MTH 3-07b MTH 3-07c MTH 4-07b Fractions 7-Aug-15Compiled by Mr. Lafferty Maths Dept. Reminder and Mixed Fractions Add & Subtract

MTH 3-07bMTH 3-07cMTH 4-07b

FractionsFractions

19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

w.m

ath

srevis

ion

.com Reminder and Mixed Fractions

Add & Subtract basic Fractions

Multiplying Fractions

Add & Sub Harder Fractions

Dividing Fractions


StarterStarter

19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

1. Solve the inequality 3x- 6=12

2. Calculate (- 29)+(- 11)+9

3. What fraction is x:

4. Simplify the fraction

5. What is the coordinate C(- 2,- 2) reflected in the x- axis?

25200

ww

w.m

ath

srevis

ion

.com

X


Mixed FractionsMixed Fractions


w.m

ath

srevis

ion

.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Understand what the Understand what the terms fraction, top-heavy terms fraction, top-heavy and mixed fraction are.and mixed fraction are.

1. We are learning theterm Fraction and Mixed Fraction.

2.2. Convert between top-Convert between top-heavy and mixed fraction.heavy and mixed fraction.

3.3. Solve problems Solve problems involving fractions.involving fractions.

ww

w.m

ath

srevis

ion

.com


Fraction Fraction ReminderReminder

A Fraction consists of 2 parts.

Top number called the NUMERATOR

Bottom number called the DENOMINATOR

35


ww

w.m

ath

srevis

ion

.com


FractionsFractions

We can sometimes ‘simplify’ a fraction by dividing by the HCF of the numerator and denominator

F15 1 and 153 and 5

F27 1 and 273 and 9

1527

33

1527

59


ww

w.m

ath

srevis

ion

.com


FractionsFractions

A fraction, like, where the numerator is bigger

than the denominator is called a ‘Top-Heavy’ fraction.

73

A number like, consisting of

a ‘whole number’ part and a ‘fraction’ part is called a Mixed fraction

35

4


ww

w.m

ath

srevis

ion

.com


Top Heavy to Top Heavy to MixedMixed

means seven thirds73

7 1 1 1 1 1 1 13 3 3 3 3 3 3 3

7 3 3 13 3 3 3

7 12

3 3


ww

w.m

ath

srevis

ion

.com


NUMERATOR DENOMINATOR


can be written as 7 373

23 7

remainder 1

12

3


ww

w.m

ath

srevis

ion

.com


NUMERATOR DENOMINATOR


can be written as 17 5175

35 17

remainder 2

23

5


ww

w.m

ath

srevis

ion

.com


Changing a mixed fraction to a top-heavy.

WHOLE NUMBER DENOMINATORthen add NUMERATOR

5 4 3

7 5 2

Mixed to Top Mixed to Top HeavyHeavy

35

4

27

5

234

375

23 quarters

37 fifths


ww

w.m

ath

srevis

ion

.com


Now try Exercise 1Ch31 (page 128)

Mixed FractionsMixed FractionsMTH 3-07bMTH 3-07cMTH 4-07b


Starter QuestionsStarter Questions


w.m

ath

srevis

ion

.com 1. Calculate the perimeter of

2. Simplify ?

3. Write 2% as a decimal

4. List the prime numbers between 20 and 30

5. Calculate

1284

7 5+2 2

5cm

7cm



w.m

ath

srevis

ion


1.1. Understand that to add Understand that to add and subtract fractions and subtract fractions the denominators must the denominators must be the same.be the same.

1. We are learning how toadd and subtract basic fractions.

2.2. To be able to do simple To be able to do simple fraction calculations.fraction calculations.

Add / Sub Fractions

ww

w.m

ath

srevis

ion

.com


Add / Sub Fractions

You can only add or subtract fractions if:

DENOMINATORS ARE THE SAME NUMBER

Example 1 Example 2

3 27 7

7 18 8

57

68

34


ww

w.m

ath

srevis

ion

.com


Add Fractions

When dealing with mixed fractions deal with ‘whole’ part first then the fraction part

3 42 1

5 5

3 42 1

5 5

73

5

24

5


ww

w.m

ath

srevis

ion

.com


Subtract Fractions


5 1

7 46 6

5 1

7 4 6 6

43

6

23

3


ww

w.m

ath

srevis

ion

.com



Add / Sub FractionsMTH 3-07bMTH 3-07cMTH 4-07b




w.m

ath

srevis

ion

.com

(2 3 4)

4 149 9

y y x

1. Calculate

2. Expand

3. Write 72% as a decimal

4. Find the LCM of 2 and 3

5. 2.5% of £600


Harder FractionsHarder Fractions


w.m

ath

srevis

ion


1.1. Understand and apply rules Understand and apply rules for adding and subtracting for adding and subtracting fractions.fractions.

