§2.6 Negative Fractions

C2 Numbers & Operations

Mr. Fintelman (FNL)

Friday October 18th

2024

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C2 Numbers & Operations

Mr. Fintelman (FNL)

Friday October 18th

2024

Slide 1 - Diapositive

Date

Friday October 18th

Paragraph

§2.6 Negative Fractions

Pages from the handbook

Pag. 83-85

Subject

Adding and subtracting negative fractions

Today is the day...

Slide 2 - Diapositive

I can already…

… do calculations that involve a fraction bar.

Prior Knowledge

Slide 3 - Diapositive

Fraction bar

\frac{​ 4 + 2 ​ ​}{​ 3 ​} =

\frac{​ 6 - 3 ​ ​}{​ 2 + 1 ​} =

\frac{​ 5 \times 2 ​ ​}{​ 1 0 - 4 ​} =

\frac{​ 3 + 5 ​ ​}{​ 2 ​} - 1 =

Slide 4 - Diapositive

After this lesson, I can…

… do calculations with negative fractions.

Goals

Slide 5 - Diapositive

Simplify Fractions

\frac{​ - 2 5 ​ ​}{​ 6 ​} = . . .

\frac{​ - 5 8 ​ ​}{​ 1 1 ​} = . . .

\frac{​ 1 7 ​ ​}{​ - 3 ​} = . . .

Slide 6 - Diapositive

Simplify Fractions

\frac{​ - 2 5 ​ ​}{​ 6 ​} = \frac{​ - 6 - 6 - 6 - 6 - 1 ​ ​}{​ 6 ​} = - 4 \frac{​ 1 ​ ​}{​ 6 ​}

\frac{​ - 5 8 ​ ​}{​ 1 1 ​} = \frac{​ - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 3 ​ ​}{​ 1 1 ​} = - 5 \frac{​ 3 ​ ​}{​ 1 1 ​}

\frac{​ 1 7 ​ ​}{​ - 3 ​} = \frac{​ - 3 - 3 - 3 - 3 - 3 - 2 ​ ​}{​ 3 ​} = - 5 \frac{​ 2 ​ ​}{​ 3 ​}

Slide 7 - Diapositive

Simplify Fractions

\frac{​ - 2 5 ​ ​}{​ 6 ​} = \frac{​ - 6 - 6 - 6 - 6 - 1 ​ ​}{​ 6 ​} = - 4 \frac{​ 1 ​ ​}{​ 6 ​}

\frac{​ - 5 8 ​ ​}{​ 1 1 ​} = \frac{​ - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 3 ​ ​}{​ 1 1 ​} = - 5 \frac{​ 3 ​ ​}{​ 1 1 ​}

\frac{​ 1 7 ​ ​}{​ - 3 ​} = \frac{​ - 3 - 3 - 3 - 3 - 3 - 2 ​ ​}{​ 3 ​} = - 5 \frac{​ 2 ​ ​}{​ 3 ​}

Slide 8 - Diapositive

Adding Fractions

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

- \frac{​ 1 ​ ​}{​ 2 ​} - \frac{​ 4 ​ ​}{​ 1 1 ​} = . . .

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

Slide 9 - Diapositive

Adding fractions

- \frac{​ 2 ​ ​}{​ 9 ​} + \frac{​ 4 ​ ​}{​ 9 ​} = \frac{​ 2 ​ ​}{​ 9 ​} = \frac{​ 1 ​ ​}{​ 3 ​}

- \frac{​ 1 ​ ​}{​ 2 ​} - \frac{​ 4 ​ ​}{​ 1 1 ​} = \frac{​ - 1 \times 1 1 ​ ​}{​ 2 \times 1 1 ​} - \frac{​ 4 \times 2 ​ ​}{​ 2 \times 1 1 ​} = - \frac{​ 1 1 ​ ​}{​ 2 2 ​} - \frac{​ 8 ​ ​}{​ 2 2 ​} = - \frac{​ 1 9 ​ ​}{​ 2 2 ​}

