Algebraic Expressions - Evaluation 3

Algebraic Expressions - Evaluation involving Decimals

Decimal addition:

Decimals may be added by the following procedure :
Add : 4.31+ 2.58
Explanation : 431 + 258 = 689
There are 2 decimal places in thenumbers being added, so the sum must have 2 decimal places.
Thus, 4.31+ 2.58 = 6.89

Decimal subtraction:

Decimals may be subtracted by the following procedure :
Subtract : 6.89 − 2.58
Explanation : 689 − 258 = 431
There are 2 decimal places in thenumbers being subtracted, so the difference must have 2 decimal places. Thus, 6.89 − 2.58 = 4.31

Decimal multiplication:

Decimals may be multiplied by the following procedure :

Decimals are multiplied like whole numbers and the decimal point placedappropriately.
The decimal point is placed such that the number ofdecimal places in the product equals

Multiply : 9.31 × 3 = 27.93
Explanation : 931 × 3 = 2793
There is 2 decimal place in 9.31 (multiplicand) and 0decimal place in 3 (multiplier).
The product must have 2 + 0 = 2 decimal places.
Thus, 9.31 × 3 = 27.93

When a decimal is multiplied by10, the decimal point shifts one place to the right.
When a decimal ismultiplied by 100, the decimal point shifts two places to the right;and so on.

Example : 9.31 × 10 = 93.1 and 9.31 × 100 = 931

Decimal division:

Decimals may be divided by the following procedure :

Decimals are divided like whole numbers and the decimal point placedappropriately.
The decimal point is placed such that the quotient has as many decimaldigits as the dividend.
If the divisor consists of decimal then first convert it into whole number by multiplying both divisor and dividend with 10, 100 and so on accordingly and follow step 1 and 2.

Divide : 27.93 ÷ 3 = 9.31
Explanation : 2793 ÷ 3 = 931
There are 2 decimal places in thedividend (27.93) so the quotient must have 2 decimal places.
Thus, 27.93 ÷ 3 = 9.31

Divide : 27.93 ÷ 0.3 = 93.1
Explanation : (27.93 × 10) ÷ (0.3 × 10) [Multiply divisor and dividend by 10]
= 279.3 ÷ 3 = 93.1
There is 1 decimal place in thedividend (279.3) so the quotient must have 1 decimal place.
Thus, 27.93 ÷ 0.3 = 93.1

When a decimal is divided by 10, the decimalpoint shifts one place to the left.
When a decimal is divided by 100,the decimal point shifts two places to the left; and so on.

Example : 93.1 ÷ 10 = 9.31 and 93.1 ÷ 100 = 0.931

Note: Zeros to the right of a decimal fraction do not change the value of the decimal.
Example : 4.31 = 4.310 = 4.3100 = 4.31000

Example for evaluating an algebraic expression involving decimals:
Find the value of the algebraic expression:
y + 12 where y = 7.3
Substitute y = 7 in the algebraic expression to get
y + 12 = 7.3 + 12 = 19.3