1. We are learning how to add and subtract fractions with different denominators. 2.2. Convert top heavy Convert top heavy

fractions to mixed fractions to mixed fractions.fractions.

ww

w.m

ath

srevis

ion

.com




How can we add or subtract fractions that have different denominators

Step 1 : Find the LCM for the denominators

Step 2 : Convert to equivalent fractions

Step 3 : Add or Subtract the numerator and simplify

Before we can add or subtract they MUST

have the same denominator

ww

w.m

ath

srevis

ion

.com 1 1

2 4



Example 1

Step 1 : Find LCM

Step 2 : Equivalent Fractions

Step 3 : Add/Subtract the numerator

and simplify


LCM of 2 and 4

4

4 4+2 1

43

ww

w.m

ath

srevis

ion

.com

1225

5 26 5



Example 1

Step 1 : Find LCM



and simplify


LCM of 5 and 6

30

30 30-

1330

ww

w.m

ath

srevis

ion

.com

910

5 36 4



Example 1

Step 1 : Find LCM



and simplify


LCM of 4 and 6

12

12 12+

1912

= =7

121

112 19 R7

ww

w.m

ath

srevis

ion

.com



Q1 and Q2

Harder FractionsHarder FractionsMTH 3-07bMTH 3-07cMTH 4-07b

ww

w.m

ath

srevis

ion

.com



How can we add /subtract mixed fractions that have different denominators


Simple !


ww

w.m

ath

srevis

ion

.com



1 22 3

2 3

1 22 3


5

43

1 22 3

6 6+

16

1

16

1= 5 +

16

= 6 76

=

LCM of 2 and 3

61

6 7 R1

ww

w.m

ath

srevis

ion

.com



7 2

7 48 3

7 28 3


3

1621

7 28 3

24 24-

524

524

= 3 +

524

= 3 =

LCM of 8 and 3

24

ww

w.m

ath

srevis

ion

.com



3 5

44 6

3 54 6


4

109

3 54 6

12 12+

712

1

712

1= 4 +

712

= 5 1912

=

LCM of 4 and 6

121

12 19 R7

ww

w.m

ath

srevis

ion

.com



Q4 to Q8


ww

w.m

ath

srevis

ion

.com


Most Difficult Most Difficult FractionsFractions

1 2

6 24 3

1 24 3


4

83

1 24 3

12 12-= 4 +

712

= 3 =

LCM of 4 and 3

12

512

-

512

-

= 45

12-

Adding a negative is the

same as subtracting

ww

w.m

ath

srevis

ion

.com


Most Difficult Most Difficult FractionsFractions

1 2

7 15 3

1 25 3


6

103

1 25 3

15 15-= 6 +

815

= 5 =

LCM of 5 and 3

15

715

-

715

-

= 67

15-

Adding a negative is the

same as subtracting

ww

w.m

ath

srevis

ion

.com



Q9 to Q15





w.m

ath

srevis

ion

.com

24 , 3 2

5

3 14 3

(2 )

56

x y and z z z xy

1. Calculate

2. I f . Find

3. Calculate 60% of £360

4. Make the following top- heavy


Multiplying Multiplying FractionsFractions


w.m

ath

srevis

ion


1.1. Understand the simply Understand the simply rules for multiplying rules for multiplying basic and mixed basic and mixed fractions.fractions.

1. We are learning how to multiply basic and mixed fractions.

2.2. Apply rules correctly.Apply rules correctly.

ww

w.m

ath

srevis

ion

.com



Example 1 Example 2

Multiply basic fractions

3 34 5

9

20

4 55 6

2030

23

1. Multiply the numerators

2. Multiply the denominators


ww

w.m

ath

srevis

ion

.com



Q1 to Q4



ww

w.m

ath

srevis

ion

.com



1. Make fractions top-heavy

Multiplying Mixed Fractions




ww

w.m

ath

srevis

ion

.com



1 13 1

2 3

7 42 3

286

4

46

Example


2

23




ww

w.m

ath

srevis

ion

.com



3 1

4 14 5

19 64 5

11420

14

520

Example


7

510




ww

w.m

ath

srevis

ion

.com



Q5 to Q10






w.m

ath

srevis

ion

.com

1

3 (4 -3 ) - 12

1 132 3

2 33 2

a a b ab

1. Calculate

2. Simplify

3. Multiply


Dividing FractionsDividing Fractions


w.m

ath

srevis

ion


1. We are learning how to divide basic and mixed fractions.

1.1. Understand how the Understand how the simply rules for dividing simply rules for dividing basic and mixed basic and mixed fractions.fractions.

2.2. Apply rules correctly.Apply rules correctly.

ww

w.m

ath

srevis

ion

.com


Always = 1


It is almost impossible to divide fractions like

by actually dividing.

Instead we change it into a multiplication by:

2335

2 53 33 55 3

2 53 3

109

1

19

2 33 5


ww

w.m

ath

srevis

ion

.com



Easy rule to remember :

Example Example

Instead of dividing by , multiply by ab

ba

5 28 3

35

8 2

1516

4 55 6

64

5 5

2425


ww

w.m

ath

srevis

ion

.com



Q1 to Q4

Dividing FractionsDividing FractionsMTH 3-07bMTH 3-07cMTH 4-07b

ww

w.m

ath

srevis

ion

.com



For mixed fractions YOU MUST make them top-heavy first !!

Example

1 13 2

2 3

7 72 3

37

2 7

2114

3 1

12 2

Instead of dividing by , multiply by ab

ba


ww

w.m

ath

srevis

ion

.com



Example 2 3 23 1

4 3

15 54 3

3154 5

4520

52

20

12

4


ww

w.m

ath

srevis

ion

.com



Q5 to Q10

Dividing FractionsDividing FractionsMTH 3-07bMTH 3-07cMTH 4-07b

Documents

MTH 3-07b MTH 3-07c MTH 4-07b Fractions 7-Aug-15Compiled by Mr. Lafferty Maths Dept. Reminder and Mixed Fractions Add & Subtract