Ordering Decimal Numbers

Numbers have an order or arrangement. The number two is between one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them.

Example: If we start with the numbers 4.3 and 8.78, the number 5.2764 would come between them, the number 9.1 would come after them and the number 2 would come before both of them.

Example: If we start with the numbers 4.3 and 4.78, the number 4.2764 would come before both of them, the number 4.9 would come after them and the number 4.5232 would come between them.

The order may be ascending (getting larger in value) or descending (becoming smaller in value).

Division of Decimals by Decimals

The procedure for the division of decimals is very similar to the division of whole numbers. Make the divisor into a whole number by multiplying both it and the dividend by the same number (such as 10, 100, 1000 etc.). An easy way to do this is to move the decimal point to the right end of the divisor and move the decimal point of the dividend the same number of places.

How to divide a four digit decimal number by a two digit decimal number (e.g. 0.424 ÷ 0.8).

• Place the divisor before the division bracket and place the dividend (0.424) under it.

        
0.8)0.424

• Multiply both the divisor and dividend by 10 so that the divisor is not a decimal but a whole number. In other words move the decimal point one place to the right in both the divisor and dividend

      
8)4.24

• Proceed with the division as you normally would except put the decimal point in the answer or quotient exactly above where it occurs in the dividend. For example:

 0.53
8)4.24
 4 0
   24
    0

Division of Decimals by Decimals

The procedure for the division of decimals is very similar to the division of whole numbers. Make the divisor into a whole number by multiplying both it and the dividend by the same number (such as 10, 100, 1000 etc.). An easy way to do this is to move the decimal point to the right end of the divisor and move the decimal point of the dividend the same number of places.

How to divide a four digit decimal number by a two digit decimal number (e.g. 0.424 ÷ 0.8).

• Place the divisor before the division bracket and place the dividend (0.424) under it.

         
0.8)0.424

• Multiply both the divisor and dividend by 10 so that the divisor is not a decimal but a whole number. In other words move the decimal point one place to the right in both the divisor and dividend

       
8)4.24

• Proceed with the division as you normally would except put the decimal point in the answer or quotient exactly above where it occurs in the dividend. For example:

  0.53
8)4.24
  4 0
    24
     0

Division of Decimals by Decimals

The procedure for the division of decimals is very similar to the division of whole numbers. Make the divisor into a whole number by multiplying both it and the dividend by the same number (such as 10, 100, 1000 etc.). An easy way to do this is to move the decimal point to the right end of the divisor and move the decimal point of the dividend the same number of places.

How to divide a four digit decimal number by a two digit decimal number (e.g 0.4131 ÷ 0.17).

• Place the divisor before the division bracket and place the dividend (0.4131) under it.

       
0.17)0.4131

• Multiply both the divisor and dividend by 100 so that the divisor is not a decimal but a whole number. In other words move the decimal point two places to the right in both the divisor and dividend

      
17)41.31

• Proceed with the division as you normally would except put the decimal point in the answer or quotient exactly above where it occurs in the dividend. For example:

  2.43
17)41.31

Division of Decimals by Decimals

The procedure for the division of decimals is very similar to the division of whole numbers. Make the divisor into a whole number by multiplying both it and the dividend by the same number (such as 10, 100, 1000 etc.). An easy way to do this is to move the decimal point to the right end of the divisor and move the decimal point of the dividend the same number of places.

How to divide a four digit decimal number by a two digit decimal number (e.g 0.4131 ÷ 0.17).

• Place the divisor before the division bracket and place the dividend (0.4131) under it.

           
0.17)0.4131

• Multiply both the divisor and dividend by 100 so that the divisor is not a decimal but a whole number. In other words move the decimal point two places to the right in both the divisor and dividend

        
17)41.31

• Proceed with the division as you normally would except put the decimal point in the answer or quotient exactly above where it occurs in the dividend. For example:

    2.43
17)41.31

Adding Decimals

How to add Decimals that have different numbers of decimal places

• Write one number below the other so that the bottom decimal point is directly below and lined up with the top decimal point.
• Add each column starting at the right side.

Example: Add 3.2756 + 11.48

 3.2756
11.48   
14.7556

Adding Decimals

How to add three or more decimal numbers that have different numbers of decimal places.

• Write the numbers in a column so the decimal points are directly lined up.
• Add each column starting at the right side.

Example: Add 23.143 + 3.2756 + 11.48

23.143

3.2756
11.48   
37.8986

Dividing Fractions by Fractions

To Divide Fractions:

• Invert (i.e. turn over) the denominator fraction and multiply the fractions
• Multiply the numerators of the fractions
• Multiply the denominators of the fractions
• Place the product of the numerators over the product of the denominators
• Simplify the Fraction

Example: Divide 2/9 and 3/12

• Invert the denominator fraction and multiply (2/9 ÷ 3/12 = 2/9 * 12/3)
• Multiply the numerators (2*12=24)
• Multiply the denominators (9*3=27)
• Place the product of the numerators over the product of the denominators (24/27)
• Simplify the Fraction (24/27 = 8/9)
• 
  
• The Easy Way. After inverting, it is often simplest to "cancel" before doing the multiplication. Canceling is dividing one factor of the numerator and one factor of the denominator by the same number.
• For example: 2/9 ÷ 3/12 = 2/9*12/3 = (2*12)/(9*3) = (2*4)/(3*3) = 8/9