How to Find Integers Equivalent Quotients
To find equivalent quotients using integers, one must understand that "equivalent" in mathematics means "equal in value". This implies that two different expressions or calculations can yield the same result, hence, they are equivalent.
For integers, equivalent quotients can be found by creating different fraction expressions that yield the same result when simplified.
Here are steps you can follow:
1. Identify the target quotient:
You first need to know what quotient you're trying to find equivalents for. For example, if we take the quotient 2, we're looking for integer fractions that simplify to 2.
2. Formulate equivalent fractions:
Remember that a quotient is simply the result of a division operation. Hence, to find equivalent quotients, you need to find pairs of integers that yield the same result when one is divided by the other.
For the quotient 2, we can easily see that the following pairs of integers yield this quotient when the first is divided by the second:
- \(4 \div 2\)
- \(6 \div 3\)
- \(10 \div 5\)
- \(20 \div 10\)
- \(-4 \div -2\) (remember, dividing two negative integers results in a positive quotient)
And so on. Thus, fractions formed by these pairs of integers (4/2, 6/3, 10/5, 20/10, -4/-2) are all equivalent to the quotient 2.
Remember that these fractions are not in simplified form. If simplified, they will all result in the fraction \(2/1\), which is simply 2.
This method can be applied to find equivalent quotients for any integer.
Examples of Equivalent Quotients with Integers
1) \(8 ÷ 4\) and \(16 ÷ 8\).
Both expressions result in \(2\), so they are equivalent quotients.
2) \(-18 ÷ -6\) and \(27 ÷ 9\).
Both expressions result in \(3\), so they are equivalent quotients.
3) \(20 ÷ -5\) and \(-40 ÷ 10\).
Both expressions result in \(-4\), so they are equivalent quotients.