**FRACTION (PECAHAN)**

IN THE CASE OF** 2 CARS ; ****2** IS THE **NUMBER** AND **CAR** IS THE **OBJECT**

AND IN THE CASE OF **3 FOOTBALLS; ****3** 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)**

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**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**