Solving Comparison Problems Using Division
Solving Comparison Problems Using Division is a Grade 4 math skill in enVision Mathematics, Chapter 6: Use Operations with Whole Numbers to Solve Problems. Students learn to find an unknown smaller quantity by dividing the larger quantity by the comparison factor.
Key Concepts
Property To find an unknown smaller quantity in a comparison problem, divide the larger quantity by the comparison factor. $$ \text{Smaller Quantity} = {\text{Larger Quantity}}\div{\text{Factor}} $$.
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.
Common Questions
How do you solve comparison problems using division?
When a problem says one amount is a certain number of times larger than another, divide the larger amount by the factor to find the smaller amount. Smaller Quantity equals Larger Quantity divided by Factor.
What is a multiplicative comparison problem?
A multiplicative comparison problem states that one amount is several times as large as another. Division is used to find the smaller amount when the larger amount and the factor are known.
What is an example of a division comparison problem?
A book costs 18 dollars, which is 3 times as much as a magazine. To find the magazine price: 18 divided by 3 equals 6 dollars.
How is division related to multiplication in comparison problems?
Division reverses multiplication. If you know the product and one factor, you can divide to find the other factor, which is how you find the smaller quantity in a multiplicative comparison.
What chapter covers division comparison problems in enVision Grade 4?
Solving comparison problems using division is covered in Chapter 6: Use Operations with Whole Numbers to Solve Problems in enVision Mathematics Grade 4.