**Chapter 1**

Learning objective:

Learning objective:

**Learning Objective:**

**Understanding**

fractions

fractions

**Simplifying and comparing fractions**

**Calculations with fractions**

What is a fraction?

a

b

A fraction is a number that can be written on this form:

Numerator

(Täljare)

Denominator

(Nämnare)

In swedish there's

a trick to remember:

T

äljare står på

t

aket

N

ämnare står

n

ederst

The english words you'll just have to memorize!

When do we use

fractions?

1

3

The fraction above could be read as:

one third

one over three

one divided by three

one out of three

Fractions are used to express

parts of something

They can also be used when decimals are too inaccurate or to express probability (sannolikhet)

Expressing parts

When expressing parts it's easiest to read the fraction as, for example:

"one out of three" or "one third"

"One third" of the circle is

purple, or "one out of three" pieces is purple

Remember that two sixths

is also one third

1

3

= 0.33333333

2

3

= 0.666666666

3

3

= ?

Fractions as probability

**Converting between decimals**

and fractions

and fractions

Page 43:

Exercises:

#1, 2, 3, 5, 7

If you finish early:

Do exercise #8, 9, and 4

simplifying

Comparing

If you multiply/divide the numerator and denominator by the same number you don't change the value of the fraction

1

3

=

2

6

x2

x2

=

200

600

x100

x100

A few examples:

Comparing fractions

How about:

4

7

or

5

9

?

Sometimes we want to compare fractions to each other to see what fraction is the larger.

What if we have a fraction with large numbers?

560

1200

A few tricks:

If it's an even number you can always divide by 2

If you add up the digits in the number and the result is divisible by 3 then the whole number is too

If it ends on a 5 or a 10 it is always divisible by 5

If it ends on a 0 it is divisible by 10

300

555

270

570

Understand how to simplify and order fractions

It's quite easy to see that

1

2

is bigger than

1

3

Order the following fractions in ascending order:

1

3

2

7

3

10

7

8

Sometimes it's easier to use logic

Ex:

What fraction is larger:

4

7

or

40000

70001

?

Write the answer on your whiteboards using the symbols <, or >

Write the answer on your whiteboards

1

3

or

1

2

?

a)

b)

Hint: Can you learn anything from a) to solve b)?

When simplifying a fraction:

Try to find a common factor to divide with

If you find the highest common factor (HCF) then you will only have to divide once.

Finding the highest common factor can sometimes be tricky - then just keep dividing with any common factors

Example:

9

27

=

3

9

=

1

3

When a fraction can't be simplified any more it's in its

simplest form

Your turn: Simplify the following fractions to their simplest form:

a)

50

100

b)

7

56

c)

32

36

Being able to switch between the forms improper fractions and mixed numbers.

Understand how to add and subtract fractions

Understand how to turn fractions in to decimal form and the other way around.

Own work:

Page 45

Exercises: #1, 2, 5, 6

What is an improper fraction?

-If the numerator is bigger than the denominator the fraction is

improper

Ex:

5

4

Converting between improper form and mixed form

Example: Changing from improper fractions to mixed numbers

7

5

=

Example: Changing from mixed numbers to improper fractions

2

3

5

=

Now try a few:

Change these improper fractions to mixed numbers:

a)

12

8

5

2

9

4

Change these mixed numbers to improper fractions

b)

c)

a)

1

2

3

b)

2

5

7

Adding and subtracting

Adding and subtracting fractions that have the same denominator is quite easy:

Ex: One quarter of a pizza plus two quarters of a pizza makes 3 quarters of a pizza

It's a bit trickier if we have both improper fractions and mixed numbers. Or fractions with different denominators

When we have both improper fractions and mixed numbers we need to change one of them before we can add

Ex:

10

4

+

1

3

4

=

When we have fractions with different denominators we need to give them a common denominator

Ex:

1

2

+

1

4

Improper fractions

Converting

Adding and subtracting

Remember the pizza?

4

4

"Four quarters of a pizza"

One more quarter would be

5

4

"Five quarters of a pizza"

Another way of writing this is:

1

1

4

Starters

All fractions can be converted into decimals

To make a fraction to a decimal, divide the numerator with the denominator (with a calculator or using long division)

Ex: Convert

3

8

into a decimal

Fractions where the denominator is 10, 100 or 1000 can quite easily be changed into decimals. It's all about moving the decimal!

Ex:

1

10

=

0.1

1

100

= 0.01

Since having a denominator of 10, 100, etc, makes it easier, we can use this as a trick!

