Calculate 2/7 of 210: Finding Pages Read in a Book

Q: Why do I multiply the fraction by 210 instead of dividing?

When finding "a fraction OF something", you always multiply! Think of it as: "What is 2 out of every 7 parts of 210?" Division would give you how many groups of 2/7 fit into 210, which isn't what we want.

Q: Can I solve this by dividing 210 by 7 first?

Yes! You can calculate $ \frac{210}{7} = 30 $ first, then multiply by 2 to get 60. This works because $ \frac{2}{7} \times 210 = 2 \times \frac{210}{7} $.

Q: How do I know if my answer makes sense?

Check that your answer is less than the total! Since Silvia read 2/7 of the book, she read less than half (which would be 105 pages). Our answer of 60 pages makes sense.

Q: What if the book had a different number of pages?

The method stays the same! Always multiply $ \frac{2}{7} $ by the total pages. For example, if there were 140 pages: $ \frac{2}{7} \times 140 = 40 $ pages read.

Q: Can I convert 2/7 to a decimal first?

You could, but it's trickier! $ \frac{2}{7} \approx 0.286 $, so 0.286 × 210 ≈ 60. However, working with the fraction directly gives you the exact answer without rounding errors.

Fraction Operations with Real-World Applications

Silvia reads $\frac{2}{7}$ of a book.

If the book has 210 pages, then how many pages has she read?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Silvia reads $\frac{2}{7}$ of a book.

If the book has 210 pages, then how many pages has she read?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information: Total pages in the book are 210.
Step 2: Apply the formula: Multiply the fraction read $\frac{2}{7}$ by the total pages (210).
Step 3: Perform the calculation to find the number of pages read.

Now, let's work through each step:

Step 1: The problem provides that the total number of pages in the book is 210.

Step 2: We use the formula: Pages read = $\frac{2}{7} \times 210$ .

Step 3: Calculate:

$\frac{2}{7} \times 210 = 2 \times \frac{210}{7} = 2 \times 30 = 60$ .

Thus, Silvia has read 60 pages.

Therefore, the solution to the problem is 60 pages.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Concept: Multiply fraction by whole number to find part
Technique: Calculate $\frac{2}{7} \times 210 = 2 \times 30 = 60$
Check: Verify that 60 + remaining pages equals 210 total ✓

Common Mistakes

Avoid these frequent errors

Adding fraction to total instead of multiplying
Don't calculate 2/7 + 210 = wrong answer! Adding gives you more than the original total, which is impossible. Always multiply the fraction by the total to find the part.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

Why do I multiply the fraction by 210 instead of dividing?

When finding "a fraction OF something", you always multiply! Think of it as: "What is 2 out of every 7 parts of 210?" Division would give you how many groups of 2/7 fit into 210, which isn't what we want.

Can I solve this by dividing 210 by 7 first?

Yes! You can calculate $\frac{210}{7} = 30$ first, then multiply by 2 to get 60. This works because $\frac{2}{7} \times 210 = 2 \times \frac{210}{7}$ .

How do I know if my answer makes sense?

Check that your answer is less than the total! Since Silvia read 2/7 of the book, she read less than half (which would be 105 pages). Our answer of 60 pages makes sense.

What if the book had a different number of pages?

The method stays the same! Always multiply $\frac{2}{7}$ by the total pages. For example, if there were 140 pages: $\frac{2}{7} \times 140 = 40$ pages read.

Can I convert 2/7 to a decimal first?

You could, but it's trickier! $\frac{2}{7} \approx 0.286$ , so 0.286 × 210 ≈ 60. However, working with the fraction directly gives you the exact answer without rounding errors.

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