Back to Algebra for
Adults.
Rules and Laws and Conventions:
Commutative Law of Addition: "Interchanging the addends does not change their sum."
Additive Identity Property: "Adding zero to any number results in the same number."
Associative Law of Addition, "The way in which numbers are added in groups of two does not change their sum."
Minuend - subtrahend = difference.
Subtrahend + difference = minuend.
Subtracting zero from any number yields the identical number.
Rule of subtracting larger numbers from smaller numbers: "To subtract a larger number from a smaller number, find the difference and set its sign to minus."
Commutative Law of Multiplication: "Interchanging factors does not change their product."
Multiplicative Identity Property: "Multiplying any number by 1 results in the same number."
Multiplicative Property of Zero: "The product of any number and zero is 0."
Associative Law of Multiplication: "The way in which numbers are multiplied in groups of two does not change their product."
To multiply a whole number by a place value, annex as many zeros to the number as there are zeros in the place value.
To multiply a number by a multiple of a place value, ignore the zeros and multiply the numbers, then annex as many zeros as you ignored.
To multiply a number by the sum of two addends, multiply the number by each addend and add the resulting products together.
Dividend / divisor = quotient.
Dividing any number by 1 results in the identical number.
If zero is divided by any nonzero number, the quotient is zero.
Division by zero is undefined.
The value of a fraction does not change if its numerator and denominator are both multiplied by the same number, excluding zero.
The value of a fraction is not changed, if its numerator and denominator are divided by the same number.
To multiply fractions:
First, multiply their numerators to obtain the numerator of the
product.
Second, multiply their denominators to obtain the denominator
of the product.
To obtain the reciprocal of a fraction, interchange its terms.
To divide a number by a nonzero fraction, multiply by its reciprocal or invert and multiply.
We can move any term across an = sign without changing the value of the equation by also moving the term across the division sign.
In the decimal equivalent of a decimal fraction, the number of decimal places of the decimal is equal to the number of zeros in the denominator.
The value of a decimal does not change when zeros are annexed to the right.
The number of decimal places in the product of two or more factors is the sum of the decimal places of the factors.
When a whole number is multiplied by a decimal number, the number of decimal places in the product is equal to the number of decimal places in the decimal number.
To multiply a decimal number by a place value, shift the decimal point to the right as many places as there are zeros in the place value.
A given number of percent is equivalent to a fraction whose numerator is the given number of percent and whose denominator is 100.
Any positive number is greater than 0.
Any negative number is less than 0.
Any positive number is greater than any negative number.
The larger of two positive numbers has the greater absolute value.
The larger of two negative number has the smaller absolute value.
To subtract a signed number, change its sign and add.
To multiply two signed numbers with like signs, multiply their absolute values. The product will be a positive number.
To multiply two signed numbers with unlike signs, multiply their absolute values. The product will be negative number.
For more than two signed numbers, the product is positive if all the numbers are positive, or if there is an even number of negatives.
To divide two signed numbers with like signs, divide the absolute value of the dividend by the absolute value of the divisor. The quotient will be positive.
To divide two signed numbers with unlike signs, divide the absolute value of the dividend by the absolute value of the divisor. The quotient will be negative.
When we multiply a number by a letter the multiplication sign
may be omitted.
Back to Algebra for Adults.
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