mixed number an improper fraction

Definition

To convert a decimal into a mixed number and an improper fraction without simplifying.

We can follow two methods.

Method 1

• We read the decimal as whole number part, tenths, hundredths and so on and write it as a mixed number.
• Using algorithm, we convert the mixed number to an improper fraction.

We read the decimal and write it as a mixed number and an improper fraction as shown in this example.

Convert 13.06 into a mixed number and an improper fraction without simplifying.

• 13.06 can be read as thirteen and six hundredths.
• This can be written as mixed number 136100 without simplifying
• This can be further converted into improper fraction as follows. [13×100+6]100=1306100.
• So, 136100=1306100, an improper fraction. withoutsimplifying

Method 2

• Here, we drop the decimal point and write the number as the numerator of a fraction.
• We count the number of digits after the decimal point.
• Next, we write 1 followed by that many zeros as the denominator of same fraction.
• We get an improper fraction by writing both the numerator and denominator.
• This improper fraction can be converted into a mixed number by long division. withoutsimplifying

Consider the same decimal number 13.06.

• Here, we drop the decimal point and write the number 1306 as the numerator of a fraction.
• We count the number of digits after the decimal point. Here, it is 2 digits.
• Next, we write 1 followed by that many zeros as the denominator of same fraction.
• So, we get 13.06=1306100
• This improper fraction can be converted into a mixed number by long division as 1306100=136100 withoutsimplifying

Example 1

Convert 4.6 to a mixed number and improper fraction without simplifying.

Solution

Step 1:

The decimal 4.6 is read as 4 and 6 tenths.

Step 2:

So, it can be written as a mixed number 4610. The mixed number has a whole number part 4 and a fractional part 610 which can be reduced to lowest terms.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 10 is multiplied with whole number 4 and the product is added to the numerator 6 to give 4 × 10 + 6 = 46.

Step 4:

This becomes the numerator of the improper fraction and 10 is retained as the denominator of the improper fraction.

Step 5:

So, 4.6=4610=4610 withoutsimplifying

Example 2

Convert 11.75 to a mixed number and improper fraction without simplifying

Solution

Step 1:

The decimal 11.75 is read as 11 and 75 hundredths.

Step 2:

So, it is written as a mixed number 1175100. The mixed number has a whole number part 11 and a fractional part 75100.

Step 3:

The same mixed number can be converted into an improper fraction as follows. The denominator 100 is multiplied with whole number 11 and the product is added to the numerator 75 to give 11 × 100 + 75 = 1175.

Step 4:

This becomes the numerator of the improper fraction and 100 is retained as the denominator of the improper fraction.

Step 5:

So, 1175100=1175100 withoutsimplifying.