Table Of Contents
- What is a Unit fraction?
- What are Whole numbers?
- What is Division?
- Divide Whole numbers by Unit fractions
- Dividing Whole numbers by Unit fractions using a tape diagram
- Dividing Whole numbers by Unit fractions using area model
- Divide Unit fractions by Whole numbers
- Dividing Unit fractions by Whole numbers using tape diagram
- Dividing Unit fractions by Whole numbers using area model
- Solved Examples
- Frequently Asked Questions
What is a Unit Fraction?
A fraction is used to represent a whole number that is divided into equal parts. The general form of a fraction is \(\frac{a}{b}. \frac{1}{2},\frac{1}{3},\) and \(\frac{3}{5}\) are some examples of fractions.
A fraction whose numerator is 1 is known as a unit fraction. In the case of unit fractions, the value of a in \(\frac{a}{b} \) will always be 1. The denominator b can be any whole number. Some examples of unit fractions are \(\frac{1}{2},\ \frac{1}{4},\ \frac{1}{7},\) and \(\frac{1}{10}\)
What are Whole Numbers?
Whole numbers are a set of numbers without fractions, decimals, or negative integers. It consists of all natural numbers and zero. In math, the set of whole numbers is represented by the letter W. W = {0, 1, 2, 3, …}
What is Division?
Division is one of the four basic operations of math. Division is the process of splitting numbers into equal parts or equal shares. If you want to share 8 chocolates among 4 of your friends, we divide to find the number of chocolates received by each person.
In this case, 8 is known as the dividend, 2 is known as the divisor and the result ‘4’ is known as the quotient. In other words, The dividend is the number being divided and the divisor is the number that divides the dividend.
This is an example of dividing a whole number by another whole number. Similarly, we can divide a whole number by a fraction or a fraction by a whole number.
Divide Whole Numbers by Unit Fractions
We can use a tape diagram or an area model to divide a whole number by a unit fraction. Suppose you want to find \(6\div\frac{1}{3}\).
Dividing Whole Numbers by Unit Fractions Using a Tape Diagram
To find \(6\div\frac{1}{3}\), we can use a tape diagram to find how many \(\frac{1}{3}\)s are there in 6. There are 6 whole units. Divide each whole into 3 equal parts.
Since there are 3 one-thirds in one whole, there are, \(6\times3=18\), one-thirds in 6 whole units.
So, \(6\div\frac{1}{3}=18\).
We can verify this result by taking \(\frac{1}{3}\) to the right hand side of the equation and multiplying it.
\(6=18\times\frac{1}{3}\)
\(6=\frac{18}{3}\)
6 = 6
Since LHS = RHS, the result is verified.
Dividing Whole Numbers by Unit Fractions Using Area Model
To find \(6\div\frac{1}{3}\), we can use an area model to find how many \(\frac{1}{3}\)s are there in 6. There are 6 whole units and we must divide each whole into 3 equal parts. Each part is \(\frac{1}{3}\).
Since there are 3 ‘one-thirds’ in a whole, there are ‘\(6\times3=18\)’ one-thirds in 6 wholes.
So, \(6\div\frac{1}{3}=18\).
In both of these models, we use the divisor to divide the model of the dividend into equal parts. That’s because the dividend is the number that is being divided and the divisor is the number that divides the dividend.
It is interesting to note that dividing a whole number by a unit fraction is the same as multiplying the whole number by the denominator of the unit fraction. This is because division is the inverse operation of multiplication.
So, \(a\div\frac{1}{b}=a\times b\). Instead of performing division to find \(8\div\frac{1}{8}\), we can find \(8\times 8\) to get 64 as the result.
Divide Unit Fractions by Whole Numbers
We can use a tape diagram or an area model to divide unit fractions by whole numbers as well. Suppose you want to find \(\frac{1}{4}\div3\); for this too you can use a tape diagram.
