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Try this!. Answers. Let’s make the cost of the yellow car a , the blue car b , the green car and the red car y . a. b. =. x 2. +£5000 . =. The blue car costs the same as the yellow car. The green and red cars cost the same. The green car is twice as expensive as the yellow car.

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Try this

Answers

Let’s make the cost of the yellow car a,

the blue car b, the green car and the red car y.

a

b

=

x 2

+£5000

=

The blue car costs the same as the yellow car.

The green and red cars cost the same.

The green car is twice as expensive as the yellow car.

The red car costs £5000 more than the blue car.


Try this

Answers

Because a = b and = y, each pair has the same value. So double the value means to add £5000.

a

b

=

x 2

+£5000

=

If double means to add £5000, a and b must have been £5000 to start with. We add £5000 for and y so each costs £10,000.


Try this

£5000

£5000

£10,000

£10,000


Expanding brackets and substitution

Expanding bracketsand substitution

Slideshow 11, Mathematics

Mr Richard Sasaki, Room 307


Objectives
Objectives

  • Review algebraic rules learned so far

  • Learn how to expand brackets (known as the Distributive Law)

  • Learn how to substitute numbers into algebraic expressions

  • Substitute into expressions with and without expansion


Main rules learned so far
Main Rules learned so far

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=


Expanding brackets
Expanding Brackets

  • A man (Mr Sasaki) lends three students a total of 2 five yen notes and 3 two-hundred yen notes each.

  • How could we express this algebraically?

4()

2+3y

Algebraically, how can we show altogether how many of each type of note I handed out?

8+12y


Expanding brackets1
Expanding Brackets

  • So, how did we get from 4(2 + 3y) to 8 + 12y?

4()

2+3y

(4 × 2)+(4 × 3y)

=

=

8+12y

To expand brackets, multiply the number on the outside by each on the inside while keeping + and – symbols.


Expanding brackets2
Expanding Brackets

  • Previous example…

4()

2+3y

(4 × 2)+(4 × 3y)

=

=

8+12y

Try expanding these with the whiteboards! Just write the answer!

2()

+y

2+2y

=

2(-y)

8+2y

=

3(-3)

6-9

3(+2y)

=

6+6y

=

4(+y)

=

1+4y

3+2

=


Expanding brackets3
Expanding Brackets

  • Make groups of 3-4 with people nearby.

  • Each group will get some paper snippets. Match each factorised expression (one with brackets) with its expansion (one with no brackets).

  • We will stop after the first three groups finish!


Answers
Answers

?

?

?

?

?

?

?

?

?

?


Worded example
Worded Example

  • Our good friend Takafumi buys 3 lollipops and 2 chocolate bars for each member of 7C. Write this as an expression in the form where , and are numbers.

()

+y

27

3

2

Please try the worksheet!


Answers1
Answers

3a + 3b

5 + 5y

-3a - 3b

6a + 4b

4 + 4y + 4z

8a - 2b

12a - 3b

6a + 4b

9a + 6b

+ y

+ y

12a + 12b

18a + 18b


Answers2
Answers

4( + y)

4 + 4y

(3 + 4) × 3

= 3(3 + 4)

= 9 + 12

4a – 6b

4(4 – 3) + 5(7y – 3)

= 1 – 12 + 35y – 15

= 1 + 35y – 27


Substitution
Substitution

  • I have 2 five yen notes and 1 two-hundred yen note.

  • How can we represent this algebraically?

2+y

Here, means the value of the 5 yen note and y means the value of the two-hundred yen note.

=

=


Substitution1
Substitution

  • If is 5 and y is 200, what is 2 + y? 2 + y is the total value of the notes.

So 2 five yen notes and a two-hundred yen note have a value of 210 Yen.

2+y

+200

=

=

=

=


Substitution2
Substitution

  • Substitution is about substituting unknowns for numbers, then being able to calculate an answer.

Examples

Calculate + y when = 4 and y = 7.

+y

4+7

11

=

=

Calculate 3 - 2y when = 4and y = 3.

-2y

(3×4)- (2×3)

=

12 - 6

6

=

=


Substitution3
Substitution

Try the worksheet!

Examples

Calculate + y when = 4 and y = 7.

11

+y

4+7

=

=

Calculate 3 - 2y when = 4and y = 3.

-2y

(3×4)- (2×3)

=

12 - 6

6

=

=

Try the following with the whiteboards!

–y; =4, y = 2

– 2 =2

+ 2y; =3, y = -1

+(-2)=10

=4

=32

=32

=-4


Try this

Answers

14

1

12

13

7

9

6 x 12 + 2 = 14

6 + 2

2(3 x 2 + 1) = 14


Try this

Answers

1= 40

1 - 20

5(2= 40

2(3 + 2y + 4z)

6 + 4y + 8z

6 x 40 + 4 x 80 + 8 x 100 = 1360 Yen

No, it could have been -4. (-4)2 = 16.


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