Solve the Fraction Expression: 3/8 + 1/2 - 1/4

Fraction Operations with Mixed Denominators

Solve the following exercise:

38+1214=? \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply 4, 2 respectively for the common denominator 8
00:09 Remember to multiply both numerator and denominator
00:22 Let's calculate the multiplications
00:29 Add under common denominator
00:36 Calculate the numerator, one operation at a time
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 exercise:

38+1214=? \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?}

2

Step-by-step solution

To solve the problem, let's work through the following steps:

  • Step 1: Identify the least common denominator (LCD) for all fractions.
    - The denominators are 8, 2, and 4. The LCM of these numbers is 8.

  • Step 2: Convert each fraction to have this common denominator of 8.
    - 38\frac{3}{8} is already with a denominator of 8.
    - 12\frac{1}{2} can be rewritten as 48\frac{4}{8} because 1×42×4=48\frac{1 \times 4}{2 \times 4} = \frac{4}{8}.
    - 14\frac{1}{4} can be rewritten as 28\frac{2}{8} because 1×24×2=28\frac{1 \times 2}{4 \times 2} = \frac{2}{8}.

  • Step 3: Perform the arithmetic operations.
    - Add 38\frac{3}{8} and 48\frac{4}{8}, which gives 3+48=78\frac{3 + 4}{8} = \frac{7}{8}.
    - Subtract 28\frac{2}{8} from 78\frac{7}{8}, giving 728=58\frac{7 - 2}{8} = \frac{5}{8}.

  • Step 4: Simplify the answer if necessary.
    58\frac{5}{8} is already in its simplest form.

Therefore, the solution to the problem is 58 \frac{5}{8} .

3

Final Answer

58 \frac{5}{8}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the least common denominator before adding or subtracting fractions
  • Technique: Convert 12 \frac{1}{2} to 48 \frac{4}{8} and 14 \frac{1}{4} to 28 \frac{2}{8}
  • Check: Verify 38+4828=58 \frac{3}{8} + \frac{4}{8} - \frac{2}{8} = \frac{5}{8}

Common Mistakes

Avoid these frequent errors
  • Adding denominators together
    Don't add denominators like 8 + 2 + 4 = 14 or numerators across different denominators = completely wrong answer! This ignores that fractions represent parts of different wholes. Always find the LCD first to make all fractions have the same denominator.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators separately?

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Because fractions represent parts of a whole! Adding 38 \frac{3}{8} and 12 \frac{1}{2} is like adding 3 pieces of pizza cut into 8 slices with 1 piece of pizza cut into 2 slices - they're different sizes!

How do I find the LCD when I have three different denominators?

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List the multiples of each denominator until you find the smallest number that appears in all lists. For 8, 2, and 4: multiples of 8 are 8, 16, 24... Since 2 and 4 both divide into 8, the LCD is 8.

What if my final answer is an improper fraction?

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That's okay! In this problem we got 58 \frac{5}{8} which is proper, but improper fractions are valid answers too. You can convert to mixed numbers if needed, but simplified improper fractions are perfectly acceptable.

Do I always subtract from left to right?

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Yes! Follow the order of operations. In 38+1214 \frac{3}{8} + \frac{1}{2} - \frac{1}{4} , first add 38+48=78 \frac{3}{8} + \frac{4}{8} = \frac{7}{8} , then subtract 7828=58 \frac{7}{8} - \frac{2}{8} = \frac{5}{8} .

Can I use decimals instead of fractions?

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You could convert to decimals, but you might get rounding errors. Since 18=0.125 \frac{1}{8} = 0.125 , working with fractions keeps your answer exact and is usually easier for this type of problem.

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