Place Value Exercise: Building the Number 40 Using Ones and Tens

Q: Why does 40 need 4 tens and not 40 ones?

Great question! While $ 40 = 40 \text{ ones} $ is mathematically correct, place value helps us organize numbers efficiently. Using $ 4 \text{ tens} + 0 \text{ ones} $ shows the structure of 40 more clearly.

Q: How do I know which visual blocks represent tens vs ones?

Look at the size and labels! Ten-blocks are larger rectangles divided into 10 squares, while one-blocks are single small squares. The diagram should clearly label "Tens" and "Ones" sections.

Q: What if a number doesn't divide evenly by 10?

Then you'll have a remainder! For example, $ 37 = 3 \text{ tens} + 7 \text{ ones} $ because $ 37 ÷ 10 = 3 $ remainder $ 7 $.

Q: Can I use other combinations like 2 tens + 20 ones for 40?

Mathematically yes, but place value representation uses the most efficient form. Always convert extra ones to tens when possible: $ 20 \text{ ones} = 2 \text{ tens} $, so the standard form is $ 4 \text{ tens} + 0 \text{ ones} $.

Q: How do I check my answer is correct?

Use multiplication to verify: $ 4 \times 10 + 0 \times 1 = 40 + 0 = 40 $ ✓. You can also count the visual blocks to double-check your work!

Place Value Composition with Tens Representation

Build the number 40 from units and tens

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Build the number 40 from units and tens

Step-by-step solution

To solve this problem, we need to represent the number 40 using tens and ones.

Step 1: Determine how many tens are in 40. Since one ten equals 10, dividing 40 by 10 gives us:

$\frac{40}{10} = 4$ . Therefore, there are 4 tens in 40.

Step 2: Determine how many ones (units) are needed. With 40 being evenly divided by 10, there are no ones required, or 0 ones:

Remainder of $\frac{40}{10}$ is 0.

Hence, the number 40 can be represented by 4 tens and 0 ones.

Therefore, the correct choice is:
- 4 boxes of tens plus 0 boxes of ones.

Therefore, the solution to the problem is $40 = 4 \text{ tens} + 0 \text{ ones}$ , which looks like this:

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: One ten equals 10 ones in place value system
Technique: Divide 40 by 10 to get 4 tens, remainder 0 ones
Check: Count visual blocks: 4 tens + 0 ones = 40 ✓

Common Mistakes

Avoid these frequent errors

Confusing tens and ones visual representations
Don't count individual squares within ten-blocks as separate tens = multiplying by 100 instead of 10! Each ten-block represents exactly 10, not the number of squares inside it. Always remember one ten-block equals 10 ones, regardless of its visual divisions.

Practice Quiz

Test your knowledge with interactive questions

What number do the blue squares below represent?

FAQ

Everything you need to know about this question

Why does 40 need 4 tens and not 40 ones?

Great question! While $40 = 40 \text{ ones}$ is mathematically correct, place value helps us organize numbers efficiently. Using $4 \text{ tens} + 0 \text{ ones}$ shows the structure of 40 more clearly.

How do I know which visual blocks represent tens vs ones?

Look at the size and labels! Ten-blocks are larger rectangles divided into 10 squares, while one-blocks are single small squares. The diagram should clearly label "Tens" and "Ones" sections.

What if a number doesn't divide evenly by 10?

Then you'll have a remainder! For example, $37 = 3 \text{ tens} + 7 \text{ ones}$ because $37 ÷ 10 = 3$ remainder $7$ .

Can I use other combinations like 2 tens + 20 ones for 40?

Mathematically yes, but place value representation uses the most efficient form. Always convert extra ones to tens when possible: $20 \text{ ones} = 2 \text{ tens}$ , so the standard form is $4 \text{ tens} + 0 \text{ ones}$ .

How do I check my answer is correct?

Use multiplication to verify: $4 \times 10 + 0 \times 1 = 40 + 0 = 40$ ✓. You can also count the visual blocks to double-check your work!

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