Adding Fractions: Calculate 2/3 + 2/7 Hour in Food Preparation Time

Q: Why can't I just add 2+2=4 and 3+7=10?

Because fractions represent parts of a whole, and you can't add parts of different-sized wholes! $ \frac{2}{3} $ means 2 parts out of 3, while $ \frac{2}{7} $ means 2 parts out of 7. You need the same-sized parts first.

Q: What if the LCM seems really big?

Don't worry! Even if the LCM seems large, it's still the most efficient way to add fractions. Large numbers are normal when working with fractions that don't have obvious common factors.

Q: Can I simplify my answer further?

Always check! For $ \frac{20}{21} $, ask: do 20 and 21 share any common factors? Since 20 = 4 × 5 and 21 = 3 × 7, they share no common factors, so it's already simplified.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's find what fraction of the hour mom spends preparing food.

00:18 To do this, we'll add up the parts based on the given data.

00:23 Next, multiply each fraction by the other fraction's denominator to find a common denominator.

00:30 Remember, multiply both the top number, called the numerator, and the bottom number, called the denominator.

00:38 Now, calculate these products carefully.

00:44 Add using the common denominator you've found.

00:51 Compute to find the new numerator.

00:56 And there you have it! That's the answer to the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

It takes Chris $\frac{2}{3}$ of an hour to prepare a salad.

In addition, he spends $\frac{2}{7}$ of an hour preparing french fries.

How long does he spend preparing food (as a fraction of an hour)?

2

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the denominators of the fractions, which are 3 and 7.
Step 2: Find the least common multiple (LCM) of these denominators.
Step 3: Rewrite each fraction using this common denominator.
Step 4: Add the modified fractions together.
Step 5: Simplify the final result if possible.

Let's apply these steps:

Step 1: The denominators are 3 and 7.

Step 2: The LCM of 3 and 7 is 21.
21 is the smallest number that both 3 and 7 divide without a remainder.

Step 3: Convert each fraction to have a denominator of 21:
For $\frac{2}{3}$ : Multiply both numerator and denominator by 7 to get $\frac{14}{21}$ .
For $\frac{2}{7}$ : Multiply both numerator and denominator by 3 to get $\frac{6}{21}$ .

Step 4: Add the fractions:
$\frac{14}{21} + \frac{6}{21} = \frac{14 + 6}{21} = \frac{20}{21}$ .

Step 5: The fraction $\frac{20}{21}$ is already in its simplest form.

Therefore, Chris spends a total of $\frac{20}{21}$ of an hour preparing food.

3

Final Answer

$\frac{20}{21}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator to add fractions
Technique: Convert $\frac{2}{3}$ to $\frac{14}{21}$ and $\frac{2}{7}$ to $\frac{6}{21}$
Check: Verify LCD is correct: 21 ÷ 3 = 7, 21 ÷ 7 = 3 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 2/3 + 2/7 = 4/10! This treats fractions like whole numbers and gives completely wrong results. Always find the LCD first, convert both fractions to equivalent fractions with the same denominator, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{9}+\frac{1}{9}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add 2+2=4 and 3+7=10?

+

Because fractions represent parts of a whole, and you can't add parts of different-sized wholes! $\frac{2}{3}$ means 2 parts out of 3, while $\frac{2}{7}$ means 2 parts out of 7. You need the same-sized parts first.

How do I find the least common multiple of 3 and 7?

+

Since 3 and 7 are both prime numbers, their LCM is simply 3 × 7 = 21. For other numbers, list multiples of each until you find the smallest one they share: 3, 6, 9, 12, 15, 18, 21... and 7, 14, 21...

What if the LCM seems really big?

+

Don't worry! Even if the LCM seems large, it's still the most efficient way to add fractions. Large numbers are normal when working with fractions that don't have obvious common factors.

Can I simplify my answer further?

+

Always check! For $\frac{20}{21}$ , ask: do 20 and 21 share any common factors? Since 20 = 4 × 5 and 21 = 3 × 7, they share no common factors, so it's already simplified.

Is there a faster way than finding the LCM?

+

For simple fractions like these, the LCM method is actually the fastest! Other methods like cross-multiplication or finding a common denominator by multiplying all denominators together often create more work.

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Adding Fractions: Calculate 2/3 + 2/7 Hour in Food Preparation Time

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