Dividing Smaller Numbers by Larger Numbers (2024)

On this Page:

1. Using Long Division
2. Examples
3. Decimal Place Examples

Division at an introductory level usually focuses mostly on examples that feature dividing larger numbers by smaller numbers.

Sometimes in Math though we can have situations where we look to go about dividing smaller numbers by larger numbers also.

We could have for example.

2 \div 5, which can also be presented as \frac{2}{5}.

It’s true that a calculator could quickly tell us the answer.

2 \div 5 = 0.4

But we want to know how to solve such sums by hand.
We can do so by using long division.

Dividing Smaller Numbers by
Larger Numbers with Long Division

For 2 \div 5.

1)
We first set the division up as normal.
\begin{array}{r}\\[-2pt]5 {\bf{|}} {\overline{\space 2 \space\space\space\space\space\space\space\space}} \end{array}

2)
Next we want to change the form of the smaller dividend, 2.
We rewrite 2 as a decimal number, which doesn’t change the value of the number at all.

Four zeroes is a fine standard amount to use, even if we may or may not need to use all of them in the division.

2 = 2.0000

But we also have to place a decimal point in the same place above.
To account for there also being a decimal point in the answer we will obtain.

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]5 {\bf{|}} {\overline{\space 2.0000 \space\space}} \end{array}

3)
We then carry out the required long division to obtain a solution.

\begin{array}{r}0. \space\space\space\space\space\space\space\space \\[-2pt]5 {\bf{|}} {\overline{2.0000}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space \\ 2 \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \end{array} => \begin{array}{r}0.4 \space\space\space\space\space\space \\[-2pt]5 {\bf{|}} {\overline{2.0000}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space \\ 2\space0 \space\space\space\space\space\space \\ {\text{--}}\space \underline{2\space0} \space\space\space\space\space\space \\ 0 \space\space\space\space\space\space\end{array}

With a result of zero obtained after the second round of multiplication and subtraction.
The long division is complete, and we have the correct answer.

2 \div 5 = 0.4


Examples

(1.1)

Solve

12 \div 25.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]25 {\bf{|}} {\overline{\space 12.0000 \space\space}} \end{array}

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space \\[-2pt]25 {\bf{|}} {\overline{\space 12.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 12 \space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space\end{array} => \begin{array}{r}0.4 \space\space\space\space\space\space\space \\[-2pt]25 {\bf{|}} {\overline{\space 12.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 12\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{10\space0} \space\space\space\space\space\space\space \\ 2\space0 \space\space\space\space\space\space\space\\ \space\\ \space\end{array} => \begin{array}{r}0.48 \space\space\space\space\space \\[-2pt]25 {\bf{|}} {\overline{\space 12.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 12\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{10\space0} \space\space\space\space\space\space\space \\ 2\space00 \space\space\space\space\space \\ {\text{--}}\space \underline{2\space00} \space\space\space\space\space \\ 0 \space\space\space\space\space\end{array}

\underline{12 \div 25 = 0.48}

(1.2)

Solve

14 \div 56.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]56 {\bf{|}} {\overline{\space 14.0000 \space\space}} \end{array}

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space \\[-2pt]56 {\bf{|}} {\overline{\space 14.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 14 \space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space\end{array} => \begin{array}{r}0.2 \space\space\space\space\space\space\space \\[-2pt]56 {\bf{|}} {\overline{\space 14.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{11\space2} \space\space\space\space\space\space\space \\ 2\space8 \space\space\space\space\space\space\space\\ \space\\ \space\end{array} => \begin{array}{r}0.25 \space\space\space\space\space \\[-2pt]56 {\bf{|}} {\overline{\space 14.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{11\space2} \space\space\space\space\space\space\space \\ 2\space80 \space\space\space\space\space \\ {\text{--}}\space \underline{2\space80} \space\space\space\space\space \\ 0 \space\space\space\space\space\end{array}

\underline{14 \div 56 = 0.25}

(1.3)

Solve

9 \div 16.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000 \space\space}} \end{array}

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 9 \space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space \\\space \\ \space \\\space \\ \space\end{array} => \begin{array}{r}0.5 \space\space\space\space\space\space\space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 9{\phantom{.}}0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{8\space0} \space\space\space\space\space\space\space \\ 1\space0 \space\space\space\space\space\space\space\\ \space\\ \space \\\space \\ \space \\\space \\ \space\end{array} => \begin{array}{r}0.56 \space\space\space\space\space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 9\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{8\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{96} \space\space\space\space\space \\ 4 \space\space\space\space\space \\\space \\ \space \\\space \\ \space\end{array} => \begin{array}{r}0.562 \space\space\space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 9\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{8\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{96} \space\space\space\space\space \\ 40 \space\space\space \\ {\text{--}}\space \underline{32} \space\space\space \\ 8 \space\space\space \\ \space \\ \space\end{array} => \begin{array}{r}0.5625 \space \\[-2pt]16 {\bf{|}} {\overline{\space 9.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 9\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{8\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{96} \space\space\space\space\space \\ 40 \space\space\space \\ {\text{--}}\space \underline{32} \space\space\space \\ 80 \space \\ {\text{--}}\space \underline{80} \space \\ 0 \space\end{array}

\underline{9 \div 16 = 0.5625}

Rounding an answer to a Decimal Place

Sometimes when dividing smaller numbers by larger numbers, it can be required to round to a specific ‘decimal place’.

