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FRACTION (PECAHAN)

IN THE CASE OF 2 CARS2 IS THE NUMBER AND CAR IS THE OBJECT

AND IN THE CASE OF 3 FOOTBALLS3 IS THE NUMBER AND FOOTBALL IS THE OBJECT

From the details above, the principle that applies in this concept proves that ADDITION OR SUBTRACTION COULD ONLY BE DONE BETWEEN THE SAME OBJECT;

EXAMPLE:

1 CAR + 2 CARS = 3 CARS OR 5 MARBLES – 2 MARBLES = 3 MARBLES

However, no addition or subtraction could be done between 2 or more different objects; EXAMPLE:     3 CARS + 2 FOOTBALLS = 3 CARS + 2 FOOTBALLS

In fraction; by taking ¼ as an example, 1 comes as a number whilst 4 as an object. However in the mathematics term, a number is also known as numerator whilst the object is known as denominator. By applying the same principle as mentioned above, a fraction could only be added or subtracted when it has the same object or denominator. Example:

2/5 + 1/5 = 3/5 (SINCE BOTH HAS THE SAME OBJECT OF 5;   2 & 1 THAT COMES AS A NUMBER COULD BE ADDED)

10/11 – 8/11 = 3/11 (SINCE BOTH HAS THE SAME OBJECT OF 11;  10 & 8 THAT COMES AS A NUMBER COULD BE SUBTRACTED)

 

STEPS OF SOLVING FRACTION – ADDITION AND SUBTRACTION FOR NUMBER THAT HAS DIFFERENT DENOMINATOR (OBJECT)

EXAMPLE 1

1 1/2  + 3 2/3 + 4 3/4   = (1/2 + 2/3 + 3/4) + (1 + 3 + 4)

In solving fraction, always start with fraction numbers and in this case 1/2 +  2/3 + 3/4

STEP 1 – UNIFORMISED THE DENOMINATOR (OBJECT)

Prepare a list of multiplication table for 2, 3 and 4; then pick the least common multiplication

1/2 = 1 x 6/ 2 x 6 = 6/12

2/3 = 2 x 4/ 3 x 4 = 8/12

3/4 = 3 x 3/ 4 x 3 = 9/12

STEP 2 – SUM UP ALL THE NEW FRACTION

6/12 + 8/12 + 9/12 = 23/12 (if the new fraction has larger numerator than denominator, convert the fraction to mixed number)

STEP 3 – CHANGE THE FRACTION TO MIXED NUMBER

23/12 = 23 ÷ 12 = 1 11/12  = 1 + 11/12

STEP 4 – SUM UP THE MIXED NUMBER

1 + 11/12 + (1 + 3 + 4) = 9 + 11/12  OR  9 11/12

EXAMPLE 2

5 3/4 – 2 2/3 – 1 1/2 = ( 3/4 – 2/3 – 1/2 ) + ( 5 – 2 – 1)

In solving fraction, always start with fraction numbers and in this case 3/4 – 2/3 – 1/2

STEP 1 – UNIFORMISED THE DENOMINATOR (OBJECT)

Prepare a list of multiplication table for 2, 3 and 4; then pick the least common multiplication

1/2 = 1 x 6/ 2 x 6 = 6/12

2/3 = 2 x 4/ 3 x 4 = 8/12

3/4 = 3 x 3/ 4 x 3 = 9/12

STEP 2 – SUBTRACT ALL THE NEW FRACTION

9/12 – 8/12 – 6/12 ; Since 9 is not sufficient to minus 8 and 2, then add 1 which is taken out of 5 to be added to 9/12; with that action will also make 5 become 4 and 1 become 12/12

The new set of fraction will read as follows :

12/12 + 9/12 – 8/12 – 6/12 = 7/12

STEP 3 – SUBTRACT ALL THE INTEGERS AND SUM UP WITH THE FRACTION ANSWER

(4 – 2 – 1) + 7/12 =1 + 7/12 OR 1  7/12