We HEART Maths !!!: 2013

Thursday, April 25, 2013

Wednesday, April 24, 2013

Tux Math

Here are some reviews on Tux Math games.

You "shoot" meteorites that are falling down by answering math problems (type the problem's answer and press Enter/Return). If you can't answer one, the meteorite does some damage to one of the penguin's igloo. Then after enough damage, the penguin in that igloo leaves (walks away).

But, once you answer a red "fiery" question that falls down real quick, you can get a cloud that comes and fixes the igloo. Then your penguin comes back! I think that's so cute!! You can only lose if all your penguins go away.

The background is always an image from space.

The options include any of the four operations, or have them mixed. You can practice specific times tables for example, which is good for my younger daughter at this time. As you go along in a game, then the questions start coming down quicker. At first they come down quite slow.

There's a training section, and there's a section where it gives you random questions. In that one, you play as long as you want, and when you stop, it'll tell you if you are in the top ten highest scores for you. If so, then you go in the "hall of fame."

Once you finish any particular type of problems (for ex. addition 0-5 or multiplication by 4), the star for that turns glowing yellow, and that's what my kids are after--they want to turn all those stars yellow. That's only in the training part, though. In the training part you have to answer a certain amount of questions.

You can make as many new "accounts" as you want and fill the "hall of fame" with you and your various nicknames.

It's just simple free game for math practice; there are no special features such as reports or training the facts you answer wrong.

Tux Math, or Tux of Math Command is software that is available as a free download for Windows, Mac, and Linux. Download it here.

My Dear Aunt Sally - game for order of operations

You've surely heard of the acronym PEMDAS for the order of operations (Please Excuse My Dear Aunt Sally) - standing for Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.

There's a new game for order of operations called My Dear Aunt Sally. You can play it free online, or purchase an inexpensive app for your tablet.

It's a very good game, and takes some thinking! You need to place the given numbers into two expressions so that the operations make the two expressions have the same value.

Here are some screenshots. The first one is the easiest level. The addition on the top has to have the same value as the multiplication/addition expression on the bottom.

It gets harder if you choose to include exponents:

You can also choose to use fractions, so it becomes harder yet

Click Here to Play

Friday, April 12, 2013

Comics

Maths Homework...

Comics - Maths Puns

http://www.smackjeeves.com/images/uploaded/comics/d/2/d26fdb4c2uIKy.jpg

:D

Funny...

$http://www.math-problem-solving.com/images/funny_math_cartoon2.gif$

Form 3 Chapter 8 - Solid Geometry 3

Form 1 Chapter 9 Lines & Angles

a. Right Angle = 90°
b. Acute Angle = 0° to 90°
c. Obtuse Angle = 90° to 180°
d. Reflex Angle = 180° to 360°

Form 1 Chapter 8 Basic Measurements

Chapter 8 Basic Measurements

Form 1 Chapter 7 Algebraic Expressions I

Chapter 7 Algebraic Expressions 1.

Simplify a fraction multiplication before multiplying

140 divided by 360, multiplied by 2, multiplied by 22 divided by 7, multiplied by 12:

140

360 × 2 × 22

7 × 12

Solution:

You can either put everything in the calculator, multiplying the top numbers, then dividing by 360 and 7.

Or, you can simplify before you multiply. This process is actually quite handy!

For example, the first fraction 140/360 can be simplified into 14/36, and then further into 7/18 before you multiply.

We get

Now, the 7 in the numerator and the 7 in the denominator cancel out.

Why? Every time we have the same number in the numerator and the denominator, and the only other operation involved is multiplication (like in our example), that number cancels out. It becomes the same situation as if you multiply by 7 and divide by 7: the result is 1. As a shortcut, we can cancel out those numbers and write 1's in their places.

Now we get

Then, 22 and 18 have a common factor 2... so that 2 cancels out. You can think of it as being...

2 × 9

2 × 11

... or you can think of it as if the fraction 22/18 was in there, which simplifies to 11/9.

One last simplification: 12 in the top and 9 in the bottom have a common factor 3... so, divide both 12 and 9 by that 3 and get:

Now it is easy to multiply mentally (regular fraction multiplication):

Thursday, April 11, 2013

Largest prime yet found!!

Largest prime yet found

Curtis Cooper at the University of Central Missouri in Warrensburg has found the largest prime number yet.

(He hasn't found the largest prime as there is no such thing -- he's just found a new prime that is larger than any other primes people have found.)