\frac{​ 2 ​ ​}{​ 3 ​} - \frac{​ 5 ​ ​}{​ 6 ​} = \frac{​ 2 \times 6 ​ ​}{​ 3 \times 6 ​} - \frac{​ 5 \times 3 ​ ​}{​ 3 \times 6 ​} = \frac{​ 1 2 ​ ​}{​ 1 8 ​} - \frac{​ 1 5 ​ ​}{​ 1 8 ​} = - \frac{​ 3 ​ ​}{​ 1 8 ​} = - \frac{​ 1 ​ ​}{​ 6 ​}

Slide 10 - Diapositive

Adding fractions - According to the book

- \frac{​ 2 ​ ​}{​ 9 ​} + \frac{​ 4 ​ ​}{​ 9 ​} = \frac{​ 2 ​ ​}{​ 9 ​} = \frac{​ 1 ​ ​}{​ 3 ​}

- \frac{​ 1 ​ ​}{​ 2 ​} - \frac{​ 4 ​ ​}{​ 1 1 ​} = - \frac{​ 1 1 ​ ​}{​ 2 2 ​} + \frac{​ 8 ​ ​}{​ 2 2 ​} = - \frac{​ 3 ​ ​}{​ 2 2 ​}

\frac{​ 2 ​ ​}{​ 3 ​} - \frac{​ 5 ​ ​}{​ 6 ​} = \frac{​ 1 2 ​ ​}{​ 1 8 ​} - \frac{​ 1 5 ​ ​}{​ 1 8 ​} = - \frac{​ 3 ​ ​}{​ 1 8 ​} = - \frac{​ 1 ​ ​}{​ 6 ​}

Slide 11 - Diapositive

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: 83, 84, 85, 86 and 87.

Assignments:

Pages: 83-85

Exercises: 83, 85, 86 and 88.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 89

Slide 12 - Diapositive

Now I can…

… do calculations with negative fractions.

Reflection

Slide 13 - Diapositive

Date

Monday October 21st 2024

Paragraph

§2.6 Negative Fractions

Pages from the handbook

Pag. 85-87

Subject

Dividing fractions

Today is the day...

Slide 14 - Diapositive

I can already…

… do calculations with negative fractions.

Prior Knowledge

Slide 15 - Diapositive

Adding Fractions

- \frac{​ 2 ​ ​}{​ 1 1 ​} - \frac{​ 7 ​ ​}{​ 1 1 ​} = . . .

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

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

Slide 16 - Diapositive

Adding fractions

- \frac{​ 2 ​ ​}{​ 1 1 ​} - \frac{​ 7 ​ ​}{​ 1 1 ​} = - \frac{​ 9 ​ ​}{​ 1 1 ​}

- \frac{​ 1 ​ ​}{​ 2 ​} - \frac{​ 5 ​ ​}{​ 1 1 ​} = \frac{​ - 1 \times 1 1 ​ ​}{​ 2 \times 1 1 ​} - \frac{​ 5 \times 2 ​ ​}{​ 2 \times 1 1 ​} = - \frac{​ 1 1 ​ ​}{​ 2 2 ​} - \frac{​ 1 0 ​ ​}{​ 2 2 ​} = - \frac{​ 2 1 ​ ​}{​ 2 2 ​}

\frac{​ 2 ​ ​}{​ 5 ​} - \frac{​ 5 ​ ​}{​ 6 ​} = \frac{​ 2 \times 6 ​ ​}{​ 5 \times 6 ​} - \frac{​ 5 \times 5 ​ ​}{​ 5 \times 6 ​} = \frac{​ 1 2 ​ ​}{​ 3 0 ​} - \frac{​ 2 5 ​ ​}{​ 3 0 ​} = - \frac{​ 1 3 ​ ​}{​ 3 0 ​}

Slide 17 - Diapositive

After this lesson, I can…

… divide fractions.

