Lesson 13: Problems About Comparing

New Concept

Comparison and elapsed-time problems use a subtraction pattern to find the difference between two values, whether they are quantities or points in time.

Problems About Comparing
Comparison problems have a subtraction pattern. We write the numbers in the equation in this order:

Or, using letters:

Elapsed-Time Problems
Elapsed time is the length of time between two events. Elapsed-time problems also have a subtraction pattern:

Or, using letters:

What’s next

This card introduces the core subtraction pattern. Next, you'll apply this pattern by solving worked examples involving populations, historical dates, and personal ages.

Property

To compare two groups and find the difference, use subtraction:

Explanation

Ever wondered who has more stuff? This is how you find out! Comparison problems use subtraction to find the 'how many more' or 'how many fewer' between two groups. Just take the bigger number, subtract the smaller one, and boom—you have the difference! It's like a math showdown to see who wins.

Full Example

Problem: The Red Team scored 415 points and the Blue Team scored 378 points. How many more points did the Red Team score?
Step 1: This is a comparison problem, so we use the subtraction pattern.
Step 2: We write the equation: Greater $-$ lesser $=$ difference, which becomes $415 - 378 = d$.
Step 3: We solve by subtracting: $415 - 378 = 37$.
Step 4: The Red Team scored 37 more points than the Blue Team.

Property

To find the amount of time that has passed (elapsed time), use this subtraction pattern:

Explanation

Want to know how long a movie is or how many years passed between historical events? That's elapsed time! Think of it as a time machine powered by subtraction. You take the later date (when an event ended) and subtract the earlier date (when it started) to find out exactly how much time passed.

Full Example

Problem: The telephone was invented in 1876. The first smartphone was released in 1994. How many years passed between these two inventions?
Step 1: This is an elapsed-time problem with a subtraction pattern: $l - e = d$.
Step 2: The later year is 1994 and the earlier year is 1876. The equation is $1994 - 1876 = d$.
Step 3: We subtract to find the difference: $1994 - 1876 = 118$.
Step 4: There were 118 years between the invention of the telephone and the first smartphone.

Contextual Explanation

Just subtracting years to find someone's age can trick you! This is because the person might not have had their birthday yet in the current year. 'Verifying' means you double-check the details, like the month and day, to make sure your answer is actually correct and not just a quick guess.

Full Example

Problem: It's October 2025. Your friend was born in December 2013. Is your friend 12 years old?
Step 1: Calculate the difference in years: $2025 - 2013 = 12$.
Step 2: Verify the months. The current month is October (Month 10). The birth month is December (Month 12).
Step 3: Analyze the result. Since your friend's birthday in December hasn't happened yet, they haven't completed their 12th year. They are still 11 years old. Verification saved you from being wrong!