Compare small numbers by a fraction of large numbers

### 1.1. Knowledge to remember

#### 1.1.1. For example

The length of line segment CD is 3 times the length of line segment AB.

We say that: Length of line segment AB is equal to \(\frac{1}{3}\) length of line segment CD.

#### 1.1.2. Problem

Mother is 30 years old, daughter is 6 years old. Ask how many times the age of the son is equal to the mother’s age?

*Solution:*

The mother’s age is several times that of her son’s age:

30 : 6 = 5 (times)

So age is equal to \(\frac{1}{5}\) mother’s age.

Answer: \(\frac{1}{5}\).

### 1.2. Solving Textbook Exercises

**Lesson 1:** Write in the blank (according to the form)

Big number | Small number | How many times bigger is the smaller number? | The small number is one part of the large number? |

8 | 2 | 4 | \(\frac{1}{4}\) |

6 | 3 | ||

ten | 2 |

__Solution guide:__

- To find the number of times larger than the smaller number, divide the larger number by the smaller number.
- Then find a small number that is a fraction of a larger number.

Big number | Small number | How many times bigger is the smaller number? | The small number is one part of the large number? |

8 | 2 | 4 | \(\frac{1}{4}\) |

6 | 3 | 2 | \(\frac{1}{2}\) |

ten | 2 | 5 | \(\frac{1}{5}\) |

**Lesson 2:** The upper compartment holds 6 books, the lower compartment holds 24 books. The number of books on the top shelf is equal to one-third of the number of books on the bottom shelf?

__Solution guide:__

* Summary:*

Top drawer: 6 books

Lower compartment: 24 books

The number of books in the upper drawer is equal to one part of the number of books in the lower shelf?

To find the solution, we divide the number of books in the lower drawer by the number of books in the upper compartment.

*Solution*

The number of books on the bottom shelf is twice as many as the number of books on the top shelf:

24 : 6 = 4 (times).

So the number of books in the upper drawer is equal to \(\frac{1}{4}\) number of books in the lower shelf.

**Lesson 3:** The number of blue squares is equal to one part of the number of white squares?

__Solution guide:__

- Count the number of blue and white squares.
- Divide the number of white squares by the number of blue squares and then answer the question.

a) There are 1 blue square, 5 white squares.

The number of white squares is more than the number of blue squares: 5 : 1 = 5 (times)

So the number of blue squares is equal to \(\frac{1}{5}\) number of white squares.

b) There are 2 blue squares, 6 white squares.

The number of white squares is more than the number of blue squares: 6 : 2 = 3 (times)

So the number of blue squares is equal to \(\frac{1}{3}\) number of white squares.

c) There are 2 blue squares, 4 white squares.

The number of white squares is more times than the number of blue squares: 4 : 2 = 2 (times)

So the number of blue squares is equal to \(\frac{1}{2}\) number of white squares.

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