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Chapter 2: Separation Techniques

Mathematics Form 1 - Unit 1 Rational Number

1.1

Integers

	Definition

	Positive and negative whole numbers including 00.

Positive numbers:

Numbers written with the '++' sign or without any sign.
Examples: +12,4,+7,1+12,4,+7,1
Positive integers are integers that have a value greater than 00.

Negative numbers:

Numbers written with the '−−' sign.
Examples: −6,−2,−15,−27−6,−2,−15,−27
Negative integers are integers that are lower than 00.

	Example

	Determine whether the following numbers is an integer. (i) 7227 (ii) 6.86.8 (iii) −12−12

	(i) 7227 is not an integer because it is a fraction. (ii) 6.86.8 is not an integer because it is a decimal. (iii) −12−12 is an integer.

Integers on a number line:

On a number line, the numbers in the positive direction are always greater than the numbers in the negative direction.

Integers in order:

1.3

Positive and Negative Fractions

Positive fractions are fractions more than 00.
Negative fractions are fractions less than 00.

The values of two or more fractions can be compared by equating the denominator first.
Then, arrange the fractions in ascending or descending order.

Combined basic arithmetic operations of positive and negative fractions:

Example

Solve:

116×(34−15)=76×(15−420)=76×1120=77120. 161×(43−51)=67×(2015−4)=67×2011=12077.

1.4

Positive and Negative Decimals

Positive decimals are decimals more than 00.
Negative decimals are decimals less than 00.

The values of two or more decimals can be compared and arranged in ascending order or descending order.

Combined basic arithmetic operations of positive and negative decimals:

Example

Calculate:

(i)

(9.37−0.63)×(−0.4)=8.74×(−0.4)=−3.496. (9.37−0.63)×(−0.4)=8.74×(−0.4)=−3.496.

(ii)

2.34+3.1÷0.2=2.34+(3.1÷0.2)=2.34+15.5=17.84. 2.34+3.1÷0.2=2.34+(3.1÷0.2)=2.34+15.5=17.84.

Rational Numbers

1.5

Rational Numbers

	Definition

	A number that can be written in fractional form pqqp, where pp and qq are integers and q≠0q=0.

Examples: −12,7.5,4−21,7.5,4

Combined basic arithmetic operations of rational numbers:

Example

Calculate:

−0.8+34×(−216)=−810+34×(−136)=−810+(−138)=−6480−13080=−19480=−21740. −0.8+43×(−261)=−108+43×(−613)=−108+(−813)=−8064−80130=−80194=−24017.

Mathematics Form 1 - Unit 1 Rational Number

1.1

Integers

	Definition

	Positive and negative whole numbers including 00.

Positive numbers:

Numbers written with the '++' sign or without any sign.
Examples: +12,4,+7,1+12,4,+7,1
Positive integers are integers that have a value greater than 00.

Negative numbers:

Numbers written with the '−−' sign.
Examples: −6,−2,−15,−27−6,−2,−15,−27
Negative integers are integers that are lower than 00.

	Example

	Determine whether the following numbers is an integer. (i) 7227 (ii) 6.86.8 (iii) −12−12

	(i) 7227 is not an integer because it is a fraction. (ii) 6.86.8 is not an integer because it is a decimal. (iii) −12−12 is an integer.