Topic 1(Operation on Numbers)

8/3/2019 Topic 1(Operation on Numbers)

http://slidepdf.com/reader/full/topic-1operation-on-numbers 1/34

Murugiah Velayutham 1

Teaching of Mathematicsin Form Two

TOPIC 1- OPERATIONS ON

NUMBERS




TOPIC 1 – Concept of Integers

The basic idea of integers can beexplained by using a horizontalnumber line or simply a number line.

0 1 2 3 4 5 6-1-2-3-4-5-6

Opposites

Negative integers Positive integers




Definitions: The number line goes on forever in both

directions. This is indicated by the arrows.

Whole numbers greater than zero are calledpositive integers. These numbers are to theright of zero on the number line.

Whole number less than zero are callednegative integers. These numbers are to theleft of zero on the number line.

The integer zero is neutral. It is neitherpositive nor negative.

Two integers are opposites if they are each thesame distance away from zero but on theopposite sides of the number line.




Negative Numbers

Please emphasize to your studentsthat we will use negative numbers inlots of different situations.

For examples:• Reading a thermometer.

• Parking car at a basement.

• Bank statements.




Reading a thermometer

Can you notice that the scales on thethermometers are different?




Negative Numbers

Buildings:Your students could have theexperience of being in the lift of a

building that goes underground.

What does the “Symbol” represents?




Number Lines and Integers

Write an integer to represent each of thefollowing situations:

10 degrees above zeroa loss of 16 dollars

a gain of 5 points

8 steps backward




Comparing Values of Two Integers

In the early afternoon thetemperature is 15oC. But by earlyevening the temperature goes downto 12oC.

What is the temperature decrease?




Comparing Values of Two Integers

During winter the temperature in theearly morning could be -3oC. But bylunch time it goes up to 6oC.

What is the temperature increase?




CONCEPT OF INTEGERS

1. Addition and SubtractionADDING:

In order to add by using the number line the

students should start from the first number andmove towards the right with the number of unitsas equal to the second number.

Example 1: Calculate -3 +5

Answer: (-3)+(5) = -3 + 5 = (+2) = 2




CONCEPT OF INTEGERS

1. Addition and SubtractionADDING: Example 2: Gopal owes his friend Ah Seng RM3.

If he borrows another RM6, how much

will he owe him altogether?

Answer: (-3)+(-6) = -9




ADDITION GLOSSARY

Example: 3 + 4 =___ Words/ Terminology Statements

Add 3 add 4 is 7.

Altogether Altogether, 3 and 4 make 7.

Increase If you increase 3 by 4 you get

More 7 is 3 more than 4.

Plus 3 plus 4 is 7.

Sum The sum of 3 and 4 is 7.Total The total of 3 and 4 is 7.




SUBTRACTING:

Mark the first number on the number line. Thenmove towards the left of it with the number ofunits as the second number given.

Example 1: Calculate +2 -4

Answer: (+2)-(+4) = - 2




SUBTRACTION GLOSSARY

Example: 8 - 5 =___ Words/ Terminology Statements

Decrease If you decrease 8 by 5 you get 3.

Difference The difference between 8 and 5 is 3.

Fewer than 3 is 5 fewer than 8.

Less than 3 is 5 less than 8.

Minus 8 minus 5 is 3.

Reduce If you reduce 8 by 5 you get 3.Subtract 8 subtract 5 is 3.

Take away 8 take away 5 is 3.




2. Multiplication and Division(a) When we multiply two integers with the same or

like signs, the result is always positive.

(b) When we multiply two integers with different orunlike signs, the result is always negative.

Positive x positive = positive (+) x (+) = (+)

Negative x negative = positive (-) x (-) = (+)

Positive x negative = negative (+) x (-) = (-)

Negative x positive = negative (-) x (+) = (-)




2. Multiplication and Division(c) When we divide two integers with the same

signs, the result is always positive.

(d) When we divide two integers with different orunlike signs, the result is always negative.

Positive ÷ positive = positive (+) ÷ (+) = (+)

Negative ÷ negative = positive (-) ÷ (-) = (+)

Positive ÷ negative = negative (+) ÷ (-) = (-)

Negative ÷ positive = negative (-) ÷ (+) = (-)




3. Combined or Mixed OperationsTo perform any computation involving a combinedor mixed operations, we introduced theBODMAS rule to the students.