It is a Mersenne prime, which means it is of the form 2P − 1, where P itself is prime. The one Cooper found is 257,885,161 − 1, and it has 17 million digits!!

So no, I'm not going to type it out here! Writing it in the form 257,885,161 − 1 is way handier, isn't it? Shows us how important exponents are. So, this new prime is 2 multiplied by itself 57,885,161 times, and then you subtract 1.

This is what Cooper himself says about the hunt for new primes:

"Every time I find one it is incredible," Cooper said. "I kind of consider it like climbing Mount Everest or finding a really rare diamond or landing somebody on the moon. It's an accomplishment. It's a scientific feat."

Logical 'imbalance' puzzles

Logical 'imbalance' puzzles
Here's something for all of us puzzle lovers: logic imbalance problems invented by Paul Salomon (HT Denise). You need to order the shapes by their 'weight':

Imbalance 4

Which shape is the heaviest? Which is the second heaviest?
Picture by Paul Salomon

Think logically - or write down some inequalities and use algebra. Pretty cool. They are simple, yet captivating. A new, creative idea! Paul also recommends you start making your own imbalance puzzles, as a more 'puzzling' exercise.

Quiz

FORM 3 - Chapter 9 scale drawing

NOTE MATH FORM 3 - 9 scale drawing from Nad0209

Form 3 Chapter 04 : Statistic

Form 3: Chapter 5 - Indices

Exercise

Tuesday, April 9, 2013

Form 5 Modern Maths Videos

Form 5 Modern Maths Videos

5 Sains Akasia

5 Sains Belian

5 Sains Cengal

5 Sains Dedali

5 Sains Meranti

5 Kemanusiaan Kemuning

Form 1 Chapter 3

FRACTIONS

A) Reading Fractions

A fraction is a number that represents a part

of a whole. It is written as p where p and q are
q
whole numbers and q # 0.

p is read as 'p over q'.
q
For example:-

(a) 3 is read as 'three over four' or three quarter.
4
(b) 2 is read as 'two over three' or 'two third'.
3
B) Representing Fractions with Diagrams.

1. Fractions can be represented with diagrams and number lines.

For example:-

In each of the diagrams above, the shaded parts are 2

out of 3 equal parts, that is 2
   3
and the bottom number is called the numerator.

For example:-

2 ( Numerator )
3 ( Denominator )

In the fraction 2, 2 is the numerator and 3 is denominator.
3
3. The numerator represents the number of equal parts

that are shaded and the denominator represents the

total number of equal parts in one whole.

4. When the numerator is the same as the denominator,

the value of the fraction is equal to 1. The figure 1

represents all the parts of a fraction.

For example:-

(a)

   (b)

Worked example

(a) Shade the diagram to represent 3
    5

(b) Write the fraction represented by the

   shaded parts in the diagram below.


Solution

(a) Shade any 4 parts.


(b) 4 parts out of 7 equal parts are shaded.

The fraction represented by the shaded

parts is 4 .
7

EQUIVALENT FRACTIONS

A)Finding Equivalent Fractions

1. Equivalent fractions are fractions having

the same value.

For example:-

(a)

The shaded parts in both the triangle are

equal.

Therefore, 1 and 2 have the same value.
   2    4
1 and 2 are equivalent fractions.
2 4
Therefore, 1 = 2 .
2   4
( when you fold the two triangle along their

vertical lines, you will find that the shaded

   portions are equal.)

(b)

The shaded parts of all the three rectangles

are equal.

Therefore, 1 , 2 , and 4 have the same value.
2 4 16

   1 = 2 = 4 are equivalent fractions.
2 4 16

Therefore,   1 = 2 = 4.
4 8 16

2. Equivalent fractions can be obtained by multiplying

the numerator and denominator by the same whole

numbers ( greater than 1 ).

For example:-

2 = 2 x 2 = 2 x 3 = 2 x 4 = 2 x 5
3 3 x 2 3 x 3 3 x 4    3 x 5

   = 4 = 6 = 8 = 10
   6 9 12 15

Worked example

List the first three equivalent fractions of

Solution



Worked example

List all the equivalent fractions of 3 with

denominators between 30 and 50.

Solution

B) Determining whether Two given

Fractions are Equivalent

To determine whether two given fractions

are equivalent or not, we can use diagrams calculation.

Worked example

Are 2 and 6 equivalent fractions ?
4 8

Solution

2 6
4 8

The shaded parts for 2 and 6 are the same.
4 8
Therefore, 2 and 6 are equivalent fractions.
4 8

Worked example

Are 1 and 3 are not equivalent fractions ?
2 4

Solution

1 and 3 are not equivalent fraction because
2 4

their shaded parts are not the same.

