Calculate 3/7 of 28: Finding Female Students in a Class

Fraction Multiplication with Whole Numbers

In a ninth grade class, there are 28 students, 37 \frac{3}{7} of whom are female.

How many females are in the class?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 How many girls are in the class?
00:03 The given ratio of girls
00:07 Multiply this ratio by total students to find number of girls
00:11 Break down 28 into factors 7 and 4
00:25 Reduce what's possible
00:28 Calculate the multiplication
00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In a ninth grade class, there are 28 students, 37 \frac{3}{7} of whom are female.

How many females are in the class?

2

Step-by-step solution

Let's write the following exercise, we'll multiply the fraction by the number of students:

37×28 \frac{3}{7}\times28

Let's multiply the numerator by 28:

3×287 \frac{3\times28}{7}

Let's solve the exercise in the numerator, we'll break down 28 into a smaller multiplication exercise:

3×7×47= \frac{3\times7\times4}{7}=

Let's reduce the 7 in the numerator and denominator of the fraction and we'll get:

3×4=12 3\times4=12

3

Final Answer

12 12

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply the numerator by the whole number first
  • Technique: Factor 28 as 7×4 to simplify 3×287 \frac{3 \times 28}{7}
  • Check: Verify 12 females + 16 males = 28 total students ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying the fraction
    Don't calculate 37+28 \frac{3}{7} + 28 = wrong answer! This gives you a mixed number, not the portion of students. Always multiply the fraction by the total: 37×28 \frac{3}{7} \times 28 .

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why do we multiply the fraction by 28?

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When we say "3/7 of the students", the word "of" means multiplication! We're finding what portion 3/7 represents out of the total 28 students.

Can I convert the fraction to a decimal first?

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Yes! 370.429 \frac{3}{7} \approx 0.429 , so 0.429 × 28 ≈ 12. But working with the fraction directly is more precise and often easier.

How do I know when to simplify during multiplication?

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Look for common factors between the numerator and any whole numbers. Here, 28 = 7 × 4, so the 7s cancel out, making the calculation much simpler!

What if the answer isn't a whole number?

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In real-world problems like counting students, check your work! You can't have a fraction of a person. If you get a decimal, you may have made an error or the problem might need rounding.

How can I check if 12 is correct?

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Two ways: 1) 12 ÷ 28 = 3/7 ✓ 2) If 12 are female, then 16 are male, and 12 + 16 = 28 total students ✓

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