Review the concept of fractions

### 1. Theory review

Write: \(\frac{2}{3}\)

Read: two thirds

Write: \(\frac{5}{10}\)

Read: five tenths

Write: \(\frac{3}{4}\)

Read: three quarters

Write: \(\frac{40}{100}\)

Read: forty one hundredths, or forty percent.

\(\frac{2}{3}\); \(\frac{5}{10}\); \(\frac{3}{4}\); \(\frac{40}{100}\) are fractions.

*Attention:*

1) Fractions can be used to record the result of division of a natural number by a non-zero natural number. The fraction can also be the quotient of the given division.

**For example:** 1 : \(3 = \frac{1}{3}\); \(4: 10 =\frac{4}{10}\); \(9: 2 = \frac{9}{2}\); …

2) Every natural number can be written as a fraction with a denominator of 1.

**For example: **\(5 = \frac {5}{1}\); \(12 = \frac {12}{1}\); \(2001 = \frac {2001}{1}\); …

3) The number 1 can be written as a fraction whose numerator and denominator are equal and non-zero.

**For example: **\(1 = \frac {9}{9}\); \(1 = \frac {18}{18}\); \(1 = \frac {100}{100}\); …

4) The number 0 can be written as a fraction with numerator 0 and denominator not 0.

**For example:** \(0 = \frac {0}{7}\); \(0 = \frac {0}{19}\); \(0= \frac {0}{125}\); …

### 2. Illustrated exercise

Lesson 1: Write the following quotients as fractions:

25 : 3; 7: 9; 125 : 13; 181 : 47; 35 : 29

Solution

The quotient of the division of a natural number by a non-zero natural number can be written as a fraction, the numerator being the divisor and the denominator the divisor.

\(\frac{{25}}{{13}}\); \(\frac{7}{9}\); \(\frac{{125}}{{13}}\); \(\frac{{181}}{{47}}\); \(\frac{{35}}{{29}}\)

Lesson 2: Write the following natural numbers as fractions with a denominator of 1:

35; 1241; 13 525; 0; 48 174

Solution

Every natural number can be written as a fraction whose numerator is a given natural number and the denominator is 1.

\(\frac{{35}}{1}\); \(\frac{{1241}}{1}\); \(\frac{{13525}}{1}\); \(\frac{0}{1}\); \(\frac{{48174}}{1}\)

Lesson 3:

a. If the divisor is 0, the order divisor is 102; 205; 361; 408; 1245, what is the order of quotient?

b. The number 1 can be considered the quotient of which numbers?

Solution

a. The number 0 divided by all non-zero natural numbers equals 0, so the quotient in the order is equal to:

\(\frac{0}{{102}} = 0;\) \(\frac{0}{{205}} = 0;\) \(\frac{0}{{361}} = 0;\ ) \(\frac{0}{{408}} = 0;\) \(\frac{0}{{1245}} = 0\)

b. The number 1 is treated as the quotient of a non-zero number divided by the number itself:

\(\frac{{17}}{{17}} = 1;\) \(\frac{{35}}{{35}} = 1;\) \(\frac{{184}}{{184) }} = 1;\) \(\frac{{365}}{{365}} = 1;\) \(\frac{{1256}}{{1256}} = 1\)

### 3. Instructions for solving textbook exercises

**Lesson 1 of the textbook page 4: **

a) Read fractions: \(\frac{5}{7};\frac{{25}}{{100}};\frac{{91}}{{38}};\frac{{60} }{{17}};\frac{{85}}{{1000}}\)

b) State the numerator and denominator of each fraction above

Solution:

a) Five out of seven

Twenty-five percent (or twenty-five percent)

Ninety-one thirty-eight

Sixty-seventeenth

Eighty-five thousandths.

b)

Fraction | \(\frac{5}{7}\) | \(\frac{{25}}{{100}}\) | \(\frac{{91}}{{38}}\) | \(\frac{{60}}{{17}}\) | \(\frac{{85}}{{1000}}\) |

Numerator | 5 | 25 | 91 | 60 | 85 |

Denominator | 7 | 100 | 38 | 17 | 1000 |

**Lesson 2 Textbook page 4: **Write the following quotients as fractions:

3:5; 75:100; 9:17

Solution

\(3:5 = \frac{3}{5};\,\,75:100 = \frac{{75}}{{100}};\,\,\,9:17 = \frac{9 }{{17}}\)

**Lesson 3 Textbook page 4:** Write the following natural numbers as fractions with a denominator of 1:

32; 105; 1000.

Solution

\(32 = \frac{{32}}{1};{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} 105 = \frac{{105}}{1};{\ mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} 1000 = \frac{{1000}}{1}\)

**Lesson 4 Textbook page 4:** Write the correct number in the blank:

a) \(1 = \frac{6}{{…}}\)

b) \(0 = \frac{{…}}{5}\)

Solution

a) \(1 = \frac{6}{1}\)

b) \(0 = \frac{0}{5}\)

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### Related posts:

- Square millimeter. Table of units of area measurement
- Square decimeter. Square Hectometers
- Review Table of units of mass measurement
- Review Table of units of length
- Practice on solving math
- Practice on mixed numbers
- Mixed numbers
- Review Multiplication and division of two fractions
- Review Addition and subtraction of two fractions

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