Worked example

Determine whether the following pairs of

fractions are equivalent.

(a) 4 and 1
8 2

(b) 4 and 1
6 3

Solution

(a)

4 and 1 are at the same position on the
8 2
number line.

Therefore, 4 and 1 are equivalent.
8 2

(b)

4 and 1 are at different positions on the
6 3
number line.

Therefore, 4 and 6 are not equivalent.
6 3

Worked example

Determine whether 2 and 4 are equivalent.
6 12
Solution

Worked example

Determine whether 3 and 5 are equivalent.
6 12
Solution

   3 and 5 are not equivalent.
6    12

C) Comparing the values of Two Fractions

1. When comparing two fractions having the same

denominator, the fraction with the bigger numerator

is greater in value.

For example:-

2. When comparing two fractions having the same

numerator, the fraction with the smaller denominator

is greater in value.

For example:-

3. To compare two fractions having different numerators,

and denominators, carry out the following steps.

Step 1 : Find the LCM of the two denominators.

Step 2 : Convert each of the given fraction with the

LCM as its denominator.

Step 3 : Compare the numerators of the fractions.

Worked example

Which is greater, 7 or 4 ?
9 5
Solution

7 = 35 ( LCM of 9 and 5 is 45 )
9 45

4 = 36
5    45

35 < 36
45 45

Therefore, 4 is greater.
    5
D) Arranging Fractions in Order

(a) Arrange 2 , 6 , 4 , 8 in increasing order.
9 9 9 9
(b) Arrange 1 , 1 , 3 and 1 in decreasing order.
2 3 4 6
Solution

(a) 2 , 4 , 6 , 8
9 9 9 9

(b) 1 = 1 x 6 = 6 ; 1 = 1 x 4 = 4 ;
2 1 x 6 12 3 3 x 4 = 12

   3 = 3 x 3 = 9 ; 1 = 1 x 2 = 2 ;
4 4 x 3 12 6 6 x 2 12

Therefore, the fractions arranged decreasing order

   are 3 , 1 , 1 , 1 .
   4 2 3 6 ( from the biggest to the smallest )

E) Simplifying Fractions

1. A fraction is in its lowers terms if the numerator and

denominator have no common factor except 1.

2. To simplify a fraction, divide the numerator and deno-

minator repeatedly by their common factors.

For example:-

3. To simplify a fraction to its lowest terms, divide the nume-

rator and the denominator by their HCF.

4. All answer must be given in their lowest terms.

Worked example

Simplify 12 to its lowest terms.
18
Solution

MIXED NUMBERS

A) Recognising Mixed Numbers

1. A mixed number is a number consisting of a

whole number and a fraction.

For example:-

2. All mixed numbers are greater than 1.

B) Representing Mixed Numbers with Diagrams

Mixed numbers can be represented by diagrams.

For example:-

C) Writing Mixed Numbers based on the given Diagrams

For example:-

D) Comparing andd Arranging Mixed Numbers

1. Like fractions, mixed numbers can be compared and

arranged by using a number line. Any number on the

number line is greater than the numbers to its left.

2. To compare and arrange mixed numbers having the

same whole number part but different fractional part,

carry out following steps.

Step 1 : Find the LCM of the dinominators.

Step 2 : Convert each of the given fractions to an equivalent

fraction with the LCM as its denominator.

Step 3 : Compare and arrange the mixed numbers.

Worked Example

Which is greater,

Arrange both mixed numbers on a number line.

Solution

The LCM of 9 and 3 is 9.


Since 3 6 is greater than 3 5 , therefore 3 2 is
   9 9 3

Worked Example

(a) Arrange 2 1 , 2 2 , 2 1 in increasing order.
2 3 6
(b) Arrange 2 3 , 1 1 , 2 1 in decreasing order.
4 3 2
Solution

(a) The LCM of 2, 3 and 6 is 6.

2 1 = 2 3 ; 2 2 = 2 4
2 6 3 6

Therefore, the mixed numbers arranged increasing

order are 2 1 , 2 1 , 2 2 .
6 2    3
(b) The LCM of 4, 3 and 2 is 2.

