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What is the difference between multiplication property of inequality and multiplication property of equality?
The multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. In contrast, the multiplication property of inequality states that if you multiply both sides of an inequality by a positive number, the inequality remains unchanged, but if you multiply by a negative number, the inequality sign must be flipped. Thus, while equality preserves its form, inequality requires careful handling based on the sign of the multiplier.
Why is it not necessary to state a division property of equality?
It follows from the multiplication property of equality. Dividing both sides of an equation by the same number (not by zero, of course) is the same as multiply both sides of the equation by the number's reciprocal. For example, dividing both sides of an equation by 2 is the same as multiplying both sides by 0.5.
When you multiply or divide two quantities by the same number that is called?
When you multiply or divide two quantities by the same number, it is called the "multiplicative property of equality." This property states that if you multiply or divide both sides of an equation by the same non-zero number, the two sides remain equal. It is fundamental in algebra and helps maintain the integrity of equations during transformations.
What is the property that states that if you add the same number to both sides of an equation the new equation will have the same solution?
Associative? Commutativity?
Which property justifies the procedure used to eliminate fractions and decimals from equations?
The property that justifies the procedure used to eliminate fractions and decimals from equations is the Multiplicative Property of Equality. This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. By multiplying through by a common denominator or a power of ten, you can effectively eliminate fractions or decimals, simplifying the equation for easier manipulation.
What is the property that states that if you multiply both sides of an equation by the same number the new equation will have the same solution?
im not a 100 percent sure but i think its.... Multiplication Property of Equality
What is an addition property of equality?
The addition property of equality states that if you add the same number to both sides of an equation, then the sides remain even. This means that the equation remains to be true.
What is the difference between multiplication property of inequality and multiplication property of equality?
The multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. In contrast, the multiplication property of inequality states that if you multiply both sides of an inequality by a positive number, the inequality remains unchanged, but if you multiply by a negative number, the inequality sign must be flipped. Thus, while equality preserves its form, inequality requires careful handling based on the sign of the multiplier.
Why is it not necessary to state a division property of equality?
It follows from the multiplication property of equality. Dividing both sides of an equation by the same number (not by zero, of course) is the same as multiply both sides of the equation by the number's reciprocal. For example, dividing both sides of an equation by 2 is the same as multiplying both sides by 0.5.
When you multiply or divide two quantities by the same number that is called?
When you multiply or divide two quantities by the same number, it is called the "multiplicative property of equality." This property states that if you multiply or divide both sides of an equation by the same non-zero number, the two sides remain equal. It is fundamental in algebra and helps maintain the integrity of equations during transformations.
What is the property that states that if you add the same number to both sides of an equation the new equation will have the same solution?
Associative? Commutativity?
Which property justifies the procedure used to eliminate fractions and decimals from equations?
The property that justifies the procedure used to eliminate fractions and decimals from equations is the Multiplicative Property of Equality. This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. By multiplying through by a common denominator or a power of ten, you can effectively eliminate fractions or decimals, simplifying the equation for easier manipulation.
The rules of algebra used to transform equations into equivalent equations?
multiply the entire equation by a numberdivide the entire equation by a numberadd numbers to both sides of the equationsubtract numbers from both sides of the equationuse the commutative property to rearrange the equationuse the associative property to rearrange the equationfactor a number out of a portion of the equation
What is the addition property of equality?
The Addition Property of Equality states that if you add the same number to both sides of an equation the two sides remain equal. Source- My mathbook.
What is multiplication property of equality?
The multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. For example, if ( a = b ), then multiplying both sides by a number ( c ) (where ( c \neq 0 )) gives ( ac = bc ). This property is fundamental in algebra for solving equations and maintaining balance in equations during manipulation.
Should the number that multiplies each side of the equation be nonzero when using multiplication property?
Yes, it should be non-zero; if you multiply both sides by zero you wipe out the equation.
Which property of equality would you use to solve the equation 14x56?
To solve the equation ( 14x = 56 ), you would use the Division Property of Equality. This property states that if you divide both sides of the equation by the same non-zero number, the two sides remain equal. In this case, you would divide both sides by 14 to isolate ( x ), resulting in ( x = 4 ).
