How do you write 17 tens three different ways and use the largest unit?
The correct answer and explanation is:
Correct Answer:
“17 tens” can be written in three different ways, including using the largest unit:
- As a number:
17 tens = 170 - As a sum of tens:
17 tens = 10 + 10 + 10 + … + 10 (seventeen times) - Using the largest unit (hundreds and tens):
17 tens = 1 hundred and 7 tens
(Since 10 tens = 100, and 7 tens = 70)
Explanation (300 words):
Place value is a foundational concept in mathematics that helps us understand how numbers are built using units like ones, tens, hundreds, and so on.
When we say “17 tens,” we’re referring to 17 groups of ten. Since each group of ten equals 10, we calculate: 17×10=17017 \times 10 = 170
This gives us the first form, writing it as a standard number: 170.
Next, to express it in an expanded or repeated addition form, we simply add the value of each ten repeatedly: 10+10+10+…+10(17 times)=17010 + 10 + 10 + \ldots + 10 \quad (\text{17 times}) = 170
This is the second way—useful for visualizing how groups build up to a larger number, especially for early learners.
The third way involves expressing 17 tens using larger place value units, such as hundreds and tens. Since:
- 10 tens = 1 hundred (or 100)
- The remaining 7 tens = 70
So, 17 tens = 1 hundred and 7 tens. This shows understanding of regrouping and how numbers can be broken down using the largest possible unit, which here is the hundred.
This third method is particularly helpful in transitioning to understanding place value in multi-digit arithmetic, especially in operations like addition or subtraction that involve regrouping or carrying.
By practicing these three forms, students build flexible thinking in math and better understand how numbers relate to place value.