1 1 is smaller than 2 1 and 2 3 .
3 2 4
2 1 = 2 2
   2 4

Therefore, the mixed numbers arranged in decreasing

order are 2 3, 2 1 , 1 1 .
4 2 3

3.4 PROPER FRACTIONS AND IMPROPER FRACTIONS

A) Determining Proper Fractions and

Improper Fractions

1. A proper fraction has a numerator which is

smaller than the denominator.

For example:-

1 , 3 , 5 , 7 , 13
2 4 7 12 30

2. An improper fraction has a numerator which

is the same as or greater than the denominator.

For example:-

3 , 4 , 7 , 10 , 12 , 15
2 3 3 10 5 9

Worked Example

Determine whether each fraction below is a proper

fraction or an improper fraction.

(a) 6 (b) 7 (c) 13
    4 7 16

Solution

(a) 6 is an improper fraction.
4

(b) 7 is an improper fraction.
7

(c) 13 is a proper fraction.
16

B) Converting Whole Numbers to Improper Fraction.

1. All whole numbers are improper fractions with

1 as their denominators.

For example:-

5 = 5 , 13 = 13 , 32 = 32
1 1 1

2. Whole numbers can be converted to improper

fractions with other denominators.

For example:-

(a) 4 = 4    4 = 4 x 12
1     1 x 12

= 4 x 8    = 48
1 x 8 ( 8 as denominator )     12 ( 12 as denominator )

= 32
8

C) Converting Mixed Numbers to Improper Fractions.

To change a mixed number to an improper fraction,

multiply the whole number by the denominator and

then add the product to the numerator. The denomi-

nator remains the same.

Worked Example

Convert these mixed numbers to improper fractions.

(a) 5 5 (b) 10 6
9 7

Solution

(b) 10 6 = 10 x 7 + 6
7    7

= 76
   7

D) Converting Improper Fractions to Mixed Numbers.

1. To change an improper fraction to a mixed number,

divide the numerator by the denominator.

2. The quotient obtained is the whole number part and

the remainder is the numerator of the fractional part.

Worked Example

Convert these improper fractions to mixed numbers.

(a) 57 (b) 92
4 8

Solution

(a) 57 = 14 1
4    4

(b) 92 = 11 4
8 8

3. Where possible, simplify the improper fraction to

its lowest terms before converting it to the mixed

number.

Worked Example

Change these improper fractions to mixed numbers

or whole numbers.

(a) 129 (b) 96
9 8

Solution

ADDITION AND SUBTRACTION OF FRACTIONS

A) Addition of Fractions

i) Adding two fractions with the same or common

denominator

1. To add two fractions with the same denominator,

keep the denominator and add the numerators.

2. Answer are always written in their lowest terms.

Worked Example

Find the value of 5 + 7 .
9    9
Solution

5 + 7 = 12
9 9 9 ( No change in the denominator. )

= 1 3 ( Change improper fraction
9 to mixed number )

= 1 1
3 ( Simplify to lowest terms )

ii) Adding two fractions with different denominators

To add two fractions with different denominators, first

find the LCM of the denominators and then convert

both the fractions with the same denominator.

Worked Example

Solve the following.

(a) 5 + 2
12 3

Solution

(a) 5 + 2 = 5 + 2 x 4
12 3 12   3 x 4 ( LCM of 3 and 12 is 12 )

= 5 + 8
12 12

= 13
12

= 1 1
12 ( Change to mixed number. )

iii) Adding whole number and fraction, a mixed

number is produced

Worked Example

Solve the following.

(a) 12 + 3 (b) 7 + 6
5    9

Solution

(a) 12 + 3 = 12 3
5    5
   ( Answer are mixed numbers. )
(b) 7 + 6 = 6 7
   9 9

iv) Adding fractions and mixed numbers

1. To add a fraction and a mixed number, keep the

whole number and add the fractional parts like

adding the fractions.

2. Answer are always written in their lowest terms.

Worked Example

Simplify

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

Solution

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

= 4 + 3
3

= 4 + 1

= 5

v) Adding two mixed numbers

Worked Example

Solve 3 5 + 4 5
9 6

Solution

vi) Adding three fractions

Before performing the addition, convert the fractions

to their respective equivalent fractions with the same

denominator.

Worked Example

Find the value of

(a) 5 + 4 + 3 1
   5 2

Solution

(a) 5 + 4 + 3 1 = 5 + 4 + 7
5    2    1 5 2

= 50 + 8 + 35
10

= 93
10

= 9 3
10

B) Problem Solving involving Addition of Fractions

Worked Example

Bag P weighs 1 4 kg. Bag R is 2 3 kg heavier than
5 10
bag P. Calculate the total mass of the two bags.

