§1.2 Simplifying Fractions

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• Middelbare school
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• Leerjaar 2

C1 Arithmetic with Letters

Mr. Fintelman (FNL)

Wednesday September 11th

2024

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...

I can already…

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

Prior Knowledge

Simplify expressions - Step by step

Determine the area of the blue shape.

Simplify expressions - Step by step

Determine the area of the blue shape.

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

Simplify expressions - Step by step

Determine the area of the blue shape.

$$=6a^2+10a+21a+35-(a^2+a-a-1)$$

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

Simplify expressions - Step by step

Determine the area of the blue shape.

$$=6a^2+10a+21a+35-(a^2+a-a-1)$$

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

$$=6a^2+10a+21a+35-a^2-a+a+1$$

Simplify expressions - Step by step

Determine the area of the blue shape.

$$=6a^2+10a+21a+35-(a^2+a-a-1)$$

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

$$=6a^2+10a+21a+35-a^2-a+a+1$$

$$=5a^2+31a+36$$

After this lesson, I can...

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

Goals

Simplify Fractions

$$\frac{6}{9}=...$$

$$\frac{18}{36}=...$$

$$\frac{25}{125}=...$$

Simplify Fractions

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

$$\frac{18}{36}=\frac{1}{2}$$

$$\frac{25}{125}=\frac{1}{5}$$

Simplify Fractions

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

$$\frac{18}{36}=\frac{1\cdot 18}{2\cdot 18}=\frac{1}{2}$$

$$\frac{25}{125}=\frac{1\cdot 25}{5\cdot 25}=\frac{1}{5}$$

Simplify Fractions with Letters

$$\frac{-6a}{9a}=...$$

$$\frac{ab}{b^2}=...$$

$$\frac{25abc}{5a}=...$$

Simplify Fractions with Letters

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

$$\frac{ab}{b^2}=\frac{a\cdot b}{b\cdot b}=...$$

$$\frac{25abc}{5a}=\frac{5bc\cdot 5a}{1\cdot 5a}=...$$

Simplify Fractions with Letters

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

$$\frac{ab}{b^2}=\frac{a\cdot b}{b\cdot b}=\frac{a}{b}$$

$$\frac{25abc}{5a}=\frac{5bc\cdot 5a}{1\cdot 5a}=5bc$$

Adding fractions without letters

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

$$\frac{1}{2}+\frac{4}{9}=\frac{9}{18}+\frac{8}{18}=\frac{17}{18}$$

Adding fractions with letters

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

$$\frac{a}{3}+\frac{5}{b}=\frac{ab}{3b}+\frac{15}{3b}=\frac{ab+15}{3b}$$

Adding fractions with letters

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

$$\frac{ab}{4}+\frac{5}{c}=...$$

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

Adding fractions with letters

$$\frac{3}{x}-\frac{7}{y}=\frac{3y}{xy}-\frac{7x}{xy}=...$$

$$\frac{ab}{4}+\frac{5}{c}=\frac{abc}{4c}+\frac{20}{4c}=...$$

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

Adding fractions with letters

$$\frac{3}{x}-\frac{7}{y}=\frac{3y}{xy}-\frac{7x}{xy}=\frac{3y-7x}{xy}$$

$$\frac{ab}{4}+\frac{5}{c}=\frac{abc}{4c}+\frac{20}{4c}=\frac{abc+20}{4c}$$

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

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

Now I can...

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

Reflection

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...

I can already…

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

Prior Knowledge

Recognizing mistakes

$$\frac{3}{x}-\frac{7}{y}=\frac{3y}{xy}+\frac{7x}{xy}=\frac{3y+7x}{xy}$$

$$\frac{ab}{4}+\frac{5}{c}=\frac{abc}{c}+\frac{20}{c}=\frac{abc+20}{c}$$

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

After this lesson, I can...

1. … multiply and divide fractions with letters.

Goals

Multiplying Fractions without Letters

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

$$\frac{6}{11}\cdot \frac{3}{7}=...$$

$$\frac{2}{3}÷\frac{4}{5}=...$$

Multiplying Fractions without Letters

$$\frac{2}{9}\cdot \frac{4}{9}=\frac{2\cdot 4}{9\cdot 9}=\frac{8}{81}$$

$$\frac{6}{11}\cdot \frac{3}{7}=\frac{6\cdot 3}{11\cdot 7}=\frac{18}{77}$$

$$\frac{2}{3}÷\frac{4}{5}=\frac{2\cdot 5}{3\cdot 4}=\frac{10}{12}=\frac{5}{6}$$

Multiplying Fractions with Letters

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

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

$$\frac{a}{b}÷\frac{4a}{5}=...$$

Multiplying Fractions with Letters

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

$$\frac{a}{3b}\cdot \frac{6b}{2c}=\frac{a\cdot 6b}{3b\cdot 2c}=\frac{6ab}{6bc}=\frac{a}{c}$$

$$\frac{a}{b}÷\frac{4a}{5}=\frac{a\cdot 5}{b\cdot 4a}=\frac{5a}{4ab}=\frac{5}{4b}$$

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

Now I can...

1. … simplify fractions with letters.
   
2. … add and subtract fractions with letters.
3. … multiply and divide fractions with letters.

Reflection