What is 3 plus zero

Multiplication and division of rational numbers

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In these explanations you will learn how to multiply and divide rational numbers.

Represent the product as a sum

In mathematics, multiplication by a natural number is the simplification of an addition problem and can therefore also be represented as a continuous addition. This is also possible with rational numbers.

Multiplication on the number line

If you multiply two positive whole numbers with each other, then you can also represent this via continued addition on the number line.
If you multiply a positive whole number by a negative whole number, then you can also represent this on the number line.

Division of rational numbers

The division of rational numbers is the opposite of multiplication.

Calculation rules for the multiplication and division of rational numbers

When multiplying or dividing two rational numbers, you have to pay attention to the signs of the numbers.
If both numbers have a positive sign, then the result is also positive. "Plus times plus is plus"
If the first number has a positive sign and the second a negative sign, the result is negative. "Plus times minus is minus"
If the first number has a negative sign and the second a positive sign, the result is negative. "Minus times plus is minus"
If both numbers have a negative sign, the result is positive. "Minus times minus is plus"

Multiplication and division by zero

When multiplied by zero, the result is always zero; division by zero is not defined. That means you can't divide by 0. But if the 0 is divided by any rational number other than 0, the result is always 0.
Multiplication by zero:

Multiplication and division by 1 and -1

The number 1 is the so-called neutral element of multiplication. That means: If you multiply any number by 1, the number does not change.
If you multiply a number by -1, only its sign changes, the amount of the number remains the same.
If you divide any number by 1, the number doesn't change.
If you divide a number by -1, only its sign changes, the amount of the number remains the same.

Multiply rational numbers skillfully

The commutative law and the associative law apply to multiplication. The commutative law (commutation law) allows you to swap the factors of a product: The associative law (connection law) allows you to dispense with brackets in products with several factors: This is why arithmetic expressions that only contain the multiplication sign are often written without brackets. Both laws together have the effect that all factors of a multiplication problem can be interchanged at will. Sometimes it is advantageous to swap the factors, for example if two factors multiplied together result in a power of ten (10, 100, 1000, ...).