Solve the Fraction Expression: 3/2 - 5/8 - 1/4

Fraction Subtraction with Multiple Denominators

32−58−14= \frac{3}{2}-\frac{5}{8}-\frac{1}{4}=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply the 4, the 2 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:22 Let's calculate the multiplication
00:35 Subtract under the common denominator
00:41 Let's calculate the numerator
00:48 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

32−58−14= \frac{3}{2}-\frac{5}{8}-\frac{1}{4}=

2

Step-by-step solution

Let's try to find the least common denominator between 2 and 8 and 4

To find the least common denominator, we need to find a number that is divisible by 2, 8, and 4

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

3×42×4−5×18×1−1×24×2=128−58−28 \frac{3\times4}{2\times4}-\frac{5\times1}{8\times1}-\frac{1\times2}{4\times2}=\frac{12}{8}-\frac{5}{8}-\frac{2}{8}

Now let's subtract:

12−5−28=7−28=58 \frac{12-5-2}{8}=\frac{7-2}{8}=\frac{5}{8}

3

Final Answer

58 \frac{5}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find least common denominator before adding or subtracting fractions
  • Technique: Convert 32 \frac{3}{2} to 128 \frac{12}{8} using LCD of 8
  • Check: Verify 128−58−28=58 \frac{12}{8} - \frac{5}{8} - \frac{2}{8} = \frac{5}{8} by adding back ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions without common denominators
    Don't subtract 32−58=3−52−8 \frac{3}{2} - \frac{5}{8} = \frac{3-5}{2-8} = wrong method! You can't subtract numerators and denominators separately when denominators are different. Always find the LCD first and convert all fractions before operating.

Practice Quiz

Test your knowledge with interactive questions

You have a pair of denominators, what is their least common multiple?

\( \boxed 2~~~\boxed5 \)

FAQ

Everything you need to know about this question

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

+

Fractions represent parts of a whole, but different denominators mean different-sized parts! You need the same-sized parts (same denominator) before you can add or subtract them.

How do I find the least common denominator quickly?

+

Look for the largest denominator first. Check if all other denominators divide evenly into it. In this problem, 8 is divisible by both 2 and 4, so 8 is our LCD!

What if my LCD seems too big?

+

Don't worry! A larger LCD is still correct. You can always simplify your final answer to lowest terms after performing the operations.

Do I multiply both the numerator and denominator?

+

Yes, always! When converting 32 \frac{3}{2} to eighths, multiply both: 3×42×4=128 \frac{3 \times 4}{2 \times 4} = \frac{12}{8} . This keeps the fraction's value the same.

How do I handle the subtraction when there are multiple terms?

+

Work from left to right! First: 128−58=78 \frac{12}{8} - \frac{5}{8} = \frac{7}{8} , then: 78−28=58 \frac{7}{8} - \frac{2}{8} = \frac{5}{8} .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Common Denominators

Solve: 4/6 - 1/3 - 1/12 Fraction Subtraction Problem
Click to solve
Solve Fraction Expression: 1/3 + 7/15 - 2/5 Step-by-Step
Click to solve

Subtraction of Fractions

Solve the Fraction Equation: Finding the Missing Term in 3/4 - ? = 2/4
Click to solve
Solve the Fraction Equation: Finding the Missing Term in 2/5 - ? = 1/5
Click to solve