We follow the same process of long division as already seen on this page.

But we would need to do one extra division beyond the decimal place we are focusing on.
As we would need to know whether we are to round up or round down.

This can be seen by looking at some examples.

Examples

(2.1)

Solve

3 \div 7 to 3 decimal places.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000 \space\space}} \end{array}

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 3 \space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.4 \space\space\space\space\space\space\space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 3{\phantom{.}}0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{2\space8} \space\space\space\space\space\space\space \\ 2 \space\space\space\space\space\space\space\\ \space\\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.42 \space\space\space\space\space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 3{\phantom{.}}0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{2\space8} \space\space\space\space\space\space\space \\ 20 \space\space\space\space\space\\ {\text{--}}\space \underline{14} \space\space\space\space\space \\ 6 \space\space\space\space\space \\\space \\ \space \\\end{array} => \begin{array}{r}0.428 \space\space\space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 3{\phantom{.}}0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{2\space8} \space\space\space\space\space\space\space \\ 20 \space\space\space\space\space\\ {\text{--}}\space \underline{14} \space\space\space\space\space \\ 60 \space\space\space \\ {\text{--}}\space \underline{56} \space\space\space \\ 4 \space\space\space \\\end{array}

Now we are at 3 decimal places as required, but another step will let us know if we are to round up or down at the 8.

=> \begin{array}{r}0.4285 \space \\[-2pt]7 {\bf{|}} {\overline{\space 3.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 3{\phantom{.}}0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{2\space8} \space\space\space\space\space\space\space \\ 20 \space\space\space\space\space\\ {\text{--}}\space \underline{14} \space\space\space\space\space \\ 60 \space\space\space \\ {\text{--}}\space \underline{56} \space\space\space \\ 40 \space \\\end{array}

Ignoring remainders 7 goes into 40 five times.
Letting us know that in the answer we round up at the 3rd decimal place.

3 \div 7 = 0.429 to 3dp

(2.2)

Solve

8 \div 14 to 3 decimal places.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000 \space\space}} \end{array}

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 8 \space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.5 \space\space\space\space\space\space\space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 8\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{7\space0} \space\space\space\space\space\space\space \\ 1\space0 \space\space\space\space\space\space\space\\ \space\\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.57 \space\space\space\space\space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 8\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{7\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{98} \space\space\space\space\space \\ 2 \space\space\space\space\space \\\space \\ \space \\\end{array} => \begin{array}{r}0.571 \space\space\space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 8\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{7\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{98} \space\space\space\space\space \\ 20 \space\space\space \\ {\text{--}}\space \underline{14} \space\space\space \\ 6 \space\space\space \\\end{array}

=> \begin{array}{r}0.5714 \space \\[-2pt]14 {\bf{|}} {\overline{\space 8.0000\space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space \\ 8\space0 \space\space\space\space\space\space\space \\ {\text{--}}\space \underline{7\space0} \space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\\ {\text{--}}\space \underline{98} \space\space\space\space\space \\ 20 \space\space\space \\ {\text{--}}\space \underline{14} \space\space\space \\ 60 \space \\\end{array}

Ignoring remainders 14 goes into 60 four times.
Letting us know that in the answer we round down at the 3rd decimal place.

8 \div 14 = 0.571 to 3dp

(2.3)

Solve

14 \div 65 to 4 decimal places.

Solution

\begin{array}{r}. \space\space\space\space\space\space\space\space\space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \end{array}

We put 5 zeroes in the dividend this time.
As a 5th step is required to let us know which way to round at the 4th decimal place.

\begin{array}{r}0. \space\space\space\space\space\space\space\space\space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14 \space\space\space\space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space \\ \space\space\space\space\space\space\space\space\space\\ \space \\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.2 \space\space\space\space\space\space\space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space\space\space \\ {\text{--}}\space \underline{13\space0} \space\space\space\space\space\space\space\space\space \\ 1\space0 \space\space\space\space\space\space\space\space\space\\ \space\\ \space \\\space \\ \space \\\end{array} => \begin{array}{r}0.21 \space\space\space\space\space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space\space\space \\ {\text{--}}\space \underline{13\space0} \space\space\space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\space\space\\ {\text{--}}\space \underline{65} \space\space\space\space\space\space\space \\ 35 \space\space\space\space\space\space\space \\\space \\ \space \\\end{array} => \begin{array}{r}0.215 \space\space\space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space\space\space \\ {\text{--}}\space \underline{13\space0} \space\space\space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\space\space\\ {\text{--}}\space \underline{65} \space\space\space\space\space\space\space \\ 350 \space\space\space\space\space \\ {\text{--}}\space \underline{325} \space\space\space\space\space \\ 25 \space\space\space\space\space \\\end{array}

