Adding Fractions: Calculate 1/6 + 2/3 Hour in Food Preparation

Fraction Addition with Common Denominators

A mother spends 16 \frac{1}{6} of an hour preparing a salad and 23 \frac{2}{3} of an hour cooking french fries.

How much time does she spend preparing food (as a fraction of an hour)?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A mother spends 16 \frac{1}{6} of an hour preparing a salad and 23 \frac{2}{3} of an hour cooking french fries.

How much time does she spend preparing food (as a fraction of an hour)?

2

Step-by-step solution

The mother spends time preparing both salad and french fries. We need to sum up these two times:

Given the times:

  • Salad: 16 \frac{1}{6} hour
  • French fries: 23 \frac{2}{3} hour

To add these fractions, we need a common denominator. The denominators are 6 and 3. The least common multiple of 6 and 3 is 6.

Convert 23 \frac{2}{3} to a fraction with a denominator of 6:

23=2×23×2=46 \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}

Now, add the fractions:

16+46=1+46=56 \frac{1}{6} + \frac{4}{6} = \frac{1 + 4}{6} = \frac{5}{6}

Therefore, the total time the mother spends preparing food is 56 \frac{5}{6} of an hour.

3

Final Answer

56 \frac{5}{6}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the least common denominator before adding fractions
  • Technique: Convert 23 \frac{2}{3} to 46 \frac{4}{6} using denominator 6
  • Check: Verify 16+46=56 \frac{1}{6} + \frac{4}{6} = \frac{5}{6} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 16+23 \frac{1}{6} + \frac{2}{3} as 1+26+3=39 \frac{1+2}{6+3} = \frac{3}{9} ! This completely ignores the need for common denominators and gives wrong results. Always find the LCD first, then add only the numerators while keeping the same denominator.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just add 1/6 + 2/3 directly?

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You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 1 apple + 2 oranges without converting to a common unit first!

How do I find the least common denominator?

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Find the smallest number that both denominators divide into evenly. For 6 and 3: since 6 ÷ 6 = 1 and 6 ÷ 3 = 2, the LCD is 6.

What if my final answer can be simplified?

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Always simplify! If you get 1012 \frac{10}{12} , divide both top and bottom by their greatest common factor to get 56 \frac{5}{6} .

Can I convert both fractions to decimals instead?

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Yes, but be careful with rounding! 16 \frac{1}{6} = 0.167... and 23 \frac{2}{3} = 0.667..., but the exact fractional answer is usually preferred.

What does 5/6 of an hour mean in real time?

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56 \frac{5}{6} hour = 5 × 10 = 50 minutes! Since each 16 \frac{1}{6} of an hour equals 10 minutes, multiply by 5 to get the total time.

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