In changing fractions we will discuss how to change fractions from improper fraction to a whole or mixed number, from mixed number to an improper fraction, from whole number into an improper fraction.

**Changing an improper fraction to a whole number or mixed number:**

Here we will learn about changing an improper fraction to a whole or mixed number.

Cut out three circle of the same size.

Fold each circle in four.

Shade 4 parts from the first circle, 4 parts from the second circle and one part from the third circle.

Total parts shaded = 9 we have 9/4 parts.

Total parts in each circle 4 which is really 2**Note:**

When the numerator of a
fraction is greater than the denominator, the fraction is greater than
1. This can be written as mixed number.

**Changing improper fractions to mixed numbers by dividing the numerator with the denominator.****1.** 9/4

= 2

Therefore,

**2.** 24/10 Try to reduce the numerator and denominator by a common denominator.

24/10 ÷ 2/2 = 12/5

Now divide numerator by denominator.

= 2

24/10 |
^{2}/_{5} |

Sometimes an improper fraction change into a whole number when there is no remainder.

**Conversion of an Improper Fraction into a Mixed Number:**

**3. Convert \(\frac{14}{3}\) into a mixed number.**

*First Method:*

Q = Quotient = 4 R = Remainder = 2 D = Divisor = 3 |

Therefore, \(\frac{14}{3}\) = 4\(\frac{2}{3}\)

*Second Method:*

\(\frac{14}{3}\) = \(\frac{12}{3}\) + \(\frac{2}{3}\)

= 4 + \(\frac{2}{3}\)

= 4\(\frac{2}{3}\)

**4. Convert \(\frac{34}{8}\) into a mixed number.**

= 4 + \(\frac{2}{8}\) = 4\(\frac{2}{8}\) = 4\(\frac{1}{4}\) Therefore, \(\frac{34}{8}\) = 4\(\frac{1}{4}\) |

**5.** \(\frac{16}{2}\) ÷ \(\frac{2}{2}\) = \(\frac{8}{1}\) = 8

**Note:**

When the denominator is 1 in an improper fraction, it becomes a whole number.

**Changing a Mixed Number to an Improper Fraction:**

This is what I took :

=

But I looked carefully. I had eaten 3 full + 1/2 chocolate.

Let us learn the mathematical way of changing mixed numbers to improper fractions.

**Mixed numbers = Denominator × Whole numbers + Numerator**

5\(\frac{1}{2}\) = 2 × 5 + 1 = \(\frac{11}{2}\)

Multiply denominator and whole number 5.

2 × 5 = 10

5\(\frac{11}{2}\) |
\(\frac{11}{2}\) |

Add the numerator 10 + 1 = 11

This becomes the new numerator.

The old denominator remains.

*Conversion of a Mixed Number to an Improper Fraction:*

**1. Convert 7\(\frac{2}{8}\) into an improper fraction.**

*First Method:*

7\(\frac{2}{8}\) = \(\frac{(7 × 8) + 2}{8}\)

= \(\frac{56 + 2}{8}\)

= \(\frac{58}{8}\)

*Second Method:*

7\(\frac{2}{8}\) = 7 + \(\frac{2}{8}\)

= \(\frac{7}{1}\) + \(\frac{2}{8}\)

L.C.M. of 1 and 8 is 8.

\(\frac{7 × 8}{1 × 8}\) + \(\frac{2}{8}\) = \(\frac{56}{8}\) + \(\frac{2}{8}\)

= \(\frac{56 + 2}{8}\)

= \(\frac{58}{8}\)

**2. Convert 5\(\frac{1}{6}\) into an improper fraction.**

*First Method:*

5\(\frac{1}{6}\) = \(\frac{(5 × 6) + 1}{6}\)

= \(\frac{30 + 1}{6}\)

= \(\frac{31}{6}\)

*Second Method:*

5\(\frac{1}{6}\) = 5 + \(\frac{1}{6}\)

= \(\frac{5}{1}\) + \(\frac{1}{6}\)

M.C.M. of 1 and 6 is 6.

\(\frac{5 × 6}{1 × 6}\) + \(\frac{1}{6}\) = \(\frac{30}{6}\) + \(\frac{1}{6}\)

= \(\frac{30 + 1}{6}\)

= \(\frac{31}{6}\)

**Changing a whole number into an improper fraction:**

7 |
7/1 |

Since the denominator shows total parts and anything whole is out of 1
part, the improper fraction is formed by using 1 as the denominator.

**Questions and Answers on Changing Fractions:**

**1. Convert the given fractions to mixed fractions:**

(i) \(\frac{11}{2}\)

(ii) \(\frac{15}{9}\)

(iii) \(\frac{25}{4}\)

(iv) \(\frac{57}{7}\)

**Answers:**

**1.** (i) 5\(\frac{1}{2}\)

(ii) 1\(\frac{6}{9}\)

(iii) 6\(\frac{1}{4}\)

(iv) 8\(\frac{1}{7}\)

**2. Convert the given mixed fractions to improper fractions:**

(i) 3\(\frac{5}{6}\)

(ii) 7\(\frac{2}{9}\)

(iii) 5\(\frac{3}{4}\)

(iv) 8\(\frac{2}{3}\)

**Answers:**

**2.** (i) \(\frac{23}{6}\)

(ii) \(\frac{65}{9}\)

(iii) \(\frac{23}{4}\)

(iv) \(\frac{26}{3}\)

**3. Change the following mixed fractions into improper fractions:**

(i) 5\(\frac{4}{7}\)

(ii) 3\(\frac{3}{4}\)

(iii) 2\(\frac{5}{9}\)

(iv) 6\(\frac{1}{8}\)

(v) 4\(\frac{2}{9}\)

**Answer:**

**3. **(i) \(\frac{39}{7}\)

(ii) \(\frac{15}{4}\)

(iii) \(\frac{23}{9}\)

(iv) \(\frac{49}{8}\)

(v) \(\frac{38}{9}\)

**4. Change into a whole number or a mixed numeral:**

(i) \(\frac{40}{8}\)

(ii) \(\frac{13}{5}\)

(iii) \(\frac{15}{12}\)

(iv) \(\frac{16}{8}\)

(v) \(\frac{25}{9}\)

**Answer:**

**4. **(i) 5

(ii) 2\(\frac{3}{5}\)

(iii) 1\(\frac{1}{4}\)

(iv) 2

(v) 2\(\frac{7}{9}\)

**Related Concept**

**Fraction of a Whole Numbers****Representation of a Fraction****Equivalent Fractions****Properties of Equivalent Fractions****Like and Unlike Fractions****Comparison of Like Fractions****Comparison of Fractions having the same Numerator****Types of Fractions****Changing Fractions****Conversion of Fractions into Fractions having Same Denominator****Conversion of a Fraction into its Smallest and Simplest Form****Addition of Fractions having the Same Denominator****Subtraction of Fractions having the Same Denominator****Addition and Subtraction of Fractions on the Fraction Number Line**

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