Divide Unit Fractions by Whole Numbers Using Tape Diagram
Use a tape diagram and divide \(\frac{1}{4}\) into 3 equal parts.
Each of the 3 equal parts of \(\frac{1}{4}\) represents \(\frac{1}{12}\) of the whole.
So, \(\frac{1}{4}\div 3=\frac{1}{12}\)
We can verify this result by moving 3 to the RHS and multiplying it.
\(\frac{1}{4}=\frac{1}{12}\times3=\frac{3}{12}\)
\(\frac{1}{4}=\frac{1}{4}\)
Since LHS = RHS, the result is verified.
Divide Unit Fractions by Whole numbers Using Area Model
Divide \(\frac{1}{4}\) into 3 equal parts using an area model.
Each of the 3 equal parts of \(\frac{1}{4}\) represents \(\frac{1}{12}\) of the whole.
So, \(\frac{1}{4}\div3=\frac{1}{12}\)
Note that dividing \(\frac{1}{4}\) by 3 is the same as finding
\(\frac{1}{3}\) of \(\frac{1}{4}\).
So, \(\frac{1}{4}\div3=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}\)
Solved Examples
Example 1: Divide \(5\div\frac{1}{2}\).
Solution:
Use a tape diagram to find how many \(\frac{1}{2}\)s are in 5. There are 5 whole units and divide each whole into \(\frac{1}{2}\). Each part represents \(\frac{1}{2}\).
Since there are two halves in one whole, there are \(5\times2=10\) halves in 5 whole units.
So, \(5\div\frac{1}{2}=10\).
We can verify this result by taking \(\frac{1}{2}\) to the right hand side of the equation and multiplying it.
\(5=10\times\frac{1}{2}\)
\(5=\frac{10}{2}\)
5 = 5
Since LHS = RHS, the result is verified.
Example 2: Divide \(2\div\frac{1}{7}\).
Solution:
In this case, the dividend is 2, and the divisor is \(\frac{1}{7}\).
So, \(2\div\frac{1}{7}=2\times7=14\)
Example 3: Divide \(\frac{1}{8}\div4\).
Solution:
Dividing \(\frac{1}{8}\div4\) is the same as finding \(\frac{1}{4}\) of \(\frac{1}{8}\).
\(\frac{1}{8}\div4=\frac{1}{4}\) of \(\frac{1}{8}\)
\(=\frac{1}{4}\times\frac{1}{8}=\frac{1}{4\times8}\)
\(=\frac{1}{32}\)
Example 4: Emily went for a 12-mile run and she saw a lamp post every quarter mile. How many lamp posts did she pass in her 12-mile run?
Solution:
Distance covered by Emily = 12 miles.
The distance between each lamp post \(= \frac{1}{4}\) miles
Total number of lamp posts she passed \(= 12\div\frac{1}{4}\)
Dividing 12 by \(\frac{1}{4}\) is the same as finding
\(12\times4\).
\(12\div\frac{1}{4}=12\times4\)
= 48
So, Emily passed 48 lamp posts in her 12-mile run.
Example 5: Raya bought \(\frac{1}{2}\) pound sugar to bake a cake for a small party. If the party is attended by 8 people and the cake is divided equally among them, find the sugar content present in each slice of the cake.
Solution:
Half pound of sugar was used to bake the cake and it was divided into 8 slices.
So, the sugar content in 1 slice \(= \frac{1}{2}\div8\)
Dividing \(\frac{1}{2}\) by 8 is the same as finding \(\frac{1}{2}\) of \(\frac{1}{8}\).
\(\frac{1}{2}\div8=\frac{1}{2}\times\frac{1}{8}\)
\(=\frac{1}{2\times8}=\frac{1}{16}\)
So, each slice had \(\frac{1}{16}\) pounds of sugar in it.
Multiplication is the inverse operation of division. Multiplying \(a\times b\) and dividing \(a\div\frac{1}{b}\) gives the same result.