Solve Mixed Fraction Operations: (2/3 ÷ 3/4) + 1/9

Fraction Division with Mixed Operations

Complete the following exercise:

23:34+19=? \frac{2}{3}:\frac{3}{4}+\frac{1}{9}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem step by step.
00:09 Here's a helpful tip: instead of dividing, we can multiply by the reciprocal. This makes things easier!
00:16 To find the reciprocal, we simply flip the fraction upside down - the numerator becomes the denominator, and vice versa.
00:24 Now, remember this important rule: when multiplying fractions, multiply the numerators together, and do the same for the denominators.
00:32 Let's work out these multiplications carefully.
00:38 Now we can add the fractions using a common denominator.
00:43 Let's calculate the numerator part next.
00:47 Here's an important fact to remember: whenever you divide a number by itself, you always get 1.
00:54 And there we have it! We've successfully solved the problem. Great job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

23:34+19=? \frac{2}{3}:\frac{3}{4}+\frac{1}{9}=\text{?}

2

Step-by-step solution

To solve this fraction problem, follow these steps:

  • Step 1: Evaluate the Division:
    The expression starts with 23÷34 \frac{2}{3} \div \frac{3}{4} . To divide fractions, multiply by the reciprocal:
    23×43=2×43×3=89 \frac{2}{3} \times \frac{4}{3} = \frac{2 \times 4}{3 \times 3} = \frac{8}{9}
  • Step 2: Add Fractions:
    Now add 89 \frac{8}{9} to 19 \frac{1}{9} . Since the denominators are the same, add the numerators directly:
    89+19=8+19=99=1 \frac{8}{9} + \frac{1}{9} = \frac{8 + 1}{9} = \frac{9}{9} = 1

Thus, the solution to the expression 23:34+19 \frac{2}{3}:\frac{3}{4} + \frac{1}{9} is 1 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Multiply by reciprocal to divide fractions
  • Technique: 23÷34=23×43=89 \frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{4}{3} = \frac{8}{9}
  • Check: Verify 89+19=99=1 \frac{8}{9} + \frac{1}{9} = \frac{9}{9} = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding fractions first before division
    Don't try to add 34+19 \frac{3}{4} + \frac{1}{9} first = wrong order of operations! This ignores that division comes before addition in PEMDAS. Always complete the division 23÷34 \frac{2}{3} \div \frac{3}{4} first, then add.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{1}{4}:\frac{1}{2}=\text{?} \)

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal when dividing fractions?

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Dividing by a fraction is the same as multiplying by its flip! When you divide by 34 \frac{3}{4} , you multiply by 43 \frac{4}{3} instead. This makes the calculation much easier.

What's the order of operations with fractions?

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Follow PEMDAS just like with whole numbers! Division comes before addition, so solve 23÷34 \frac{2}{3} \div \frac{3}{4} first, then add 19 \frac{1}{9} .

How do I add fractions with the same denominator?

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When denominators match, just add the numerators and keep the same denominator. 89+19=8+19=99 \frac{8}{9} + \frac{1}{9} = \frac{8+1}{9} = \frac{9}{9} .

Why does 9/9 equal 1?

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Any fraction where the numerator equals the denominator equals 1! Think of it as 9 pieces out of 9 total pieces = the whole thing = 1.

What if I get a different answer?

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Check your work step by step! Make sure you divided first, then added. Also verify that 23×43=89 \frac{2}{3} \times \frac{4}{3} = \frac{8}{9} by multiplying across.

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