Filipino Titles
CHAPTER 1 – THE REAL NUMBER SYSTEM
1 .1 – THE CONCEPT OF OPPOSITES
Any movement from an initial point on the number line going to the right is represented by a positive sign (+) ,while a movement to the left is represented by a negative sign (-).These numbers are sometimes called directed numbers or signed numbers.
e.g.
1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS
1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ,add without regard to the signs.Then affix the common sign of the integers.To add two integers with different signs ,consider the distance of each integer from zero (that is, consider the absolute value of each addend).Subtract the shorter distance from the longer distance.
In the answer ,use the sign of the number farther from zero. e.g. 82 + (-62) + 29 + (-25) = (82 + 29) + (-62 + -25) = 111 + (-87) = 24
1.2.2 – SUBTRACTION OF INTEGERS
To find the difference between two signed numbers ,add the negative (or the opposite) of the subtrahend to the minuend.
e.g. a. -62 – (-135) = -62 + 135 = 73 b. 29 - 86 = 29 + (-86) = -57
1.2.3 – MULTIPLICATION OF THE INTEGERS
The product of two integers with the same sign is positive.The product of two integers with different signs is negative.
e.g. a. -20 x 15 = -300 b. -15 x (-35) = 525 c. -45 x (-45) = -2025
1.2.4 – DIVISION OF INTEGERS
The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.
e.g. a. 165 ÷ 15 = 11 b. -180 ÷ (-12) = 15 c. -990 ÷ 22 = -45
1.3 – THE ABSOLUTE VALUE OF A NUMBER
The absolute value of a number is the distance on the number line between the number and zero without any regard to its direction.Thus ,the absolute value of any number is a nonnegative number.
e.g. ǀ-10ǀ + ǀ15ǀ - ǀ6ǀ = 10 + 15 -6 = 25 – 6 = 19
1.4 – OPERATIONS ON FRACTIONS
1.4.1 – ADDITION AND SUBTRACTION OF FRACTIONS
If a ,b ,and c are
1 .1 – THE CONCEPT OF OPPOSITES
Any movement from an initial point on the number line going to the right is represented by a positive sign (+) ,while a movement to the left is represented by a negative sign (-).These numbers are sometimes called directed numbers or signed numbers.
e.g.
1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS
1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ,add without regard to the signs.Then affix the common sign of the integers.To add two integers with different signs ,consider the distance of each integer from zero (that is, consider the absolute value of each addend).Subtract the shorter distance from the longer distance.
In the answer ,use the sign of the number farther from zero. e.g. 82 + (-62) + 29 + (-25) = (82 + 29) + (-62 + -25) = 111 + (-87) = 24
1.2.2 – SUBTRACTION OF INTEGERS
To find the difference between two signed numbers ,add the negative (or the opposite) of the subtrahend to the minuend.
e.g. a. -62 – (-135) = -62 + 135 = 73 b. 29 - 86 = 29 + (-86) = -57
1.2.3 – MULTIPLICATION OF THE INTEGERS
The product of two integers with the same sign is positive.The product of two integers with different signs is negative.
e.g. a. -20 x 15 = -300 b. -15 x (-35) = 525 c. -45 x (-45) = -2025
1.2.4 – DIVISION OF INTEGERS
The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.
e.g. a. 165 ÷ 15 = 11 b. -180 ÷ (-12) = 15 c. -990 ÷ 22 = -45
1.3 – THE ABSOLUTE VALUE OF A NUMBER
The absolute value of a number is the distance on the number line between the number and zero without any regard to its direction.Thus ,the absolute value of any number is a nonnegative number.
e.g. ǀ-10ǀ + ǀ15ǀ - ǀ6ǀ = 10 + 15 -6 = 25 – 6 = 19
1.4 – OPERATIONS ON FRACTIONS
1.4.1 – ADDITION AND SUBTRACTION OF FRACTIONS
If a ,b ,and c are