Ex:

22

25

Try a few:

34

50

8

25

a)

b)

c)

3

20

d)

3

30

Ex:

8

40

Work out the following:

0.4 x 10

19 x 10

1.9 x 10

19

10

If done early: Find a fraction that lies exactly between 3/5 and 4/7

Important fractions to remember:

1

2

= 0.5

1

3

= 0.333...

1

4

= 0.25

1

5

= 0.2

Converting from a fraction to a decimal

Ex: Write 0.12 as a fraction

Make the decimal into a fraction with one in the denominator, then find a number to multiply with that will get rid of the decimals.

Own work:

Page 47

#1, 2ab, 3abcgh, 4abc

Half of a field is potatoes, one quarter is lettuce, and the rest is evenly divided by tomatoes, onions and peppers. What fraction of the field is tomatoes?

**Rounding**

Learning objective:

Understanding how to round a number to the nearest 10, 100, 1000 or to decimal places

First we need to make sure that we remember the place values

When is rounding used?

If exact numbers aren't important

Pi is calculated to

12 100 000 000 050 decimal places and all of them are needed!

- For example if there are 8346 people at a game we would say that there were about 8000

We use rounding to make big numbers or numbers with many decimals easier to work with

- It's about 20 degrees outside

When is rounding NOT good?

So how is rounding done?

When we round we look at

the number after the number we want to round to.

-If it is less than 5 round down

-If it is 5 or more, round up

Ex: Round 2692.499 to the nearest 100, 10, 1, 0.1 (one decimal place) and 0.01 (two decimal place)

Own work:

Pg 181 #1-3, 5, 6, 8

Pi- day 3/14

Learning objective: Understanding how to round numbers in order to make calculations easier

Adding: Try to round "one up and one down"

Subtracting: Try to round both down or both up

Multiplication: Round one down and one up. Start by rounding the smallest to the nearest number

Division: Round both up or both down. The numerator should usually increase/decrease more than the denominator.

**Factors, multiples and primes**

Learning objective:

Understand the concept of multiples and connect it with multiplication

Understand the properties of factors (factor pairs)

Identify prime numbers

When is this used?

Multiples help us understand patterns. (you often do things every two days, every three days, etc.

Factors help break down numbers

Prime numbers are often used by banks to create bank accounts or other things that need to be crypted

Multiples

Multiples are similar to the multiplication table

Ex: Multiples of 2 are: 2, 4, 6, 8, 10...

Ex: Multiples of 3 are: 3, 6, 9, 12 15...

Ex: Multiples of 5 are: 5, 10, 15, 20...

Exercise: Anna and Bengt are taking math classes. Anna is going every third lesson and Bengt is going every fifth lesson. When will be the first time they have class at the same time?

Factors

Factors of a number are those which divide that number evenly

Ex: Factors of 12 are: 1, 2, 3, 4, 6 and 12 since all these numbers divide 12 evenly.

Exercise: List all factors of 80

Exercise: List all factors of 54

Highest common factor (HCF) and lowest common multiple (LCM)

HCF: Is the largest factor that is shared by two numbers.

Ex: Highest common factor of 12 and 30 is 6

LCM: Is the smallest multiple that is shared by two numbers.

Ex:

Lowest common multiple of 3 and 8 is 24

Exercise: Find the highest common factor of 63 and 27

Exercise: Find the lowest common multiple of 9 and 12

Primes!

Primes have exactly two factors: 1 and itself

Primes follow no patterns. You will have to memorize!

Class work:

Page 183: #1abef, 4a, 6ab

Extra: #7abc

Ex: In a lottery there are 40 tickets and 10 of them are winning tickets. The probability of winning is

1

4

Fractions and decimals

Fractions are usually smaller than 1 and most fractions can be expressed as a decimal

0

1

1

4

= 0,25

2

4

= 0,5

To find the decimal form of a fraction,

divide the numerator with the denominator

4

4

= 1

Finding the whole

120 students said that tacos was their favorite food. That meant that 3/4 of the students had tacos as their favorite food. How many students preferred something other than tacos?

Learning objective:

Understanding the concept of fractions

Being able to recognize improper fractions and switch between different forms, e.g. mixed form and decimal form

Improper fractions

and mixed form

A fraction were the numerator is greater than the denominator is called an

improper fraction

Ex:

5

4

These fractions can also be written in a

mixed form

5

4

=

4

4

+

1

4

=

1

1

4

Fraction =

Part

The whole