at the end is the remainder.
Step 1
Step 1 - Step 2a - Check whether the divisor fits into the digits taken so far. If it does not, include the next digit from the dividend.
In this problem: We look at \(2\). \(8\) does not fit yet, so we include the next digit \(9\) to make \(29\).
| 8 | 2 | 9 |
Step 2
Step 2 - Step 2b - Divide the current number by the divisor and write that digit on top, then multiply the divisor by it. Take that product away to get the remainder. That part is Subtraction of Large Numbers.
In this problem: We look at \(29\). \(8\) fits \(3\) times. Multiply: \(8 \times 3 = 24\). Subtract: \(29 - 24 = 5\).
| 3 | ||
| 8 | 2 | 9 |
| - | 2 | 4 |
| 5 |
Problem
Approach
Step-by-step method
- Write the two numbers in columns, aligned on the right (ones under ones). Put the − sign to the left of the bottom number, and draw a line underneath.
- Starting from the rightmost column, subtract column-by-column moving right to left. If you cannot subtract in a column, borrow from the column to the left, then subtract. This repeats once for every column, moving right to left.
Step 1
Step 1 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(9 - 4 = 5\) → write \(5\) under the ones column.
| 2 | 9 | |
| − | 2 | 4 |
| 5 | ||
Step 2
Step 2 - Subtract the bottom digit from the top digit in this column and write the result underneath the line.
In this problem: \(2 - 2 = 0\) → this is a leading zero, so nothing is written under the tens column.
| 2 | 9 | |
| − | 2 | 4 |
| 5 | ||
Final Answer
Final Answer
Step 3
Step 3 - The answer to that division is the whole number, and what is left over becomes the numerator over the same denominator.
In this problem: \(3\) goes in front as the whole number, and the \(5\) left over becomes the numerator over \(8\).
Step 4
Step 4 - Simplify the fraction part if you can. This step is Simplifying of Fractions.
In this problem: The only number that divides both \(5\) and \(8\) is \(1\), so the fraction part stays as it is.
Final Answer