Lesson 31: Word Problems About Comparing

New Concept

One way to compare two numbers is to subtract to find their difference. We use the formula:

Why it matters

Understanding comparison is your first step in translating real-world situations into the language of algebra. Mastering this structure allows you to model and solve complex problems, from tracking inventory to analyzing scientific data.

What’s next

Next, you’ll apply this formula to solve word problems asking “how many more?” or “how many fewer?” to find the difference between quantities.

To compare two numbers and find the difference, you subtract the smaller number from the larger number. This method is used to find 'how many more' or 'how many fewer'. The formula is:

Example

Eighty is how much greater than fifty-five? $80 - 55 = 25$. To find the difference between 120 and 95, you calculate: $120 - 95 = 25$. A giraffe is 18 feet tall and a zebra is 6 feet tall. How much taller is the giraffe? $18 - 6 = 12$ feet.

Explanation

Think of this as finding the height difference between two towers! This isn't a 'take away' story where things disappear. You are simply measuring the gap between a bigger amount and a smaller one. Subtraction is your trusty measuring tape to find out exactly 'how much more' or 'how much less' one is compared to the other.

Property

When a problem asks you to find 'how many more,' it is asking you to find the difference between a larger quantity and a smaller one. You solve it by subtracting the smaller number from the larger number. This tells you the surplus or extra amount.

Example

Liam scored 95 points and Ava scored 68. How many more points did Liam score? $95 - 68 = 27$. A book has 250 pages and you have read 145. How many more pages do you need to read? $250 - 145 = 105$.

Explanation

Whenever a word problem asks you 'how many more,' it's a secret code that means it's time to subtract! You are just comparing two numbers to see how much extra the bigger one has. Imagine you have more cookies than your friend; the difference is the pile of extra cookies you get to enjoy while they watch.

Property

When a problem asks 'how many fewer' or 'how much less,' you are still finding the difference between two numbers. The calculation is identical to finding 'how many more': subtract the smaller value from the larger value to find the difference between them.

Example

The blue team has 25 players and the red team has 32. How many fewer players does the blue team have? $32 - 25 = 7$. A small pizza has 6 slices and a large one has 10. How many fewer slices does the small pizza have? $10 - 6 = 4$.

Explanation

Don't let the words 'how many fewer' trick your brain! It sounds different, but it's just the other side of the same subtraction coin. You are still finding the exact same gap between two numbers. The math doesn't change: it's always the big number minus the small number. You are just phrasing the answer differently.