Lesson 2: Continue to Solve Comparison Problems

Property

Solving a division problem, such as $A \div B = ?$, is the same as finding the unknown factor in the related multiplication equation, $B \times ? = A$.
The quotient of the division is the unknown factor.

Examples

Property

Multiplication and division are inverse operations, which means they "undo" each other. For any number $x$ and any non-zero number $a$:

Examples

Property

To find an unknown smaller quantity in a comparison problem, divide the larger quantity by the comparison factor.

Examples

• A book costs 18 dollars, which is 3 times as much as a magazine. To find the cost of the magazine, you calculate: $18 \div 3 = 6$. The magazine costs 6 dollars.
• A bus traveled 120 miles. This is 4 times the distance a car traveled. To find the distance the car traveled, you calculate: $120 \div 4 = 30$. The car traveled 30 miles.

Explanation

This skill applies the inverse relationship between multiplication and division to solve real-world problems. When a problem states that one amount is a certain number of times larger than another, it describes a multiplicative comparison. If you know the larger amount and the factor, you can use division to find the original, smaller amount. This is like working backward from a multiplication equation to find a missing factor.