We will discuss here all the properties of multiplication of decimal numbers.

1. The product of a decimal and a whole number multiplied in any order remains the same.

**For Example:**

(i) 0.9 × 12 = 12 × 0.9 = 10.8

(ii) 1.1 × 30 = 30 × 1.1 = 33.0

(iii) 2.1 × 14 = 14 × 2.1 = 29.4

(iv) 1.8 × 11 = 11 × 1.8 = 19.8

(v) 0.7 × 17 = 17 × 0.7 = 11.9

2. The product of two decimal numbers remains the same, even if the order is changed.

**For Example:**

(i) 2.5 × 3.5 = 3.5 × 2.5 = 8.75

(ii) 1.4 × 0.8 = 0.8 × 1.4 = 1.12

(iii) 4.2 × 2.1 = 2.1 × 4.2 = 8.82

(iv) 0.5 × 1.5 = 1.5 × 0.5 = 0.75

(v) 3.7 × 1.9 = 1.9 × 3.7 = 7.03

3. The product of a decimal fraction and 1 is the decimal fraction itself.

**For Example:**

(i) 1.092 × 1 = 1.092

(ii) 1.002 × 1 = 1.002

(iii) 12.619 × 1 = 12.619

(iv) 2.519 × 1 = 2.519

(v) 0.127 × 1 = 0.127

4. The product of a decimal fraction and zero is zero.

**For Example:**

(i) 891.56 × 0 = 0

(ii) 1.009 × 0 = 0

(iii) 0.008 × 0 = 0

(iv) 42.19 × 0 = 0

(v) 16.35 × 0 = 0

5. While performing multiplication in decimals, the numbers can be taken in any order and the product remains the same.

**For Example:**

(i) 1.02 × (11.2 × 2.3) = 1.02 × 25.76 = 26.2752 |
(1.02 × 2.3) × 11.2 = 2.346 × 11.2 = 26.2752 |

So the product of more than two decimals does not change if their grouping order is changed.

Therefore, 1.02 × (11.2 × 2.3) = (1.02 × 2.3) × 11.2

(ii) (1.20 × 0.3) × 1.18 = 0.3 × (1.18 × 1.20)

0.36 × 1.18 = 0.3 × 1.416

0.4248 = 0.4248

Therefore, (1.20 × 0.3) × 1.18 = 0.3 × (1.18 × 1.20)

Since, we know the product of two decimals or more does not change if their grouping order is changed.

**● Decimal.**

**Expanded form of Decimal Fractions.**

**Changing Unlike to Like Decimal Fractions.**

**Comparison of Decimal Fractions.**

**Conversion of a Decimal Fraction into a Fractional Number.**

**Conversion of Fractions to Decimals Numbers.**

**Addition of Decimal Fractions.**

**Problems on Addition of Decimal Fractions**

**Subtraction of Decimal Fractions.**

**Problems on Subtraction of Decimal Fractions**

**Multiplication of a Decimal Numbers.**

**Multiplication of a Decimal by 10, 100, 1000**

**Multiplication of a Decimal by a Decimal.**

**Properties of Multiplication of Decimal Numbers.**

**Problems on Multiplication of Decimal Fractions**

**Division of a Decimal by a Whole Number.**

**Division of Decimal Fractions by Multiples.**

**Division of a Decimal by a Decimal.**

**Division of a whole number by a Decimal.**

**Properties of Division of Decimal Numbers**

**Problems on Division of Decimal Fractions**

**Conversion of fraction to Decimal Fraction.**

**5th Grade Numbers Page**

**5th Grade Math Problems**

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