Multiplication

### 1.1. Knowledge to remember

Multiplication of natural numbers, fractions, and decimals all have the following properties:

Commutative properties:

a×b=b×a

Combined properties:

(a×b)×c=a×(b×c)

Multiply a sum by a number:

(a+b)×c=a×c+b×c

Multiplication with a factor of 11:

1×a=a×1=a

Multiplication with a factor of 0:

0×a=a×0=0

### 1.2. Solving exercises in the textbook Practice page 162

**Lesson 1 Textbook page 162**

Calculate

\(\begin{array}{l}

a)4802 \times 324\\

6120 \times 205\\

b)\frac{4}{{17}} \times 2\\

\frac{4}{7} \times \frac{5}{{12}}\\

c)35.4 \times 6.8\\

21.76 \times 2.05

\end{array}\)

**Solution guide:**

b) \(\frac{4}{{17}} \times 2 = \frac{8}{{17}}\)

\(\frac{4}{7} \times \frac{5}{{12}} = \frac{{4 \times 5}}{{7 \times 12}} = \frac{{20}}{ {84}} = \frac{5}{{21}}\)

Lesson 2 Textbook page 162

Mental arithmetic

\(\begin{array}{l}

a)3,25 \times 10;\,\,3,25 \times 0.1\\

b)417.56 \times 100;\,\,\,417.56 \times 0.01\\

c)28.5 \times 100;\,\,28.5 \times 0.01

\end{array}\)

*Solution guide:*

a) 3.25×10=32.5

3.25×0.1=0.325

b) 417.56×100=41756

417.56×0.01=4.1756

c) 28.5×100=2850

28.5×0.01=0.285.

Lesson 3 Textbook page 162

Calculate by the most convenient way:

a) 2.5×7,8×4;

b) 0.5×9.6×2;

c) 8.36×5×0.2;

d) 8.3×7.9+7.9×1.7.

*Solution guide:*

a) 2.5×7.8×4=(2.5×4)×7.8=10×7.8=78;

b) 0.5×9.6×2=(0.5×2)×9.6=1×9.6=9.6;

c) 8.36×5×0.2=8.36×(5×0.2)=8.36×1=8.36

d) 8.3×7.9+7.9×1.7 =(8.3+1.7)×7.9=10×7,9=79.

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