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§1.2 Simplifying Fractions

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 11th

2024

1 / 32

Slide 1: Slide

WiskundeMiddelbare schoolvwoLeerjaar 2

This lesson contains 32 slides, with text slides.

Lesson duration is: 90 min

Items in this lesson

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 11th

2024

Slide 1 - Slide

Date

Wednesday September 11th 2024

Paragraph

§1.2 Simplifying Fractions

Pages from the handbook

Pag. 17-19

Subject

Simplify fractions with letters.

Add and subtract fractions with letters.

Today is the day...

Slide 2 - Slide

I can already…

… simplify an expression with the following rule: a(b + c) = ab + ac
… simplify an expression with the following rule: (a + b)(c + d) = ac + ad + bc + bd
… simplify expressions that contain brackets.

Prior Knowledge

Slide 3 - Slide

Simplify expressions - Step by step

Determine the area of the blue shape.

Slide 4 - Slide

Simplify expressions - Step by step

Determine the area of the blue shape.

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

Slide 5 - Slide

Simplify expressions - Step by step

Determine the area of the blue shape.

= 6 a^{​ 2 ​ ​} + 10 a + 21 a + 35 - (a^{​ 2 ​ ​} + a - a - 1)

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

Slide 6 - Slide

Simplify expressions - Step by step

Determine the area of the blue shape.

= 6 a^{​ 2 ​ ​} + 10 a + 21 a + 35 - (a^{​ 2 ​ ​} + a - a - 1)

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

= 6 a^{​ 2 ​ ​} + 10 a + 21 a + 35 - a^{​ 2 ​ ​} - a + a + 1

Slide 7 - Slide

Simplify expressions - Step by step

Determine the area of the blue shape.

= 6 a^{​ 2 ​ ​} + 10 a + 21 a + 35 - (a^{​ 2 ​ ​} + a - a - 1)

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

= 6 a^{​ 2 ​ ​} + 10 a + 21 a + 35 - a^{​ 2 ​ ​} - a + a + 1

= 5 a^{​ 2 ​ ​} + 31 a + 36

Slide 8 - Slide

After this lesson, I can...

… simplify fractions with letters.
… add and subtract fractions with letters.

Goals

Slide 9 - Slide

Simplify Fractions

\frac{​ 6 ​ ​}{​ 9 ​} = . . .

\frac{​ 1 8 ​ ​}{​ 3 6 ​} = . . .

\frac{​ 2 5 ​ ​}{​ 1 2 5 ​} = . . .

Slide 10 - Slide

Simplify Fractions

\frac{​ 6 ​ ​}{​ 9 ​} = \frac{​ 2 ​ ​}{​ 3 ​}

\frac{​ 1 8 ​ ​}{​ 3 6 ​} = \frac{​ 1 ​ ​}{​ 2 ​}

\frac{​ 2 5 ​ ​}{​ 1 2 5 ​} = \frac{​ 1 ​ ​}{​ 5 ​}

Slide 11 - Slide

Simplify Fractions

\frac{​ 6 ​ ​}{​ 9 ​} = \frac{​ 2 \cdot 3 ​ ​}{​ 3 \cdot 3 ​} = \frac{​ 2 ​ ​}{​ 3 ​}

\frac{​ 1 8 ​ ​}{​ 3 6 ​} = \frac{​ 1 \cdot 1 8 ​ ​}{​ 2 \cdot 1 8 ​} = \frac{​ 1 ​ ​}{​ 2 ​}

\frac{​ 2 5 ​ ​}{​ 1 2 5 ​} = \frac{​ 1 \cdot 2 5 ​ ​}{​ 5 \cdot 2 5 ​} = \frac{​ 1 ​ ​}{​ 5 ​}

Slide 12 - Slide

Simplify Fractions with Letters

\frac{​ - 6 a ​ ​}{​ 9 a ​} = . . .

\frac{​ a b ​ ​}{​ b ^{​ 2 ​ ​} ​} = . . .

\frac{​ 2 5 a b c ​ ​}{​ 5 a ​} = . . .

Slide 13 - Slide

Simplify Fractions with Letters

\frac{​ - 6 a ​ ​}{​ 9 a ​} = \frac{​ - 2 \cdot 3 a ​ ​}{​ 3 \cdot 3 a ​} = . . .

\frac{​ a b ​ ​}{​ b ^{​ 2 ​ ​} ​} = \frac{​ a \cdot b ​ ​}{​ b \cdot b ​} = . . .

\frac{​ 2 5 a b c ​ ​}{​ 5 a ​} = \frac{​ 5 b c \cdot 5 a ​ ​}{​ 1 \cdot 5 a ​} = . . .

