Solve the Fraction Equation: (3/4 × 1/2) - 1/4

Fraction Operations with Mixed Arithmetic

Solve the following exercise:

34⋅12−14=? \frac{3}{4}\cdot\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
00:07 Let's solve this problem together.
00:10 Always do multiplication and division first, before addition and subtraction.
00:16 Multiply the top numbers together, then multiply the bottom numbers together.
00:21 Now, let's calculate these products.
00:24 Next, multiply the fraction by two to get the same bottom number, or denominator.
00:30 And don't forget, multiply both the top and bottom.
00:34 Great! Let's calculate these products now.
00:38 Subtract using the shared bottom number, the common denominator.
00:44 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

34⋅12−14=? \frac{3}{4}\cdot\frac{1}{2}-\frac{1}{4}=\text{?}

2

Step-by-step solution

To solve the problem 34⋅12−14 \frac{3}{4} \cdot \frac{1}{2} - \frac{1}{4} , follow these steps:

  • Step 1: Perform the multiplication operation:
    Calculate 34⋅12 \frac{3}{4} \cdot \frac{1}{2} :
    Multiply the numerators: 3×1=3 3 \times 1 = 3 .
    Multiply the denominators: 4×2=8 4 \times 2 = 8 .
    Thus, 34⋅12=38 \frac{3}{4} \cdot \frac{1}{2} = \frac{3}{8} .
  • Step 2: Perform the subtraction operation:
    Now, subtract 14 \frac{1}{4} from 38 \frac{3}{8} .
    Before subtracting, we need a common denominator. The least common denominator of 8 8 and 4 4 is 8 8 .
    Convert 14 \frac{1}{4} to have a denominator of 8 8 :
    14=1×24×2=28 \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} .
    Now, subtract the fractions:
    38−28=3−28=18 \frac{3}{8} - \frac{2}{8} = \frac{3 - 2}{8} = \frac{1}{8} .

Therefore, the solution to the problem is 18 \frac{1}{8} .

3

Final Answer

18 \frac{1}{8}

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Multiply fractions first, then subtract from result
  • Technique: Convert 14 \frac{1}{4} to 28 \frac{2}{8} using common denominator 8
  • Check: Verify 38−28=18 \frac{3}{8} - \frac{2}{8} = \frac{1}{8} by adding back ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators when multiplying fractions
    Don't calculate 34×12 \frac{3}{4} \times \frac{1}{2} as 36 \frac{3}{6} = wrong result! This confuses addition rules with multiplication. Always multiply numerators together and denominators together when multiplying fractions.

Practice Quiz

Test your knowledge with interactive questions

Solve the following:

\( \frac{5}{9}:\frac{7}{18}= \)

FAQ

Everything you need to know about this question

Why do I multiply the fractions first instead of subtracting first?

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You must follow the order of operations (PEMDAS)! Multiplication comes before subtraction, so calculate 34×12 \frac{3}{4} \times \frac{1}{2} first to get 38 \frac{3}{8} , then subtract.

How do I know what common denominator to use?

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Find the least common multiple (LCM) of the denominators. Since 8 is already a multiple of 4, the LCM of 8 and 4 is 8. Convert 14 \frac{1}{4} to 28 \frac{2}{8} by multiplying top and bottom by 2.

Can I convert everything to decimals instead?

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Yes, but be careful! 34=0.75 \frac{3}{4} = 0.75 , 12=0.5 \frac{1}{2} = 0.5 , so 0.75 × 0.5 - 0.25 = 0.375 - 0.25 = 0.125 = 18 \frac{1}{8} . Fractions are often more precise!

What if I get confused about which fraction to convert?

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Always convert fractions to have the largest denominator from your problem. Here, 8 is larger than 4, so convert 14 \frac{1}{4} to eighths, not the other way around.

How can I double-check my multiplication of fractions?

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Remember: multiply across! 34×12=3×14×2=38 \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8} . You can also think: 'half of three-quarters' gives you three-eighths.

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