Solve: (1/2 × 1/2) + 3/4 - Mixed Fraction Operations

Fraction Operations with Order of Operations

12×12+34= \frac{1}{2}\times\frac{1}{2}+\frac{3}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this problem step by step!
00:08 First, multiply the numerators together. Then, multiply the denominators together.
00:13 Next, calculate these multiplications carefully.
00:17 Now, add the results using the common denominator.
00:25 Then, work out what the new numerator is.
00:29 Remember, any number divided by itself equals one.
00:35 And there you have it! We've solved the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12×12+34= \frac{1}{2}\times\frac{1}{2}+\frac{3}{4}=

2

Step-by-step solution

To solve 12×12+34\frac{1}{2} \times \frac{1}{2} + \frac{3}{4}, follow these steps:

  • Step 1: Multiply 12×12\frac{1}{2} \times \frac{1}{2} by using the multiplication of fractions formula:
    12×12=1×12×2=14\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}.
  • Step 2: Add 14\frac{1}{4} to 34\frac{3}{4}.
    Since 14\frac{1}{4} and 34\frac{3}{4} already have the same denominator, the addition can be done directly:
    14+34=1+34=44=1\frac{1}{4} + \frac{3}{4} = \frac{1 + 3}{4} = \frac{4}{4} = 1.

Therefore, the correct solution to the expression is 1 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Always multiply fractions before adding to other fractions
  • Technique: 12×12=14 \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} then add to 34 \frac{3}{4}
  • Check: Final answer 44=1 \frac{4}{4} = 1 when simplified correctly ✓

Common Mistakes

Avoid these frequent errors
  • Adding all fractions first without following order of operations
    Don't add 12+34=54 \frac{1}{2} + \frac{3}{4} = \frac{5}{4} first = completely wrong answer! This ignores multiplication priority and gives 58 \frac{5}{8} instead of 1. Always multiply first, then add the result.

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 before adding in this problem?

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Because of order of operations (PEMDAS)! Multiplication always comes before addition. You must solve 12×12 \frac{1}{2} \times \frac{1}{2} first to get 14 \frac{1}{4} , then add 34 \frac{3}{4} .

How do I multiply fractions like 1/2 × 1/2?

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Multiply the numerators together and the denominators together: 1×12×2=14 \frac{1 \times 1}{2 \times 2} = \frac{1}{4} . It's that simple!

Why can I add 1/4 + 3/4 directly?

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Because they have the same denominator (4)! When denominators match, just add the numerators: 1+34=44=1 \frac{1+3}{4} = \frac{4}{4} = 1 .

What if I got 7/8 as my answer?

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That's a common mistake! You probably added all three fractions without multiplying first. Remember: 12×12 \frac{1}{2} \times \frac{1}{2} must be done before any addition.

How do I know when to simplify fractions?

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Always simplify when the numerator and denominator have common factors! Since 44=1 \frac{4}{4} = 1 , write your final answer as 1, not as a fraction.

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