Slide 14 - Slide

Simplify Fractions with Letters

\frac{​ - 6 a ​ ​}{​ 9 a ​} = \frac{​ - 2 \cdot 3 a ​ ​}{​ 3 \cdot 3 a ​} = - \frac{​ 2 ​ ​}{​ 3 ​}

\frac{​ a b ​ ​}{​ b ^{​ 2 ​ ​} ​} = \frac{​ a \cdot b ​ ​}{​ b \cdot b ​} = \frac{​ a ​ ​}{​ b ​}

\frac{​ 2 5 a b c ​ ​}{​ 5 a ​} = \frac{​ 5 b c \cdot 5 a ​ ​}{​ 1 \cdot 5 a ​} = 5 b c

Slide 15 - Slide

Adding fractions without letters

\frac{​ 2 ​ ​}{​ 9 ​} + \frac{​ 4 ​ ​}{​ 9 ​} = \frac{​ 6 ​ ​}{​ 9 ​} = \frac{​ 2 ​ ​}{​ 3 ​}

\frac{​ 1 ​ ​}{​ 2 ​} + \frac{​ 4 ​ ​}{​ 9 ​} = \frac{​ 9 ​ ​}{​ 1 8 ​} + \frac{​ 8 ​ ​}{​ 1 8 ​} = \frac{​ 1 7 ​ ​}{​ 1 8 ​}

Slide 16 - Slide

Adding fractions with letters

\frac{​ 2 ​ ​}{​ x ​} + \frac{​ 4 ​ ​}{​ x ​} = \frac{​ 6 ​ ​}{​ x ​}

\frac{​ a ​ ​}{​ 3 ​} + \frac{​ 5 ​ ​}{​ b ​} = \frac{​ a b ​ ​}{​ 3 b ​} + \frac{​ 1 5 ​ ​}{​ 3 b ​} = \frac{​ a b + 1 5 ​ ​}{​ 3 b ​}

Slide 17 - Slide

Adding fractions with letters

\frac{​ 3 ​ ​}{​ x ​} - \frac{​ 7 ​ ​}{​ y ​} = . . .

\frac{​ a b ​ ​}{​ 4 ​} + \frac{​ 5 ​ ​}{​ c ​} = . . .

5 + \frac{​ 2 a ​ ​}{​ b ​} = . . .

Slide 18 - Slide

Adding fractions with letters

\frac{​ 3 ​ ​}{​ x ​} - \frac{​ 7 ​ ​}{​ y ​} = \frac{​ 3 y ​ ​}{​ x y ​} - \frac{​ 7 x ​ ​}{​ x y ​} = . . .

\frac{​ a b ​ ​}{​ 4 ​} + \frac{​ 5 ​ ​}{​ c ​} = \frac{​ a b c ​ ​}{​ 4 c ​} + \frac{​ 2 0 ​ ​}{​ 4 c ​} = . . .

5 + \frac{​ 2 a ​ ​}{​ b ​} = \frac{​ 5 b ​ ​}{​ b ​} + \frac{​ 2 a ​ ​}{​ b ​} = . . .

Slide 19 - Slide

Adding fractions with letters

\frac{​ 3 ​ ​}{​ x ​} - \frac{​ 7 ​ ​}{​ y ​} = \frac{​ 3 y ​ ​}{​ x y ​} - \frac{​ 7 x ​ ​}{​ x y ​} = \frac{​ 3 y - 7 x ​ ​}{​ x y ​}

\frac{​ a b ​ ​}{​ 4 ​} + \frac{​ 5 ​ ​}{​ c ​} = \frac{​ a b c ​ ​}{​ 4 c ​} + \frac{​ 2 0 ​ ​}{​ 4 c ​} = \frac{​ a b c + 2 0 ​ ​}{​ 4 c ​}

5 + \frac{​ 2 a ​ ​}{​ b ​} = \frac{​ 5 b ​ ​}{​ b ​} + \frac{​ 2 a ​ ​}{​ b ​} = \frac{​ 5 b + 2 a ​ ​}{​ b ​}

Slide 20 - Slide

Worktime

You work neatly by…
… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 22, 23, 25, 26 and 28.

Assignments:

Pages: 17-19

Exercises: 23, 24, 25, 26 and 28.

Assignments from the planning of WEEK 3:

Extra:

Exercises: 27

Slide 21 - Slide

Now I can...

… simplify fractions with letters.
… add and subtract fractions with letters.

Reflection

Slide 22 - Slide

Date

Monday September 23rd 2024

Paragraph

§1.2 Simplifying Fractions

Pages from the handbook

Pag. 20-22

Subject

Multiply and divide fractions with letters

Today is the day...

Slide 23 - Slide

I can already…

… simplify fractions with letters.
… add and subtract fractions with letters.

