Solve Decimal Addition: 0.7 + 0.4 Using Visual Blocks

Q: Why do I get 11 when adding 7 + 4 in the tenths place?

That's correct! $ 7 + 4 = 11 $ tenths. But since 10 tenths = 1 whole, you write down 1 tenth and carry 1 whole to the ones place.

Q: How do the visual blocks help me understand the answer?

The blocks show visual proof! Count the filled sections: 0.7 fills 7 tenths, 0.4 fills 4 more tenths. Together that's 11 tenths, which equals 1 whole block plus 1 tenth = 1.1.

Q: What if I wrote 0.11 instead of 1.1?

That's a place value error! 0.11 means 1 tenth + 1 hundredth, but we have 1 whole + 1 tenth. Always check: does your answer make sense with the visual model?

Q: Do I always need to carry when adding decimals?

Only when the sum in any place value is 10 or greater. If 7 + 4 = 11, you carry. If it were 3 + 4 = 7, no carrying needed!

Q: How can I check my decimal addition without the visual?

Use estimation! $ 0.7 $ is close to 1, and $ 0.4 $ is close to 0.5. So 1 + 0.5 = 1.5, and 1.1 is reasonably close to this estimate.

Decimal Addition with Visual Representation

$0.7+0.4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We will use long addition for calculation

00:08 We will place the decimal point in the appropriate position

00:12 We will start by adding the smallest appropriate digits

00:21 We will place the units and remember 1 above

00:29 We will add 1 to this calculation

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$0.7+0.4=$

Step-by-step solution

To solve this problem, we will add the two decimal fractions $0.7$ and $0.4$ .

Let's break down the process:

Step 1: Align the numbers by their decimal points:
$\phantom{+}0.7$
$+0.4$
Step 2: Add the numbers column by column starting from the rightmost place (tenths place):
$7 + 4 = 11$
Step 3: Write down the 1 in the tenths place and carry over 1 to the units place. There is no whole number component in this addition, so simply add the carry to $0$ which is $1 + 0 = 1$ .
Step 4: Combine the results to find the total: $1.1$ .

Thus, the sum of $0.7$ and $0.4$ is $\mathbf{1.1}$ .

The correct choice is 1: 1.1.

Final Answer

1.1

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Line up decimal points when adding decimal numbers
Column Addition: Add tenths place: 7 + 4 = 11 (carry the 1)
Visual Check: Count filled blocks to verify 1 whole + 1 tenth = 1.1 ✓

Common Mistakes

Avoid these frequent errors

Adding without regrouping when sum exceeds 10
Don't write 0.11 when adding 7 + 4 in tenths place = wrong place value! This ignores the fact that 10 tenths equals 1 whole. Always regroup by carrying 1 to the ones place and writing 1 in tenths place.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I get 11 when adding 7 + 4 in the tenths place?

That's correct! $7 + 4 = 11$ tenths. But since 10 tenths = 1 whole, you write down 1 tenth and carry 1 whole to the ones place.

How do the visual blocks help me understand the answer?

The blocks show visual proof! Count the filled sections: 0.7 fills 7 tenths, 0.4 fills 4 more tenths. Together that's 11 tenths, which equals 1 whole block plus 1 tenth = 1.1.

What if I wrote 0.11 instead of 1.1?

That's a place value error! 0.11 means 1 tenth + 1 hundredth, but we have 1 whole + 1 tenth. Always check: does your answer make sense with the visual model?

Do I always need to carry when adding decimals?

Only when the sum in any place value is 10 or greater. If 7 + 4 = 11, you carry. If it were 3 + 4 = 7, no carrying needed!

How can I check my decimal addition without the visual?

Use estimation! $0.7$ is close to 1, and $0.4$ is close to 0.5. So 1 + 0.5 = 1.5, and 1.1 is reasonably close to this estimate.

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