Bracket

Power Of

Division

Multiplication

AdditionSubtraction




3. Combined or Mixed Operations

Example 1:

Try to solve the following questions:

(a) 7 – (-6 +2) + (-5) =

(b) - 12 – (-6) – (- 3) =

(c) 3 x (-4) ÷ (-2) =

(d) 10 ÷ (-6) x (-12) =

(e) -6 + (8 ÷ (-2)) x 3 + 5 =




Fractions and Decimals

1. Positive and Negative FractionsRepresentation of Fractions on a Number Line

0

Please note that:

• Fractions to the right of zero has a positive value.

• Fractions to the left of zero has a negative value.

• A positive fraction is a fraction with a “+”sign andnormally is omitted.

• A negative fraction is a fraction with a “-” sign.




Fractions and Decimals

2. Positive and Negative DecimalsRepresentation of Decimals on a Number Line

-0.5 -0.3 0 +0.2 +0.3 +0.5

Please note that:

• Decimals to the right of zero has a positive value.

• Decimals to the left of zero has a negative value.

• A positive decimal is a decimal with a “+”sign andnormally is omitted.

• A negative decimal is a decimal with a “-” sign.




Fractions and Decimals To represent a decimal on a number line, divideeach segment of the number line into ten equalparts.

Example :

To represent 8.4 on a number line, divide thesegment between 8 and 9 into ten equal parts.

8.0 8.4 9.0

The arrow is four parts to the right of 8 whereit points at 8.4.




Arithmetic Involving Integers,

Fractions & Decimals 1. Adding and Subtracting Decimals

Be sure to line up the terms so that all

the decimal points are in a vertical line.Example:




2. Multiplying Decimals

Example 1:

Example 2:10 x 0.6284 = 6.284 (1 zero, 1 space right)

100 x 0.6284 = 62.84 (2 zeroes, 2 spaces right)

1000 x 0.6284 = 628.4 (3 zeroes, 3 spaces right)

10,000 x 0.6284 = 6284 (4 zeroes, 4 spaces right)

100,000 x 0.6284 = 62,840 (5 zeroes, 5 spaces right)




3. Dividing Decimals

Example 1:




4. Adding & Subtracting Fractions

Adopt the following steps:1. Change any mixed numbers to improper fractions.

2. Find the lowest common multiple of thedenominators.

3. Express all fractions with the same denominator.4. Add the numerators to obtain the numerator of

the answer; and then simplify the fraction, ifpossible.

5. Write the answer either as an proper fraction oras a mixed number as appropriate.




4. Adding & Subtracting Fractions

Example:

Answer:




5. Multiplications of Fractions

Adopt the following steps:1. Change any mixed numbers to improper fractions.

2. Cancel any factors common to both thenumerator and denominator.

3. Multiply the remaining terms in the numeratorand in the denominator.

4. Write the answer either as a proper fraction oras a mixed number as appropriate.




5. Multiplication of Fractions

Example:

Answer:




6. Division of Fractions

Adopt the following steps:1. Change mixed numbers into improper fractions.

2. Multiply the first fraction by the reciprocal ofthe second fraction

In General:

Example:

Simplify




7. Directed Numbers

Directed numbers are those numbersthat include integers, fractions anddecimals.

Example:

Solve the following

Try also Self-check 1.1 in page 23




Word Problems With Mixed Operations

Once the students have mastered theconcept well, we can gradually introducesome examples that related to directednumbers in our daily life i.e. the word

problems.Example 1:

A diver was diving 118 m below sea level.

He went down 15 m and came up 40 magain. How far below sea level did he dive?




Word Problems With Mixed Operations

Example 2:During winter, town B records a temperatureof -7oC. In summer, the temperature rises to+33oC. What is the difference between thetwo temperatures?

Example 3:

The price of 6 pendrives is RM132. Shamsul

bought 12 pendrives and paid RM300. Howmuch money was returned to him?

Topic 1(Operation on Numbers)

Documents

Transcript of Topic 1(Operation on Numbers)