Prior Knowledge

Slide 24 - Slide

Recognizing mistakes

\frac{​ 3 ​ ​}{​ x ​} - \frac{​ 7 ​ ​}{​ y ​} = \frac{​ 3 y ​ ​}{​ x y ​} + \frac{​ 7 x ​ ​}{​ x y ​} = \frac{​ 3 y + 7 x ​ ​}{​ x y ​}

\frac{​ a b ​ ​}{​ 4 ​} + \frac{​ 5 ​ ​}{​ c ​} = \frac{​ a b c ​ ​}{​ c ​} + \frac{​ 2 0 ​ ​}{​ c ​} = \frac{​ a b c + 2 0 ​ ​}{​ c ​}

5 + \frac{​ 2 a ​ ​}{​ b ​} = \frac{​ 5 ​ ​}{​ b ​} + \frac{​ 2 a ​ ​}{​ b ​} = \frac{​ 5 + 2 a ​ ​}{​ b ​}

Slide 25 - Slide

After this lesson, I can...

… multiply and divide fractions with letters.

Goals

Slide 26 - Slide

Multiplying Fractions without Letters

\frac{​ 2 ​ ​}{​ 9 ​} \cdot \frac{​ 4 ​ ​}{​ 9 ​} = . . .

\frac{​ 6 ​ ​}{​ 1 1 ​} \cdot \frac{​ 3 ​ ​}{​ 7 ​} = . . .

\frac{​ 2 ​ ​}{​ 3 ​} \div \frac{​ 4 ​ ​}{​ 5 ​} = . . .

Slide 27 - Slide

Multiplying Fractions without Letters

\frac{​ 2 ​ ​}{​ 9 ​} \cdot \frac{​ 4 ​ ​}{​ 9 ​} = \frac{​ 2 \cdot 4 ​ ​}{​ 9 \cdot 9 ​} = \frac{​ 8 ​ ​}{​ 8 1 ​}

\frac{​ 6 ​ ​}{​ 1 1 ​} \cdot \frac{​ 3 ​ ​}{​ 7 ​} = \frac{​ 6 \cdot 3 ​ ​}{​ 1 1 \cdot 7 ​} = \frac{​ 1 8 ​ ​}{​ 7 7 ​}

\frac{​ 2 ​ ​}{​ 3 ​} \div \frac{​ 4 ​ ​}{​ 5 ​} = \frac{​ 2 \cdot 5 ​ ​}{​ 3 \cdot 4 ​} = \frac{​ 1 0 ​ ​}{​ 1 2 ​} = \frac{​ 5 ​ ​}{​ 6 ​}

Slide 28 - Slide

Multiplying Fractions with Letters

\frac{​ a ​ ​}{​ 3 ​} \cdot \frac{​ a ​ ​}{​ b ​} = . . .

\frac{​ a ​ ​}{​ 3 b ​} \cdot \frac{​ 6 b ​ ​}{​ 2 c ​} = . . .

\frac{​ a ​ ​}{​ b ​} \div \frac{​ 4 a ​ ​}{​ 5 ​} = . . .

Slide 29 - Slide

Multiplying Fractions with Letters

\frac{​ a ​ ​}{​ 3 ​} \cdot \frac{​ a ​ ​}{​ b ​} = \frac{​ a \cdot a ​ ​}{​ 3 \cdot b ​} = \frac{​ a ^{​ 2 ​ ​} ​ ​}{​ 3 b ​}

\frac{​ a ​ ​}{​ 3 b ​} \cdot \frac{​ 6 b ​ ​}{​ 2 c ​} = \frac{​ a \cdot 6 b ​ ​}{​ 3 b \cdot 2 c ​} = \frac{​ 6 a b ​ ​}{​ 6 b c ​} = \frac{​ a ​ ​}{​ c ​}

\frac{​ a ​ ​}{​ b ​} \div \frac{​ 4 a ​ ​}{​ 5 ​} = \frac{​ a \cdot 5 ​ ​}{​ b \cdot 4 a ​} = \frac{​ 5 a ​ ​}{​ 4 a b ​} = \frac{​ 5 ​ ​}{​ 4 b ​}

Slide 30 - Slide

Worktime

You work neatly by…
… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 22, 23, 25, 26, 28, 30, 33, 35, 36 and 37.

Assignments:

Pages: 17-22

Exercises: 23, 24, 25, 26, 28, 30, 35, 36 and 38.

Assignments from the planning of WEEK 3:

Extra:

Exercises: 27

Slide 31 - Slide

Now I can...

… simplify fractions with letters.
… add and subtract fractions with letters.
… multiply and divide fractions with letters.

Reflection

Slide 32 - Slide

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