Basic Basic Mathematical Mathematical

SkillsSkills

Operations with DecimalsOperations with Decimals

Frengie G. BotoyFrengie G. Botoy

Jagupit NHS, PhilippinesJagupit NHS, Philippines

Addition of DecimalsAddition of Decimals

To add decimals, arrange To add decimals, arrange the numbers so that their the numbers so that their decimal points fall in a decimal points fall in a column. Then perform the column. Then perform the operation.operation.

ExampleExample

27.93 + 6.427.93 + 6.4►First line up the decimal places, then First line up the decimal places, then

perform the operationperform the operation

27.9327.93

+ + 6.4 6.4

34.3334.33

Subtraction of DecimalSubtraction of Decimal

23.07 – 2.323.07 – 2.3►First line up the decimal places, then First line up the decimal places, then

perform the operationperform the operation

23.0723.07

- - 2.3 2.3

20.7720.77

Multiplication of Multiplication of DecimalsDecimals

••Multiply the Multiply the multiplicandmultiplicand by by the the multipliermultiplier

• • the the productproduct will have a will have a many as the combined many as the combined decimal places of both the decimal places of both the multiplicand and multiplier.multiplicand and multiplier.

ExampleExample

0.470.47multiplicandmultiplicand

XX .7 .7multipliermultiplier

0.3290.329 productproduct

Division of DecimalsDivision of Decimals

►To divide a decimal with To divide a decimal with whole number, divide the whole number, divide the dividenddividend by the by the divisordivisor

►The The quotientquotient has the same has the same number of decimal places number of decimal places as that in the dividendas that in the dividend

ex.ex.

0.0810.081 quotientquotient

divisordivisor 7 7 0.5670.567 dividenddividend

00

5656

5656

77

77

00

Rounding Off Numbers Rounding Off Numbers and Decimalsand Decimals

If the number to be dropped If the number to be dropped is between 0 and 4, is between 0 and 4, round round downdown the numbers preceding the numbers preceding it and replace all digits that it and replace all digits that follow with zeroes. follow with zeroes.

Examples:Examples:

453453 450 (nearest ten) 450 (nearest ten)

6.754 6.754 6.75 (nearest 6.75 (nearest hundredth)hundredth)

432 432 400 (nearest 400 (nearest hundred)hundred)

Rounding Off Numbers Rounding Off Numbers and Decimalsand Decimals

If the number to be If the number to be dropped is between 6 and dropped is between 6 and 9, 9, round upround up the numbers the numbers preceding it and replace preceding it and replace all digits that follow with all digits that follow with zeroes. zeroes.

Examples:Examples:

237237 240 (nearest ten) 240 (nearest ten)

25.687 25.687 25.69 (nearest 25.69 (nearest hundredth)hundredth)

2967 2967 3000 (nearest thousand) 3000 (nearest thousand)

Rounding Off Numbers Rounding Off Numbers and Decimalsand Decimals

If the number to be dropped If the number to be dropped is is exactly 5exactly 5 and it is and it is preceded by an preceded by an even numbereven number retain the preceding numberretain the preceding number

Examples:Examples:

334455 340 (nearest ten) 340 (nearest ten)

23.23.665 5 23.6 (nearest 23.6 (nearest tenth)tenth)

998855 980 (nearest ten) 980 (nearest ten)

Rounding Off Numbers Rounding Off Numbers and Decimalsand Decimals

If the number to be If the number to be dropped is dropped is exactly 5exactly 5 and it and it is preceded by an is preceded by an odd odd number,number, add 1 to the add 1 to the preceding numberpreceding number

Examples:Examples:

331155 320 (nearest ten) 320 (nearest ten)

23.23.335 5 23.4 (nearest 23.4 (nearest tenth)tenth)

997755 980 (nearest ten) 980 (nearest ten)

Addition of IntegersAddition of Integers

A. A. The sum of two The sum of two integers with integers with like signs is like signs is the sum of their the sum of their absolute absolute values with the values with the common common sign prefixed before sign prefixed before the the sum.sum.

Ex.Ex.

(-14) + (-7) = -21(-14) + (-7) = -21

(+3) + (+2) = +5(+3) + (+2) = +5

B.B. The sum of two The sum of two integers with integers with different different signs is the difference signs is the difference

of their absolute of their absolute values with the values with the sign of sign of the integer of larger the integer of larger absolute value prefixed absolute value prefixed before before the difference.the difference.

Ex.Ex.

(-14) + (+2) = -12(-14) + (+2) = -12

(-12) + (+28) = +16(-12) + (+28) = +16

Subtraction of Subtraction of IntegersIntegers

To subtract two integers, To subtract two integers, change the sign of the change the sign of the subtrahend and proceed subtrahend and proceed with the process of with the process of addition.addition.

Ex.Ex.

(-14) – (+8) = -22(-14) – (+8) = -22

(+35) – (-15) = +50(+35) – (-15) = +50

(-12) – (-28)(-12) – (-28) = +16 = +16

Multiplication of Multiplication of IntegersIntegers

The product of two The product of two integers having like integers having like signs is positivesigns is positive

Ex.Ex.

(-5) x (-2) = +10(-5) x (-2) = +10

(2) x (10) = 20(2) x (10) = 20

Multiplication of Multiplication of IntegersIntegers

The product of two The product of two integers having integers having unlike signs is unlike signs is negative.negative.

Ex.Ex.

(-4) x (7) = -28(-4) x (7) = -28

(+12) x (-5) = -60(+12) x (-5) = -60

Division of IntegersDivision of Integers

The quotient of two The quotient of two integers having like integers having like signs is positive.signs is positive.

Ex.Ex.

(-12) / (-4) = +3(-12) / (-4) = +3

(12) / (4) = 3(12) / (4) = 3

Division of IntegersDivision of Integers

The quotient of two The quotient of two integers having integers having unlike signs is unlike signs is negative.negative.

Ex.Ex.

(+12) / (-4) = -3(+12) / (-4) = -3

(-15) / (5) = -3(-15) / (5) = -3

The EndThe End