Find Male Students: Calculating with 3/7 Female Ratio in 28-Student Class

Q: Why can't I just calculate 3/7 of 28 to get the male students?

Because $ \frac{3}{7} $ represents the female portion! If you calculate $ \frac{3}{7} \times 28 = 12 $, you get 12 females, not males.

Q: What does 'complement' mean in fractions?

A complement is what you need to add to reach the whole (1). If $ \frac{3}{7} $ are female, then $ \frac{4}{7} $ must be male because $ \frac{3}{7} + \frac{4}{7} = \frac{7}{7} = 1 $

Q: Can I solve this by subtraction instead?

Yes! Calculate females first: $ \frac{3}{7} \times 28 = 12 $, then subtract: $ 28 - 12 = 16 $ males. Both methods work!

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

Multiply the whole number by the numerator, then divide by the denominator: $ 28 \times \frac{4}{7} = \frac{28 \times 4}{7} = \frac{112}{7} = 16 $

Fraction Problems with Complementary Parts

There are 28 students in a 9th grade class, $\frac{3}{7}$ of whom are female.

How many male students are there in the class?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's figure out how many boys are in the class.

00:12 We know the number of girls already.

00:18 Now, subtract this part from the total to find the boys.

00:23 Next, convert it to a proper fraction.

00:29 Find a common denominator.

00:36 This gives us the fraction of boys.

00:41 Multiply this fraction by the total class size.

00:51 Make sure to move the multiplication to the numerator.

00:58 Now, simplify the fraction by dividing the top and bottom.

01:16 Do the multiplication.

01:22 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There are 28 students in a 9th grade class, $\frac{3}{7}$ of whom are female.

How many male students are there in the class?

Step-by-step solution

Let's first split 28 into two fractions:

The first fraction will represent the girls:

$\frac{3}{7}$

The second fraction will represent the boys:

$1-\frac{3}{7}=\frac{7}{7}-\frac{3}{7}=\frac{4}{7}$

Now let's multiply the number of students by the fraction that represents the boys:

$28\times\frac{4}{7}$

Let's then multiply the numerator by 28:

$\frac{4\times28}{7}$

Now we can divide both the numerator and denominator by 7:

$\frac{4\times28:7}{7:7}=$

Finally, let's solve the division exercises in the numerator and denominator to get our answer:

$\frac{4\times4}{1}=4\times4=16$

Final Answer

$16$

Key Points to Remember

Essential concepts to master this topic

Complementary Rule: When fractions add to 1, use subtraction to find complement
Technique: Calculate $1 - \frac{3}{7} = \frac{4}{7}$ for male fraction
Check: Female 12 + Male 16 = 28 total students ✓

Common Mistakes

Avoid these frequent errors

Directly calculating 3/7 of students instead of finding complement
Don't calculate $\frac{3}{7} \times 28 = 12$ for males = wrong gender! This gives you the number of females, not males. Always find the complement fraction first: $1 - \frac{3}{7} = \frac{4}{7}$ for males.

Practice Quiz

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Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why can't I just calculate 3/7 of 28 to get the male students?

Because $\frac{3}{7}$ represents the female portion! If you calculate $\frac{3}{7} \times 28 = 12$ , you get 12 females, not males.

How do I find what fraction represents the males?

Since all students are either male or female, the fractions must add to 1. So males = $1 - \frac{3}{7} = \frac{7}{7} - \frac{3}{7} = \frac{4}{7}$

What does 'complement' mean in fractions?

A complement is what you need to add to reach the whole (1). If $\frac{3}{7}$ are female, then $\frac{4}{7}$ must be male because $\frac{3}{7} + \frac{4}{7} = \frac{7}{7} = 1$

Can I solve this by subtraction instead?

Yes! Calculate females first: $\frac{3}{7} \times 28 = 12$ , then subtract: $28 - 12 = 16$ males. Both methods work!

How do I multiply a whole number by a fraction?

Multiply the whole number by the numerator, then divide by the denominator: $28 \times \frac{4}{7} = \frac{28 \times 4}{7} = \frac{112}{7} = 16$

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