# HELP WITH FRACTIONS - CONVERSION FROM IMPROPER TO MIXED AND MIXED TO IMPROPER

Go to
Help With Fractions
through Fun Games.

For details, see near

Fractions
if you have not already done so.

half, quarter, three fourth
with examples and exercises.

concept of fraction in general
with examples and exercises.

Here, we will see definitions of proper fractions,
improper fractions and mixed fractions.

We will also see problems on
conversion from improper fractions to mixed fractions
and mixed fractions to improper fractions.

### Proper, Improper and Mixed fractions

A fraction in which Numerator is less than the
Denominator is called a proper fraction.

Examples of proper fraction :
1⁄3, 2⁄5, 3⁄7, 13⁄17

The value of a proper fraction is always less than one.

A fraction in which Numerator is greater than
or equal to the Denominator
is called an improper fraction.

Examples of improper fraction :
4⁄3, 7⁄2, 12⁄12, 29⁄11

improper fractions have values
greater than or equal to 1.

A combination of a whole number and a
proper fraction is called a mixed fraction.

Examples of mixed fraction :
2  12,    3  45,    7  34,    29  815

### Conversion of improper to mixed fractions : Help With Fractions

An improper fraction with numerator greater than its
denominator can be converted into a mixed fraction,
with a whole number and a proper fraction.

Let us convert the improper fractions
in the examples above to mixed fractions.

### Solved Example 1 of Help With Fractions: Improper to Mixed Fraction

Convert 4⁄3 into mixed fraction.

The denominator is 3 which means
each unit is divided into 3 equal parts.

The numerator shows that there are 4 such parts.

4 parts = 3 parts + 1 part
= 1 unit in full + 1 part
out of 3 parts in another unit

Numerically it can be shown as follows.

4⁄3 = (3 + 1)⁄3 = 3⁄3 + 1⁄3 = 1 + 1⁄3 = 1  13

or we can show the division of 4 by 3,
using the Long Division method.

```
Dividend
Divisor   3 )   4   ( 1   Quotient
3
---
1   Remainder
---

```

4⁄3 = 1  13. Ans.

Dividend⁄Denominator
= Quotient + Remainder⁄Denominator

### Solved Example 2 of Help With Fractions: Improper to Mixed Fraction

Convert 7⁄2 into mixed fraction.

```
Dividend
Divisor   2 )   7   ( 3   Quotient
6
---
1   Remainder
---

```

Using the formula
Dividend⁄Denominator
= Quotient + Remainder⁄Denominator

7⁄2 = 3  12. Ans.

### Solved Example 3 of Help With Fractions: Improper to Mixed Fraction

Convert 29⁄11 into mixed fraction.

Now we will directly find the answer
by long division method.

```
Dividend
Divisor   11 )   29   ( 2   Quotient
22
---
7   Remainder
---

```

Using the formula
Dividend⁄Denominator
= Quotient + Remainder⁄Denominator

29⁄11 = 2  711. Ans.

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### Solved Example 4 of Help With Fractions: Mixed to Improper Fraction

Convert 3  45 into improper fraction

The denominator of the mixed fraction is 5.
The whole number 3 of the mixed
fraction tells us to take 3 units
containing 5 parts each.
i.e. 5 + 5 + 5 = 15 parts.
The numerator 4 of the prper fraction
4⁄5 tells us to take
4 parts of another unit of 5 parts.
Thus we have 15 + 4 = 19 parts altogether.
Thus 3  45 can be shown as 19⁄5.

Numerically it can be shown as follows.

3  45 = 3 + 4⁄5 = 5⁄5 + 5⁄5 + 5⁄5 + 4⁄5
= (5 + 5 + 5 + 4)⁄5
= (3 x 5 + 4)⁄5 = 19⁄5

Thus, 3  45 = (3 x 5 + 4)⁄5. Ans.

We can formulate like this:

Whole Number  (Numerator⁄Denominator)
= (Whole Number x Denominator
+ Numerator)⁄Denominator

### Solved Example 5 of Help With Fractions: Mixed to Improper Fraction

Convert 7  34 into improper fraction

Applying the Formula
Whole Number  (Numerator⁄Denominator)
= (Whole Number x Denominator + Numerator)⁄Denominator

we get 7  34 = (7 x 4 + 3)⁄4 = 31⁄4. Ans.

### Solved Example 6 of Help With Fractions: Mixed to Improper Fraction

Convert 29  815 into improper fraction

Applying the Formula
Whole Number  (Numerator⁄Denominator)
= (Whole Number x Denominator + Numerator)⁄Denominator

we get 29  815 = (29 x 15 + 8)⁄15 = 443⁄15. Ans.

### Exercise on Help With Fractions : Conversion from improper to mixed and mixed to improper fractions

Problems on Help With Fractions :

1. Convert the following imroper
fractions to mixed fractions
1. 9⁄2
2. 67⁄10
3. 11⁄3
4. 13⁄4
5. 37⁄5
6. 78⁄7
7. 23⁄6
8. 49⁄8
9. 52⁄9
10. 98⁄11

2. Convert the following mixed
fractions to imroper fractions
1. 2  12
2. 2  34
3. 3  14
4. 4  23
5. 5  67
6. 7  89
7. 6  37
8. 9  19
9. 8  1011
10. 7  1113
For Answers see at the bottom of the Page.

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The following links will take you to Help
With Fractions on other topics of Fractions

Equivalent Fractions

Comparing Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Simplifying Fractions

Fraction word Problems

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### Answers to Exercise on Help With Fractions : Conversion from improper to mixed and mixed to improper fractions

Answers to Problems on Help With Fractions :

1.
1. 4  12
2. 6  710
3. 3  23
4. 3  14
5. 7  25
6. 11  17
7. 3  56
8. 6  18
9. 5  79
10. 8  1011
1. 5⁄2
2. 11⁄4
3. 13⁄4
4. 14⁄3
5. 41⁄7
6. 71⁄9
7. 45⁄7
8. 82⁄9
9. 98⁄11
10. 102⁄13

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