10 divided by what equals 4
The Correct Answer and Explanation is :
The correct answer is: [ \frac{10}{2.5} = 4 ]
To determine what number 10 divided by equals 4, we can set up the equation:
[ \frac{10}{x} = 4 ]
where ( x ) is the unknown number we are trying to find. To solve for ( x ), we can multiply both sides of the equation by ( x ) to eliminate the fraction:
[ 10 = 4x ]
Next, we can isolate ( x ) by dividing both sides by 4:
[ x = \frac{10}{4} ]
Simplifying ( \frac{10}{4} ) gives us:
[ x = 2.5 ]
Thus, 10 divided by 2.5 equals 4:
[ \frac{10}{2.5} = 4 ]
Explanation:
This problem involves basic algebraic manipulation, specifically working with fractions and equations. When we start with the equation ( \frac{10}{x} = 4 ), we recognize that we need to find a number that, when 10 is divided by it, results in 4. To solve for ( x ), we use multiplication to eliminate the fraction, which is a common technique in algebra.
Dividing 10 by ( x ) equates to saying that we are distributing the total (10) into parts that, when totaled, equal 4 parts of whatever size ( x ) is. The multiplication by ( x ) helps to clarify the relationship between the total and the parts. After isolating ( x ) by dividing both sides by 4, we simplify the fraction ( \frac{10}{4} ) to arrive at our solution of 2.5.
Understanding this process emphasizes the importance of algebra in solving equations and can help build a strong foundation for more complex mathematical concepts. Knowing how to manipulate equations accurately is a key skill in both academic settings and real-life problem-solving situations.