Solution

1. Understand the problem

Given information :

Bag P weighs 1 4 kg.
5
Bag R is 2 3 kg heavier than bag P.
10
Find : Total mass of bags P and R.

2. Devise a plan

Use addition.

3. Carry out the plan

1 4 + 2 3 + 1 4 = 9 + 23 + 9
   5 10 5 5 10 5

= 18 + 23 + 18
10

= 59
10

= 5 9
10
Therefore, the total mass of bags P and R is 5 9 kg.
10
4. Check

1 4 + 2 3 = 9 + 23
5 10 5 10

= 18 + 23
10

= 41
10

41 + 9 = 41 + 18
10 5 10

= 59 = 5 9
10 10

c) Subtraction of Fractions

i) Subtracting fraction with the same or common

denominator.

1. To subtract two fractions with the same denominator,

keep the denominator and subtract the numerators.

2. Answers are always written in their lowest terms.

Worked Example

Solve 9 - 3 .
14 14

Solution

9 - 3 = 9 - 3
14 14 14 ( subtract. )

= 6
14

= 3 ( lowest terms )
7

ii) Subtracting fractions with different denominators

To subtract two fractions with different denominators,

first find the LCM of the denominators and then convert

both the fractions to their respective equivalent fractions

with the same denominator.

Worked Example

Solve 5 - 3
6 8

Solution

5 - 3 = 5 x 4 - 3 x 3
6 8 24 24 ( LCM of 6 and 8 is 24. )

= 20 - 9
24

= 11
24

iii) Subtracting a fraction from a whole number

To subtracting two fraction from a whole number,

convert the whole number to an improper fraction

with a common denominator as the fraction.

Worked Example

Solve the following.

Solution

iv) Subtracting a fraction from a mixed number

To subtract a fraction from a mixed number, carry

out the following steps.

Step 1 : Convert the mixed number to an improper

fraction.

Step 2 : Find the LCM of the denominators.

Step 3 : Convert both the fractions to their respective

equivalent fractions with the same denominator.

Worked Example

Simplify the following.

(a) 5 5 - 3
6 4

Solution

(a) 5 5 - 3 = 35 - 3
6 4 6 4

= 70 - 9
12

= 61
12

= 5 1
   12

v) Subtracting two mixed numbers

Worked Example

Simplify 5 1 - 3 5
4 6

Solution



vi) Subtracting three fractions

Carry out the subtractions of three fractions

from left to right.

Worked Example

Simplify

(a) 9 - 1 - 1
10 2 5

Solution

D) Problem Solving involving Subtraction of Fractions

Worked Example

Puan Aishah bought 5 kg of cooking oil. She used

up 3 2 kg. Find the amount of oil remained.
5

Solution

1. Understand the problem

Given information :

3 2 kg from the 5 kg of oil was used.
   5
Find : Amount of oil remained

2. Devise a plan

Use subtraction.

3. Carry out the plan

5 - 3 2 = 5 17
5 5

= 25 - 17
5

= 8
5

= 1 3
5
Therefore, amount of oil remained was 1 3 kg.
5

4. Check

3 2 + 1 3 = 17 + 8
   5    5    5    5

= 25
5

= 5

MULTIPLICATION AND DIVISION OF FRACTIONS

A) Multiplication of Fractions

i) Multiplying a whole number by a fraction

Multiplying of a whole number by a fraction

or a mixed number is the repeated addition

of the fraction or the mixed number.

Worked Example

Solve 6 x 3
4

Solution

Method 1 : By using diagrams

6 x 3
4

Method 2 : By repeated addition

6 x 3 = 3 + 3 + 3 + 3 + 3 + 3
4 4 4 4 4 4 4

= 18
4

= 4 1
2

Method 3 : By multiplying directly

Method 4 : By cancellation

ii) Multiplying a fraction by a whole number

Worked Example

Find the value of 4 x 25.
5

Solution

Method 1 : By multiplying directly

4 x 25 = 100
5 5

= 20

Method 2 : By cancellation

iii) Multiplying two fractions

Evaluate 2 x 3
3    8

Solution

Method 1 : By using diagrams

2 x 3
3    8

Method 2 : By cancellation

2 x 3
3 8

iv) Multiplying two mixed numbers ( including

whole numbers )

In multiplication involving a mixed number, change

the mixed number to an improper fraction first.

Worked Example

Simplify each of the following.

