Solve 25-(-5)+(-6)-4: Mixed Operations with Negative Numbers

Integer Operations with Negative Number Rules

Solve the following problem:

25(5)+(6)4= 25-(-5)+(-6)-4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Negative times negative is always positive
00:07 Open parentheses
00:18 Calculate one operation at a time from left to right
00:26 Positive times negative is always negative
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

Solve the following problem:

25(5)+(6)4= 25-(-5)+(-6)-4=

2

Step-by-step solution

Let's remember the rule:

(x)=+x -(-x)=+x

Let's write the exercise in the appropriate form:

25+5+(6)4= 25+5+(-6)-4=

Let's solve the exercise from left to right:

25+5=30 25+5=30

We obtain the following exercise:

30+(6)4= 30+(-6)-4=

Let's remember the rule:

+(x)=x +(-x)=-x

Let's write the exercise in the appropriate form:

3064= 30-6-4=

Let's solve the exercise from left to right:

306=24 30-6=24

244=20 24-4=20

3

Final Answer

20 20

Key Points to Remember

Essential concepts to master this topic
  • Rule: Subtracting a negative number equals adding its positive
  • Technique: Convert (5) -(-5) to +5 +5 first
  • Check: Substitute back: 25+564=20 25+5-6-4 = 20

Common Mistakes

Avoid these frequent errors
  • Treating double negatives incorrectly
    Don't calculate 25(5) 25-(-5) as 255=20 25-5 = 20 ! This ignores the negative sign rule and gives wrong results. Always remember that (x)=+x -(-x) = +x , so 25(5)=25+5 25-(-5) = 25+5 .

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why does subtracting a negative number become addition?

+

Think of it like this: subtracting means taking away, and a negative number represents debt. When you take away debt, you're actually gaining money! So (5)=+5 -(-5) = +5 .

Should I solve from left to right or use order of operations?

+

For addition and subtraction only, work from left to right. Since there are no parentheses, exponents, or multiplication/division here, just go step by step: 25+5=30 25+5 = 30 , then 306=24 30-6 = 24 , then 244=20 24-4 = 20 .

What's the difference between +(-6) and just -6?

+

They're exactly the same! +(6)=6 +(-6) = -6 . The plus sign before a negative number doesn't change anything - it's like saying add negative six, which is the same as subtracting six.

How do I keep track of all these signs?

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First, convert all double negatives to positives. Then rewrite the expression clearly: 25+564 25+5-6-4 . This makes it much easier to calculate step by step!

Can I group the positive and negative numbers separately?

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Yes! You can calculate 25+5=30 25+5 = 30 (positives) and 6+4=10 6+4 = 10 (negatives), then do 3010=20 30-10 = 20 . This grouping method often prevents calculation errors.

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