Solve: (18/6) - (-1/4) | Mixed Fraction Operations

Fraction Operations with Negative Signs

(+186)(14)= (+\frac{18}{6})-(-\frac{1}{4})=

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1

Understand the problem

(+186)(14)= (+\frac{18}{6})-(-\frac{1}{4})=

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Simplify the given expression (+186)(+\frac{18}{6}).
  • Recognize that subtracting a negative fraction, ((14))(-(-\frac{1}{4})), is equivalent to adding its positive counterpart.
  • Perform the addition to find the final result.

Now, let's work through each step:

Step 1: Simplify the expression 186\frac{18}{6}.

Divide 18 by 6:

186=3\frac{18}{6} = 3

Step 2: Recognize the operation with the negative fraction:

Subtracting a negative is equivalent to adding a positive:

(3(14))=3+14(3 - (-\frac{1}{4})) = 3 + \frac{1}{4}

Step 3: Perform the addition:

Convert 3 to a fraction with a common denominator of 4:

3=1243 = \frac{12}{4}

Add the fractions:

124+14=134\frac{12}{4} + \frac{1}{4} = \frac{13}{4}

Step 4: Convert the fraction 134\frac{13}{4} to a decimal:

134=3.25\frac{13}{4} = 3.25

Therefore, the solution to the problem is 3.25\mathbf{3.25}.

3

Final Answer

3.25 3.25

Key Points to Remember

Essential concepts to master this topic
  • Negative Signs: Subtracting a negative equals adding the positive
  • Technique: Convert 3(14) 3 - (-\frac{1}{4}) to 3+14 3 + \frac{1}{4}
  • Check: Convert answer back: 134=3.25 \frac{13}{4} = 3.25 matches given choices ✓

Common Mistakes

Avoid these frequent errors
  • Treating double negative as still negative
    Don't keep the negative when subtracting (14) -(-\frac{1}{4}) = wrong answer like 2.75! This ignores the rule that two negatives make a positive. Always change subtraction of negative to addition of positive.

Practice Quiz

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What is the additive inverse number of \( 87 \)

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

+

Think of it like removing a debt! If you remove a debt of $0.25, you actually gain $0.25. So (14) -(-\frac{1}{4}) becomes +14 +\frac{1}{4} .

Should I simplify 18/6 first or deal with the negative second?

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Always simplify first! Convert 186=3 \frac{18}{6} = 3 , then handle the negative: 3(14)=3+14 3 - (-\frac{1}{4}) = 3 + \frac{1}{4} .

How do I add a whole number and a fraction?

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Convert the whole number to a fraction with the same denominator. So 3=124 3 = \frac{12}{4} , then add: 124+14=134 \frac{12}{4} + \frac{1}{4} = \frac{13}{4} .

Should my final answer be a fraction or decimal?

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Check what format the answer choices use! Here they show 3.25, so convert your fraction: 134=13÷4=3.25 \frac{13}{4} = 13 ÷ 4 = 3.25 .

What if I got 2.75 instead of 3.25?

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You probably forgot to change the double negative! Remember: 3(14) 3 - (-\frac{1}{4}) becomes 3+14 3 + \frac{1}{4} , not 314 3 - \frac{1}{4} .

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