Multiply a decimal by a natural number

### 1.1. Knowledge to remember

**a) Example 1:** Triangle ABC has three equal sides, each side is 1.2m long. How many meters is the perimeter of that triangle?

We have to do the multiplication: 1,2 x 3 = ? (m)

We have: 1.2m = 12dm

So: 1.2 x 3 = 3.6 (m)

Usually we set the calculation and then do the following:

- Perform multiplication like natural numbers.
- The decimal part of the number 1,2 has one digit, we use commas to separate the product of one digit from right to left.

**b) Example 2:** 0.46 x 12 = ?

We set and do the following:

- Perform multiplication like natural numbers
- The decimal part of the number 0.46 has two digits, we use commas to separate the product of two digits from right to left.
- To multiply a decimal by a natural number, do the following:
- Perform multiplication like natural numbers.
- Count how many digits are in the decimal part of the decimal, and then use commas to separate the number of digits from right to left.

### 1.2. Solving textbook exercises page 56

**Lesson 1 Textbook page 56**

Calculate then calculate:

a) 2.5×7 b) 4.18×5

c) 0.256×8 d) 6.8×15

__Solution guide:__

a) \(\frac{{ \times \begin{array}{*{20}{c}}

{2,5}\\

{\,\,\,\,7}

\end{array}}}{{17,5}}\)

b) \(\frac{{ \times \begin{array}{*{20}{c}}

{4,18}\\

{\,\,\,\,\,\,\,5}

\end{array}}}{{20,90}}\)

c) \(\frac{{ \times \begin{array}{*{20}{c}}

{0,256}\\

{\,\,\,\,\,\,\,\,\,\,8}

\end{array}}}{{\,\,2,048}}\)

d) \(\frac{{ \times \begin{array}{*{20}{c}}

{6,8}\\

{1\,\,\,5}

\end{array}}}{{\frac{\begin{array}{l}

340\\

48

\end{array}}{{102.0}}}}\)

Lesson 2 Textbook page 56

Write the correct number in the blank:

Factor | 3.18 | 8.07 | 2,389 |

Factor | 3 | 5 | ten |

Tich |

__Solution guide:__

We have: 3.28×3=9.54

8.07×5=40.35

2.389×10=23.89

So we have the following table of results:

Factor | 3.18 | 8.07 | 2,389 |

Factor | 3 | 5 | ten |

Tich | 9.54 | 40.35 | 23.89 |

Lesson 3 Textbook page 56

A car travels 42.6km per hour. How many kilometers did the car travel in 4 hours?

__Solution guide:__

The number of kilometers that the car travels in 4 hours is:

42.6×4=170.4(km)

Answer: 170.4km

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