Solve: (3/4 × 1/2) + 5/8 Fraction Expression

Fraction Operations with Mixed Addition Multiplication

34×12+58= \frac{3}{4}\times\frac{1}{2}+\frac{5}{8}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Make sure to multiply numerator by numerator and denominator by denominator
00:08 Calculate the multiplications
00:13 Add with the common denominator
00:19 Calculate the numerator
00:22 Any number divided by itself always equals 1
00:25 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

34×12+58= \frac{3}{4}\times\frac{1}{2}+\frac{5}{8}=

2

Step-by-step solution

To solve the problem 34×12+58 \frac{3}{4} \times \frac{1}{2} + \frac{5}{8} , we'll follow these steps:

  • Step 1: Multiply the fractions 34×12 \frac{3}{4} \times \frac{1}{2} .
  • Step 2: Add the result to 58 \frac{5}{8} .

Now, let's work through the steps:

Step 1: Compute the product of the first two fractions:
34×12=3×14×2=38 \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}

Step 2: Add the resulting fraction to 58 \frac{5}{8} by finding a common denominator:

The fractions 38\frac{3}{8} and 58\frac{5}{8} already have the same denominator, so we can simply add them:
38+58=3+58=88=1 \frac{3}{8} + \frac{5}{8} = \frac{3 + 5}{8} = \frac{8}{8} = 1

Therefore, the solution to the problem is 1 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Multiply fractions first, then add the result
  • Technique: Multiply numerators together: 34×12=38 \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}
  • Check: Verify common denominators match before adding: 38+58=88=1 \frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1

Common Mistakes

Avoid these frequent errors
  • Adding all three numbers before multiplying
    Don't add 34+12+58 \frac{3}{4} + \frac{1}{2} + \frac{5}{8} = wrong result! This ignores the multiplication sign and violates order of operations. Always multiply 34×12 \frac{3}{4} \times \frac{1}{2} first, then add 58 \frac{5}{8} to that result.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I multiply before adding in this problem?

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Because of the Order of Operations (PEMDAS)! Multiplication comes before addition, so you must calculate 34×12 \frac{3}{4} \times \frac{1}{2} first to get 38 \frac{3}{8} , then add 58 \frac{5}{8} .

How do I multiply fractions like 3/4 × 1/2?

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Simply multiply the numerators together and multiply the denominators together: 3×14×2=38 \frac{3 \times 1}{4 \times 2} = \frac{3}{8} . No need to find common denominators when multiplying!

What if the fractions don't have the same denominator when adding?

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You need to find a common denominator first! In this problem, both 38 \frac{3}{8} and 58 \frac{5}{8} already have denominator 8, so you can add directly.

Can the answer be a whole number like 1?

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Absolutely! When fractions add up perfectly, like 88 \frac{8}{8} , they equal whole numbers. Always simplify your final answer to its simplest form.

How do I check if my answer of 1 is correct?

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Substitute back into the original expression: 34×12+58=38+58=88=1 \frac{3}{4} \times \frac{1}{2} + \frac{5}{8} = \frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1

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