Solve (a+b)÷(3/4): Division with Algebraic Expression and Fractions

Division by Fractions with Algebraic Expressions

Solve the following problem:

(a+b):(3/4)=? (a+b):(3/4)=\text{?}

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Step-by-step video solution

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00:00 Solve
00:03 Let's write division as a fraction
00:11 Division is also multiplication by the reciprocal
00:23 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 problem:

(a+b):(3/4)=? (a+b):(3/4)=\text{?}

2

Step-by-step solution

Begin by writing the exercise as a fraction:

(a+b):34= (a+b):\frac{3}{4}=

Proceed to write the fraction in reverse order for the purpose of obtaining a multiplication exercise:

(a+b)×43= (a+b)\times\frac{4}{3}=

Finally we obtain the following result:

43(a+b) \frac{4}{3}(a+b)

3

Final Answer

43(a+b) \frac{4}{3}(a+b)

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by a fraction means multiply by its reciprocal
  • Technique: (a+b)÷34=(a+b)×43 (a+b) \div \frac{3}{4} = (a+b) \times \frac{4}{3}
  • Check: Final answer should have fraction multiplied by entire expression ✓

Common Mistakes

Avoid these frequent errors
  • Distributing fraction to only one term
    Don't write 43a+b \frac{4}{3}a + b = wrong distribution! This breaks the parentheses rule and creates an incorrect expression. Always keep the parentheses intact: 43(a+b) \frac{4}{3}(a+b) .

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I flip the fraction when dividing?

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Division by a fraction is the same as multiplication by its reciprocal! When you divide by 34 \frac{3}{4} , you multiply by 43 \frac{4}{3} instead.

Do I need to distribute the fraction to each term?

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No! Keep the parentheses intact. The fraction 43 \frac{4}{3} multiplies the entire expression (a+b) (a+b) , not individual terms.

What's the difference between : and ÷ symbols?

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Both symbols mean division! The colon (:) and division sign (÷) are just different ways to write the same operation.

How do I check if my answer is correct?

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Your final answer should be 43(a+b) \frac{4}{3}(a+b) . This means the entire algebraic expression is multiplied by the reciprocal fraction.

Can I simplify this expression further?

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Not unless you know specific values for a and b! The expression 43(a+b) \frac{4}{3}(a+b) is already in its simplest form.

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