## Math 6 Chapter 3 Lesson 1: Expanding the concept of fractions

## 1. Summary of theory

**Generality: **People call \(\frac{a}{b}\) where \(a,b \in Z, b\neq 0\) is a fraction, a is the numerator (numerator), b is the denominator (denominator). ) of the fraction.

**Eg:** \(\frac{1}{2};\frac{{ – 2}}{3};\frac{3}{{ – 4}};\frac{{ – 5}}{{ – 6}}; …\) are fractions.

**Attention: **

– The integer a is also written as a fraction as \(\dfrac{a}{1}\).

Negative fraction: is a fraction whose numerator and denominator are integers with different signs.

Positive Fraction: A fraction whose numerator and denominator are integers of the same sign.

## 2. Illustrated exercise

**Question 1: **Give three examples of fractions. Give the numerator and denominator of each fraction.

**Solution guide**

– Fraction \(\displaystyle{{ – 7} \over 8}\), where -7 is the numerator, 8 is the denominator

– Fraction \(\displaystyle {{ 14} \over 5}\), where 14 is the numerator, 5 is the denominator

– Fraction \(\displaystyle {9 \over 2}\), where 9 is the numerator, 2 is the denominator

**Verse 2:** Which of the following spellings gives us a fraction?

a) \(\dfrac{4}{7}\) b) \(\dfrac{0.25}{-3}\) c) \(\dfrac{-2}{5}\)

d) \(\dfrac{6,23}{7,4}\) e) \(\dfrac{3}{0}\)

**Solution guide**

How to write fractions as a, c

How to write b, d with numerator is a decimal, so we don’t give a fraction

How to write e has a denominator of 0 so it doesn’t give us a fraction

**Question 3:** Can all integers be written as fractions? For example.

**Solution guide**

Every integer can be written as a fraction

**Eg: **The number 3 can be written as a fraction as \(\dfrac{3}{1}\)

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Which of the following spellings gives us a fraction: \(\dfrac{2}{0};\dfrac{5,34}{3};\dfrac{4}{2,4};\dfrac{- 1}{4};\dfrac{2}{-7}\)

**Verse 2:** Write the following divisions as fractions:

a) \(5:13\)

b) \(-2:9\)

c) \(k:(-5)\),\(k \in Z\)

**Question 3:** Use 2 digits 11 and 13 to write fractions that can be formed from these 2 numbers (only write once). Same for the two numbers 0 and -6.

### 3.2. Multiple choice exercises

**Question 1: **Among the numbers: 0, 2, -5. How many fractions can be formed with the numerator and denominator being 2 of these 3 numbers. (different denominator)

A. 2

B. 4

C. 6

D. 8

**Verse 2: **How much of the picture are the red squares? Use a fraction to represent that part number

A. \(\frac{4}{16}\)

B. \(\frac{4}{12}\)

C. \(\frac{4}{32}\)

D. \(\frac{4}{8}\)

**Question 3: **Given 5 numbers \(0\neq a,b,c,d,e \in Z\). How many fractions can be formed in all with the numerator and denominator of the given 5 numbers. Know that the numerator and denominator must be different.

A. 14

B. 16

C. 18

D. 20

**Question 4: **Which of the following is a fraction:

A. \(\frac{1,25}{4}\)

B. \(\frac{1}{-5}\)

C. \(\frac{2}{0}\)

D. \(\frac{6,4}{-9}\)

**Question 5: **Given the numbers: -1, 2, 3. how many fractions can be made in all with the numerator and denominator being 2 of the 3 numbers. (fractions with different numerators and denominators)

A. 2

B. 4

C. 6

D. 8

## 4. Conclusion

Through this lesson, you should know the following:

- Know the concept of fractions
- Recognize fractions.

.

=============