Goals

Slide 18 - Diapositive

Reciprocal

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

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

\frac{​ 3 4 5 ​ ​}{​ 5 6 7 ​} \cdot \frac{​ 5 6 7 ​ ​}{​ 3 4 5 ​} =

Slide 19 - Diapositive

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{​ 2 0 ​ ​}{​ 2 0 ​} = 1

\frac{​ 3 4 5 ​ ​}{​ 5 6 7 ​} \cdot \frac{​ 5 6 7 ​ ​}{​ 3 4 5 ​} = \frac{​ 3 4 5 \cdot 5 6 7 ​ ​}{​ 5 6 7 \cdot 3 4 5 ​} = \frac{​ 1 9 5 6 1 5 ​ ​}{​ 1 9 5 6 1 5 ​} = 1

Slide 20 - Diapositive

Dividing fractions

Slide 21 - Diapositive

Dividing fractions

\frac{​ 2 ​ ​}{​ 3 ​} \div \frac{​ 2 ​ ​}{​ 3 ​} =

\frac{​ 4 ​ ​}{​ 5 ​} \div \frac{​ 8 ​ ​}{​ 9 ​} =

\frac{​ 1 2 ​ ​}{​ 1 3 ​} \div \frac{​ 3 ​ ​}{​ 4 ​} =

Slide 22 - Diapositive

Dividing fractions

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

\frac{​ 4 ​ ​}{​ 5 ​} \div \frac{​ 8 ​ ​}{​ 9 ​} = \frac{​ 4 ​ ​}{​ 5 ​} \cdot \frac{​ 9 ​ ​}{​ 8 ​} = \frac{​ 4 \cdot 9 ​ ​}{​ 5 \cdot 8 ​} = \frac{​ 3 6 ​ ​}{​ 4 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 ​}

\frac{​ 1 2 ​ ​}{​ 1 3 ​} \div \frac{​ 3 ​ ​}{​ 4 ​} = \frac{​ 1 2 ​ ​}{​ 1 3 ​} \cdot \frac{​ 4 ​ ​}{​ 3 ​} = \frac{​ 1 2 \cdot 4 ​ ​}{​ 1 3 \cdot 3 ​} = \frac{​ 4 8 ​ ​}{​ 3 9 ​} = 1 \frac{​ 3 ​ ​}{​ 1 3 ​}

Slide 23 - Diapositive

Dividing fractions

1 \frac{​ 2 ​ ​}{​ 3 ​} \div 2 \frac{​ 2 ​ ​}{​ 3 ​} =

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

Slide 24 - Diapositive

Dividing fractions

1 \frac{​ 2 ​ ​}{​ 3 ​} \div 2 \frac{​ 2 ​ ​}{​ 3 ​} = \frac{​ 5 ​ ​}{​ 3 ​} \div \frac{​ 8 ​ ​}{​ 3 ​} =

2 \frac{​ 4 ​ ​}{​ 5 ​} \div 2 \frac{​ 2 ​ ​}{​ 5 ​} = \frac{​ 1 4 ​ ​}{​ 5 ​} \div \frac{​ 1 2 ​ ​}{​ 5 ​} =

Slide 25 - Diapositive

Dividing fractions

1 \frac{​ 2 ​ ​}{​ 3 ​} \div 2 \frac{​ 2 ​ ​}{​ 3 ​} = \frac{​ 5 ​ ​}{​ 3 ​} \div \frac{​ 8 ​ ​}{​ 3 ​} = \frac{​ 5 ​ ​}{​ 3 ​} \cdot \frac{​ 3 ​ ​}{​ 8 ​} = \frac{​ 1 5 ​ ​}{​ 2 4 ​}

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

\frac{​ 7 0 ​ ​}{​ 6 0 ​} = 1 \frac{​ 1 0 ​ ​}{​ 6 0 ​} = 1 \frac{​ 1 ​ ​}{​ 6 ​}

Slide 26 - Diapositive

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: 83, 84, 85, 86, 87, 91, 92, 93, 94 and 95.

Assignments:

Pages: 83-87

Exercises: 83, 85, 86, 88, 91, 92, 93, 94 and 95.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 89 and 96.

Slide 27 - Diapositive

Now I can…

… divide fractions.

Reflection

Slide 28 - Diapositive

§2.6 Negative Fractions

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Plus de leçons comme celle-ci

Last lesson Chapter 2

2.3 Fractions

§1.2 Simplifying Fractions

§2.5 Multiplying and Dividing Negative Numbers

§2.4 Negative Numbers

§1.3 Multiplying, Adding and Subtracting Powers

Simplification

§1.1 Expanding Brackets