Solve: 5.2 - 7.4 + 12.4 + 3.2 + 6.6 Decimal Operations

Q: Why can I rearrange the order of operations in this problem?

You can rearrange because of the substitution property - addition and subtraction operations can be reordered when you keep track of positive and negative signs correctly.

Q: How do I know which terms to group together?

Look for decimal pairs that will create whole numbers! For example, $ 12.4 - 7.4 = 5 $ and $ 5.2 + 9.8 = 15 $ make calculations much easier.

Q: What if I make a mistake with the decimal points?

Line up the decimal points when adding! Write numbers vertically with decimals aligned, or count decimal places carefully when working horizontally.

Q: Is there a faster way to check my answer?

Yes! Add all the positive terms first: $ 5.2 + 12.4 + 3.2 + 6.6 = 27.4 $, then subtract the negative term: $ 27.4 - 7.4 = 20 $.

Q: Why does the solution show 5.2 + 9.8 = 15?

This uses strategic grouping! After computing $ 3.2 + 6.6 = 9.8 $, they grouped $ 5.2 + 9.8 $ because these decimals add to make a whole number, simplifying the final step.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's arrange the exercise so it will be easy for us to solve

00:14 Let's solve each operation separately

00:33 Let's arrange the exercise so it will be easy for us to solve

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

^{$5.2-7.4+12.4+3.2+6.6=\text{?}$}

2

Step-by-step solution

To make things simpler, we use the substitution property and arrange the exercise in the following manner:

$5.2+12.4-7.4+3.2+6.6=$

Keep in mind that the subtraction operation here gives us a whole number:

$12.4-7.4=5$

Now we obtain the exercise

$5.2+5+3.2+6.6=$

We solve the addition exercise:

$3.2+6.6=9.8$

And we obtain the exercise:

$5.2+5+9.8=$

We arrange the exercise using the substitution property to make fiding the solution simpler:

$5.2+9.8+5=$

We solve the exercise from left to right:

$5.2+9.8=15$

$15+5=20$

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic

Order: Rearrange terms using substitution property for easier calculation
Technique: Group decimals that create whole numbers: $12.4 - 7.4 = 5$
Check: Add all positive terms then subtract negative: 27.4 - 7.4 = 20 ✓

Common Mistakes

Avoid these frequent errors

Computing operations strictly left to right without rearranging
Don't solve 5.2 - 7.4 = -2.2 first and continue with negative numbers! This makes calculations harder and increases error risk. Always rearrange using substitution property to group terms that simplify to whole numbers first.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why can I rearrange the order of operations in this problem?

+

You can rearrange because of the substitution property - addition and subtraction operations can be reordered when you keep track of positive and negative signs correctly.

How do I know which terms to group together?

+

Look for decimal pairs that will create whole numbers! For example, $12.4 - 7.4 = 5$ and $5.2 + 9.8 = 15$ make calculations much easier.

What if I make a mistake with the decimal points?

+

Line up the decimal points when adding! Write numbers vertically with decimals aligned, or count decimal places carefully when working horizontally.

Is there a faster way to check my answer?

+

Yes! Add all the positive terms first: $5.2 + 12.4 + 3.2 + 6.6 = 27.4$ , then subtract the negative term: $27.4 - 7.4 = 20$ .

Why does the solution show 5.2 + 9.8 = 15?

+

This uses strategic grouping! After computing $3.2 + 6.6 = 9.8$ , they grouped $5.2 + 9.8$ because these decimals add to make a whole number, simplifying the final step.

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Solve: 5.2 - 7.4 + 12.4 + 3.2 + 6.6 Decimal Operations

Decimal Addition with Strategic Grouping

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