(a) 2 4 x 20
5

Solution

v) Multiplying three fractions ( including whole

numbers and mixed numbers )

Worked Example

Evaluate 2 1 x 9 x 1 1
3    14 12

Solution

B) Problem Solving involving Multiplication of Fractions

Worked Example

In a class of 48 pupils, 5 are girls. How many
12
girls are there in the class ?

Solution

1. Understand the problem

Given information :

5 of 48 pupils are girls.
12

  Find : Number of girls

2. Devise a plan

Use multipcation.

3. Carry out the plan


Therefore, there are 20 girls in the class.

4. Check



C) Division of Fractions

i) Dividing a quantity into parts.

Diagrams can be used to show the division of

a quantity.

For example:-

ii) Dividing a fraction by a whole number

1. To perform division involving fractions, multiply

the dividend by the reciprocal of the divisor.

2. Answer are always written in their lowest terms.

Worked Example

Divide the shaded portion into 4 equal parts.

Solution

Worked Example

Simplify the following.

(a) 2 ÷ 4
5

Solution

iii) Dividing a fraction by a fraction

Diagrams can be used to show the division

of a fraction by another fraction.

For example:-

Worked Example

Simplify 2 ÷ 4
3 5

Solution

iv) Dividing a whole number by a fraction

Division of a whole number by a fraction

is process of finding the number of times

the fraction is contained in that number.

For example:-

Worked Example

Simplify the following.

(a) 6 ÷ 3
8

Solution

v) Dividing a mixed number by a mixed number

1. To perform a division involving mixed numbers,

always convert the mixed numbers into improper

fraction first.

2. Answer are always written in their lowest terms.

Worked Example

Simplify each of the following.

(a) 1 1 ÷ 1 7
4    8

(b) 1 1 ÷ 8 ÷ 1
3 9    6

Solution

D) Problem Solving involving Division of Fractions

Worked Example

2 1 kg of flour is put equally into 15 packets.
4

Find the mass of each packets.

Solution

1. Understand the problem

Given information :

2 1 kg of flour is put equally into 15 packets.
4
Find : Mass of each packet of flour

2. Devise a plan

Use division

3. Carry out the plan

2 1 ÷ 15 = 9 ÷ 15
4 4

= 9 x 1 = 9 = 3 kg.
4 15    60 20

Therefore, the mass of each packet is 3 kg.
20

4. Check

Mass of 15 packets of flour

= 15 x 3 kg = 2 1 kg
20    4

COMBINED OPERATIONS OF +, -, x, ÷ OF FRACTIONS

A) Combined Operations of any Two Operations

Worked Example

Simplify the following.

(a) 11 + 3 - 1    (b) 6 - 4 1 + 2 3
12 4 1 5 10

Solution

Worked Example

Simplify the following.

(a) 3 + 5 x 1 1 (b) 2 5 ÷ 1 1 - 1 1
5 8 5 8 6    2

Solution

B) Combined Operation involving Brackets

1. To perform a calculation involving any two combined

  operations of addition,subtraction,multiplication,divi-

sion or brackets, always work the calculation within

the brackets first.

2. Then, do the multiplication or division before the addition

or subtraction, working from left to right.

Worked Example

Simplify

Solution

C) Problem Solving involving any Two Operations

Worked Example

Mr Lee bought 3 1 litres of orange juice. He bought
2
9 litre of water melon less than orange juice. How
10
much fruit juice did he buy altogether?

Solution

1. Understand the problem

Given information :

Volume of orange juice bought = 3 1
2
Volume of water melon juice bought is 9 litre less
   10
than volume of orange juice.

Find : The volume of fruit juice bought.

2. Devise a plan

Perform subtraction followed by addition.

3. Carry out the plan

3 1 - 9 + 3 1 = 7 - 9 + 7
2 10    2    2    10    2

  = 35 - 9 + 35
10

= 61
10

= 6 1
10

Therefore, he bought 6 1 litres of fruit juice.
10
altogether.

4. Check

3 1 - 9 = 7 - 9
2 10 2    10

= 35 - 9
10

= 26
10

   26 + 7 = 26 + 35
   10 2    10

= 61 = 6 1
10 10

Worked Example

Fatimah bought 10m of coth. She cut out 3 pieces,

each 2 3 long. Find the length of the remaining cloth.
4
Solution

10 - 3 x 2 3 = 10 - 3 x 11
      4 4

= 10 - 33
4

= 40 - 33
4

= 7 = 1 3 m
4 4

Lenght of remaining cloth is 1 3 m.
4

We HEART Maths !!!