Problems About Comparing
Problems about comparing have a 'greater minus lesser equals difference' structure (g - l = d). To find how much more one quantity is than another, subtract the lesser from the greater. If a mountain is 14,410 feet tall and a building is 1,454 feet tall, the difference is 14,410 minus 1,454 = 12,956 feet. This Grade 7 math skill from Saxon Math, Course 2 teaches students to identify comparison problems and write the correct subtraction equation, distinguishing this type from separating problems — a critical step for accurate word problem analysis.
Key Concepts
Property The difference is found by subtracting the lesser number from the greater number. $$ \text{greater} \text{lesser} = \text{difference} $$ $$ g l = d $$.
Examples How many more employees work at a factory with 1320 people than one with 897? $1320 897 = 423$ employees. The number 620,000 is how much less than 1,000,000? $1,000,000 620,000 = 380,000$. How much taller is a 58 inch sibling than a 55 inch sibling? $58 55 = 3$ inches.
Explanation Think like a detective! When a problem asks 'how much greater?' or 'how much less?', you're hunting for the 'difference.' This is just the gap between two numbers. To crack the case, you simply need to subtract the smaller value from the bigger one. It’s the easiest way to solve the mystery!
Common Questions
What is a comparing problem in math?
A comparing problem asks how much more (or less) one quantity is than another. The structure is: greater - lesser = difference, or g - l = d.
What equation do I write for a comparing problem?
Write g - l = d, where g is the greater amount, l is the lesser amount, and d is the difference. If you know two of the three values, solve for the third.
How do I identify a comparing problem?
Look for words like 'how much more,' 'how much greater,' 'how many more,' or 'how much less.' If the problem asks for the difference between two quantities, it is a comparing problem.
What is the difference between a comparing problem and a separating problem?
A separating problem starts with a whole and removes part of it. A comparing problem finds the difference between two separate quantities. Both use subtraction but for different reasons.
When do students learn about comparing problems?
Problem type identification (comparing, separating, combining) is introduced in Grade 3-5 and formalized in Grade 7. Saxon Math, Course 2 covers comparing problems in Chapter 3.
How do I find the greater amount if I know the lesser and the difference?
Add the lesser and the difference: g = l + d. If a school has 245 more students than a library has books, and the library has 800 books, the school has 800 + 245 = 1,045 students.
How do comparing problems connect to inequality concepts?
Comparing problems establish the idea that quantities have an ordered relationship. This directly connects to inequalities (greater than, less than) and the number line concepts in algebra.