Conversion of Mixed Fractions into Improper Fractions

To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerator of the improper fraction. Its denominator is the same as the
denominator of the fractional part i.e.,

Mixed Fractions into Improper Fractions

In conversion of mixed fractions into improper fractions, we may follow the following steps:

Step I: Obtain the mixed fraction. 

Step II: Identify the whole number and the numerator (top) and denominator (bottom) of the proper fraction.


Step III: Multiply the whole number by the denominator of the proper fraction and add the result to the numerator of the proper fraction.

Step IV: Write the fraction having numerator equal to the number obtained in step III and denominator same as the denominator of the fraction in step II. Thus,

Conversion of Mixed Fractions into Improper Fractions

For Example:

1. Convert 3\(\frac{5}{6}\) into an improper fraction:

Solution:

3\(\frac{5}{6}\) = \(\frac{3 × 6 + 5}{6}\) = \(\frac{18 + 5}{6}\) = \(\frac{23}{6}\)



2. Express each of the following mixed fractions as improper fractions:

(i) Convert 8\(\frac{4}{7}\) into an improper fraction.

8\(\frac{4}{7}\) means 8 whole and \(\frac{4}{7}\).

Conversion of Mixed Fractions into Improper Fractions

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


Solution:

8\(\frac{4}{7}\) = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + \(\frac{4}{7}\)

or, 8\(\frac{4}{7}\) = \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{7}{7}\) + \(\frac{4}{7}\) = \(\frac{60}{7}\),           [\(\frac{7}{7}\) means 1)

We can also convert a mixed number into an improper fraction as follows.

First multiply the whole number by denominator. Here (8 × 7) + 4 = 60. Now, put the sum as the numerator of the required improper fraction and the denominator remains the same.

8\(\frac{4}{7}\) = \(\frac{(8 × 7) + 4}{7}\) = \(\frac{56 + 4}{7}\) = \(\frac{60}{7}\)

Thus, 8\(\frac{4}{7}\) = \(\frac{60}{7}\)


(ii) 3\(\frac{2}{7}\)

= \(\frac{(3 × 7) + 2}{7}\)

= \(\frac{21 + 2}{7}\)

= \(\frac{23}{7}\)


(iii) 4\(\frac{5}{9}\)

= \(\frac{(4 × 9) + 5}{9}\)

= \(\frac{36 + 5}{9}\)

= \(\frac{41}{9}\)

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

= \(\frac{(3 × 5) + 2}{5}\)

= \(\frac{15 + 2}{5}\)

= \(\frac{17}{5}\)


(v) 7\(\frac{1}{4}\)

= \(\frac{(7 × 4) + 1}{4}\)

= \(\frac{28 + 1}{4}\)

= \(\frac{29}{4}\)


Conversion of a Mixed Fraction into an Improper Fraction:

3. Let us convert 5\(\frac{4}{5}\) into an improper fraction.

Step I: Multiply the whole number 5 by the denominator 5.  [5 × 5 = 25]

Step II: Add the numerator to it.   [25 + 4 = 29]

Step III: This gives the numerator of the improper fraction.  [\(\frac{29}{7}\)]

Denominator will remain the same. So. 5\(\frac{4}{5}\) = \(\frac{29}{7}\)


Worksheet on Conversion of Mixed Fractions into Improper Fractions:

1. Convert the following into Improper Fractions:

(i) 4\(\frac{1}{3}\)

(ii) 2\(\frac{1}{2}\)

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

(iv) 7\(\frac{4}{9}\)

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


Answer:

1. (i) \(\frac{13}{3}\)

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

(iii) \(\frac{14}{3}\)

(iv) \(\frac{67}{9}\)

(v) \(\frac{33}{7}\)

You might like these

Fraction

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions



Number Page

6th Grade Page

From Conversion of Mixed Fractions into Improper Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Addition and Subtraction of Fractions | Solved Examples | Worksheet

    Jul 18, 24 03:08 PM

    Addition and subtraction of fractions are discussed here with examples. To add or subtract two or more fractions, proceed as under: (i) Convert the mixed fractions (if any.) or natural numbers

    Read More

  2. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Jul 18, 24 01:19 AM

    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  3. Fractions in Descending Order |Arranging Fractions an Descending Order

    Jul 18, 24 01:15 AM

    We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First…

    Read More

  4. Fractions in Ascending Order | Arranging Fractions | Worksheet |Answer

    Jul 18, 24 01:02 AM

    Comparison Fractions
    We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we fi…

    Read More

  5. Worksheet on Comparison of Like Fractions | Greater & Smaller Fraction

    Jul 18, 24 12:45 AM

    Worksheet on Comparison of Like Fractions
    In worksheet on comparison of like fractions, all grade students can practice the questions on comparison of like fractions. This exercise sheet on comparison of like fractions can be practiced

    Read More