Last lesson Chapter 2

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Numbers & Operations

Wednesday October 16th

2024

Date	Wednesday October15th
Paragraph	§2.6 Negative Fractions
Pages from the handbook	Pag. 83-85
Subject	Adding and subtracting negative fractions

Today is the day...

I can already…

1. … do calculations that involve a fraction bar.

Prior Knowledge

Fraction bar

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

$$\frac{6-3}{2+1}=$$

$$\frac{5\times 2}{10-4}=$$

$$\frac{3+5}{2}-1=$$

After this lesson, I can…

1. … do calculations with negative fractions.
   

Goals

Simplify Fractions

$$\frac{-25}{6}=...$$

$$\frac{-58}{11}=...$$

$$\frac{17}{-3}=...$$

Simplify Fractions

$$\frac{-25}{6}=\frac{-6-6-6-6-1}{6}=-4\frac{1}{6}$$

$$\frac{-58}{11}=\frac{-11-11-11-11-11-3}{11}=-5\frac{3}{11}$$

$$\frac{17}{-3}=\frac{-3-3-3-3-3-2}{3}=-5\frac{2}{3}$$

Simplify Fractions

$$\frac{-25}{6}=\frac{-6-6-6-6-1}{6}=-4\frac{1}{6}$$

$$\frac{-58}{11}=\frac{-11-11-11-11-11-3}{11}=-5\frac{3}{11}$$

$$\frac{17}{-3}=\frac{-3-3-3-3-3-2}{3}=-5\frac{2}{3}$$

Adding Fractions

$$-\frac{2}{9}+\frac{4}{9}=...$$

$$-\frac{1}{2}-\frac{4}{11}=...$$

$$\frac{2}{3}-\frac{5}{6}=...$$

Adding fractions

$$-\frac{2}{9}+\frac{4}{9}=\frac{2}{9}$$

$$-\frac{1}{2}-\frac{4}{11}=\frac{-1\times 11}{2\times 11}-\frac{4\times 2}{2\times 11}=-\frac{11}{22}-\frac{8}{22}=-\frac{19}{22}$$

$$\frac{2}{3}-\frac{5}{6}=\frac{2\times 6}{3\times 6}-\frac{5\times 3}{3\times 6}=\frac{12}{18}-\frac{15}{18}=-\frac{3}{18}=-\frac{1}{6}$$

Adding fractions - According to the book

$$-\frac{2}{9}+\frac{4}{9}=\frac{2}{9}$$

$$-\frac{1}{2}-\frac{4}{11}=-\frac{11}{22}+\frac{8}{22}=-\frac{3}{22}$$

$$\frac{2}{3}-\frac{5}{6}=\frac{12}{18}-\frac{15}{18}=-\frac{3}{18}=-\frac{1}{6}$$

Worktime

You work neatly by…

1. … reading the theory (again) before asking a question to your classmate.
2. … raising a hand before asking a question to the teacher.
3. … if the teacher is busy, remember your question and move on.
   

Help:

Summary on page 90

Assignments:

Mixed exercises First part

Assignments from the planning of WEEK 1:

Extra:

Exercises on page 99

Now I can…

1. … do calculations with negative fractions.

Reflection

Date	Monday October 28th 2024
Paragraph	Mixed Exercises
Pages from the handbook	Pag. 88-89
Subject	Mixed

Today is the day...

I can already…

1. … do calculations with negative fractions.

Prior Knowledge

Adding Fractions

$$-\frac{2}{11}-\frac{7}{11}=...$$

$$-\frac{1}{2}-\frac{5}{11}=...$$

$$\frac{2}{5}-\frac{5}{6}=...$$

Adding fractions

$$-\frac{2}{11}-\frac{7}{11}=-\frac{9}{11}$$

$$-\frac{1}{2}-\frac{5}{11}=\frac{-1\times 11}{2\times 11}-\frac{5\times 2}{2\times 11}=-\frac{11}{22}-\frac{10}{22}=-\frac{21}{22}$$

$$\frac{2}{5}-\frac{5}{6}=\frac{2\times 6}{5\times 6}-\frac{5\times 5}{5\times 6}=\frac{12}{30}-\frac{25}{30}=-\frac{13}{30}$$

After this lesson, I can…

1. … divide fractions.
   

Goals

Reciprocal

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

$$\frac{4}{5}\cdot \frac{5}{4}=$$

$$\frac{345}{567}\cdot \frac{567}{345}=$$

Reciprocal

$$\frac{2}{3}\cdot \frac{3}{2}=\frac{2\cdot 3}{3\cdot 2}=\frac{6}{6}=1$$

$$\frac{4}{5}\cdot \frac{5}{4}=\frac{4\cdot 5}{5\cdot 4}=\frac{20}{20}=1$$

$$\frac{345}{567}\cdot \frac{567}{345}=\frac{345\cdot 567}{567\cdot 345}=\frac{195615}{195615}=1$$

Dividing fractions

Dividing fractions

$$\frac{2}{3}÷\frac{2}{3}=$$

$$\frac{4}{5}÷\frac{8}{9}=$$

$$\frac{12}{13}÷\frac{3}{4}=$$

Dividing fractions

$$\frac{2}{3}÷\frac{2}{3}=\frac{2}{3}\cdot \frac{3}{2}=\frac{2\cdot 3}{3\cdot 2}=\frac{6}{6}=1$$

$$\frac{4}{5}÷\frac{8}{9}=\frac{4}{5}\cdot \frac{9}{8}=\frac{4\cdot 9}{5\cdot 8}=\frac{36}{40}=\frac{9}{10}$$

$$\frac{12}{13}÷\frac{3}{4}=\frac{12}{13}\cdot \frac{4}{3}=\frac{12\cdot 4}{13\cdot 3}=\frac{48}{39}=1\frac{3}{13}$$

Dividing fractions

$$1\frac{2}{3}÷2\frac{2}{3}=$$

$$2\frac{4}{5}÷2\frac{2}{5}=$$

Dividing fractions

$$1\frac{2}{3}÷2\frac{2}{3}=\frac{5}{3}÷\frac{8}{3}=$$

$$2\frac{4}{5}÷2\frac{2}{5}=\frac{14}{5}÷\frac{12}{5}=$$

Dividing fractions

$$1\frac{2}{3}÷2\frac{2}{3}=\frac{5}{3}÷\frac{8}{8}=$$

$$2\frac{4}{5}÷2\frac{2}{5}=\frac{14}{5}÷\frac{12}{5}=$$

Worktime

You work neatly by…

1. … reading the theory (again) before asking a question to your classmate.
2. … raising a hand before asking a question to the teacher.
3. … if the teacher is busy, remember your question and move on.
   

Help:

Summary on page 90

Assignments:

Mixed exercises First part

Assignments from the planning of WEEK 1:

Extra:

Exercises on page 99

Now I can…

1. … divide fractions.

Reflection