=> \begin{array}{r}0.2152 \space\space\space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space\space\space \\ {\text{--}}\space \underline{13\space0} \space\space\space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\space\space\\ {\text{--}}\space \underline{65} \space\space\space\space\space\space\space \\ 350 \space\space\space\space\space \\ {\text{--}}\space \underline{325} \space\space\space\space\space \\ 250 \space\space\space \\ {\text{--}}\space \underline{125} \space\space\space \\ 55 \space\end{array} => \begin{array}{r}0.21528 \space \\[-2pt]65 {\bf{|}} {\overline{\space 14.00000 \space}} \\{\text{--}}\space \underline{ 0 \space\space\space\space}\space\space\space\space\space\space\space\space \\ 14\space0 \space\space\space\space\space\space\space\space\space \\ {\text{--}}\space \underline{13\space0} \space\space\space\space\space\space\space\space\space \\ 1\space00 \space\space\space\space\space\space\space\\ {\text{--}}\space \underline{65} \space\space\space\space\space\space\space \\ 350 \space\space\space\space\space \\ {\text{--}}\space \underline{325} \space\space\space\space\space \\ 250 \space\space\space \\ {\text{--}}\space \underline{125} \space\space\space \\ 550 \space\end{array}

Ignoring remainders 65 goes into 550 eight times.
Letting us know that in the answer we round up at the 4th decimal place.

14 \div 65 = 0.2154 to 4dp

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Dividing Smaller Numbers by Larger Numbers (2024)

FAQs

Dividing Smaller Numbers by Larger Numbers? ›

When a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer.

What is the remainder of a smaller number divided by a larger number? ›

When a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer.

How do you divide small decimal numbers by big numbers? ›

How do you divide a decimal by a whole number?
  1. Place the decimal point in the quotient directly above the decimal point in the dividend.
  2. Divide the same way you would divide with whole numbers.
  3. Divide until there is no remainder, or until the quotient begins to repeat in a pattern. Annex zeros, if necessary.

What is the easy division trick for large numbers? ›

2 Use halving and doubling

Another useful technique to divide large numbers mentally is to use halving and doubling, which is based on the fact that dividing by 2 is the same as multiplying by 0.5, and vice versa. For example, if you want to divide 720 by 24, you can halve both numbers until you get an easier division.

How to work out 5 divided by 8? ›

8 goes into 20 two (2) times with remainder 4. Add another 0 to the dividend and bring it down next to the 4. 8 goes into 40 five (5) times with no remainder. Therefore, 5 divided by 8 is 0.625.

What is the rule for dividing decimals? ›

Decimal division depends mainly on the divisor, which must be made into a whole number. Remember to always move the decimal point the same number of places to the right in both the divisor and dividend. You would move the decimal in the dividend the same number of places as in the divisor.

When dividing, what number goes first, top or bottom? ›

Fractions are used to show a division between two numbers, with the top being called a numerator, and the bottom the denominator. The numerator is the number which will be divided and the denominator the number we are dividing by.

What to do with the remainder in long division? ›

If there is a remainder, the result of the last subtraction will be less than the divisor. If that is the case, then the remainder is added behind the answer. This is what long division of 43 / 3 looks like. The last subtraction results in a 1, which is less than the divisor, the 3.

What is the 7 trick for division? ›

To determine whether a number is divisible by 7, you have to remove the last digit of the number, double it, and then subtract it from the remaining number. If the remainder is zero or a multiple of 7, then the number is divisible by 7. If the remainder is not zero or a multiple of 7, the number is not divisible by 7.

What is the easiest division method? ›

The chunking method is an easy division method that breaks down dividing large numbers into more manageable steps. This method involves subtracting large chunks of multiples of the divisor from the dividend until you reach zero or a remainder smaller than the divisor.

How to divide small decimals by bigger decimals? ›

First, convert the divisor into a whole number by shifting the decimal point to the right. Apply the same process to the dividend. Then, perform regular division with the new numbers. Finally, position the decimal point in the quotient to match the dividend.

What is the dividend formula? ›

Dividend = Divisor x Quotient + Remainder. It is just the reverse process of division. In the example above we first divided the dividend by divisor and subtracted the multiple with the dividend. That means, we first divided and then subtracted.

What is the remainder of a number divided by another number? ›

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

What is the remainder when you divide by? ›

The result of the division is called a “quotient.” When the dividend is not completely divided by the divisor, the leftover value is called “remainder.” Example: Divide 25 by 6. Thus, quotient and we are left with the remainder of 1. We can write this as 25 ÷ 6 → 4 R 1 , where 4 is the quotient and 1 is the remainder.

What is the remainder when the largest 4 digit number is divided by the smallest 2 digit number? ›

The largest 4 digit number = 9999. Smallest 2 digit number = 10 9999÷ 10 gives remainder 9 and quotient 999.

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