Calculate 2/3 of 30: Teacher's Essay Marking Problem

Q: Why does 'of' mean multiply in math problems?

In mathematics, 'of' indicates finding a part of something. When you want 2/3 'of' 30 essays, you're finding what portion 2/3 represents from the total 30.

Q: How do I multiply a fraction by a whole number?

Multiply the numerator (top number) by the whole number, then divide by the denominator (bottom number): $ \frac{2}{3} \times 30 = \frac{2 \times 30}{3} = \frac{60}{3} = 20 $

Q: Can I convert the fraction to a decimal first?

Yes! $ \frac{2}{3} = 0.667... $ so 0.667 × 30 ≈ 20. However, working with fractions gives you the exact answer without rounding errors.

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

Think logically: if Steve marks 2/3 of 30 essays, he should mark less than all 30 but more than half (which would be 15). Since 20 is between 15 and 30, it makes sense!

Fraction Multiplication with Whole Numbers

Steve has to mark 30 essays written by is students.

When he finishes marking $\frac{2}{3}$ essays, how many has he marked?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Steve has to mark 30 essays written by is students.

When he finishes marking $\frac{2}{3}$ essays, how many has he marked?

Step-by-step solution

To determine how many essays Steve has marked when he finishes $\frac{2}{3}$ of the total, we perform the following calculation:

Step 1: Identify the total number of essays, which is 30.
Step 2: Determine the fraction of essays that are marked, $\frac{2}{3}$ .
Step 3: Multiply the total essays by the fraction marked:

$\frac{2}{3} \times 30 = \frac{2 \times 30}{3} = \frac{60}{3} = 20$

Therefore, Steve has marked 20 essays.

Thus, the correct number of essays Steve has marked is $\boxed{20}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: To find fraction of a number, multiply fraction by the number
Technique: $\frac{2}{3} \times 30 = \frac{2 \times 30}{3} = \frac{60}{3} = 20$
Check: Does 20 make sense as 2/3 of 30? Yes, since 3/3 would be 30 ✓

Common Mistakes

Avoid these frequent errors

Adding the fraction to the whole number instead of multiplying
Don't add 2/3 + 30 = 30⅔! This gives a number larger than the total, which makes no sense. The phrase 'of' in math means multiplication. Always multiply the fraction by the whole number to find the part.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{9}☐\frac{3}{9}$

FAQ

Everything you need to know about this question

Why does 'of' mean multiply in math problems?

In mathematics, 'of' indicates finding a part of something. When you want 2/3 'of' 30 essays, you're finding what portion 2/3 represents from the total 30.

How do I multiply a fraction by a whole number?

Multiply the numerator (top number) by the whole number, then divide by the denominator (bottom number): $\frac{2}{3} \times 30 = \frac{2 \times 30}{3} = \frac{60}{3} = 20$

Can I convert the fraction to a decimal first?

Yes! $\frac{2}{3} = 0.667...$ so 0.667 × 30 ≈ 20. However, working with fractions gives you the exact answer without rounding errors.

How do I know if my answer makes sense?

Think logically: if Steve marks 2/3 of 30 essays, he should mark less than all 30 but more than half (which would be 15). Since 20 is between 15 and 30, it makes sense!

What if the fraction doesn't divide evenly?

Sometimes you'll get a fraction or decimal as your final answer, and that's okay! For example, $\frac{1}{3}$ of 10 essays would be $\frac{10}{3} = 3\frac{1}{3}$ essays.

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