Calculate 3/7 of 56: Finding Girls in a First Grade Class

Q: Why do I multiply 56 by 3 instead of dividing by 7 first?

You can do either! 56 × 3 ÷ 7 = 168 ÷ 7 = 24 or 56 ÷ 7 × 3 = 8 × 3 = 24. Both methods work because multiplication and division can be done in any order.

Q: How do I know if 3/7 means 'multiply' and not 'divide'?

The phrase '3/7 of them are girls' means you want part of the whole group. 'Of' in math problems usually means multiply, so $ \frac{3}{7} \times 56 $ gives you the number of girls.

Q: What if I get a decimal or fraction as my answer?

In this problem, you should get a whole number because you can't have part of a student! If you get 24.5 girls, double-check your calculation - the answer should be exactly 24.

Q: How can I check if 24 is the right answer?

Ask yourself: If 24 out of 56 students are girls, is that really 3/7? Calculate $ \frac{24}{56} = \frac{3}{7} $ by dividing both by 8. Yes, it checks out!

Q: Why does 56 divide evenly by 7?

This problem was designed so the answer is a whole number! 56 ÷ 7 = 8, which means 56 is a multiple of 7. Not all fraction problems work out this neatly in real life.

Fraction Multiplication with Whole Numbers

There are 56 students in a 1st grade school class.

$\frac{3}{7}$ of them are girls.

How many girls are there in the class?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There are 56 students in a 1st grade school class.

$\frac{3}{7}$ of them are girls.

How many girls are there in the class?

Step-by-step solution

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

Step 1: Identify the total number of students - 56 students.
Step 2: Recognize that the fraction of students who are girls is $\frac{3}{7}$ .
Step 3: Multiply the total number of students by the fraction to find the number of girls.

Now, let's work through each step:
Step 1: We are given that there are 56 students in total.
Step 2: The fraction of the students who are girls is $\frac{3}{7}$ .
Step 3: To find the number of girls, compute:

$\text{Number of girls} = 56 \times \frac{3}{7}$

Perform the calculation:

$56 \times \frac{3}{7} = \frac{56 \times 3}{7}$

Simplify by canceling the common factor between 56 and 7:

$= \frac{168}{7} = 24$

Therefore, the solution to the problem is 24.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply the whole number by the numerator, keep denominator
Technique: Calculate 56 × 3 = 168, then divide by 7
Check: Verify 24 × 7 ÷ 3 = 56 students total ✓

Common Mistakes

Avoid these frequent errors

Adding the fraction to the whole number instead of multiplying
Don't add 56 + 3/7 = 56.43! This gives a meaningless result that's larger than the total. Always multiply the whole number by the fraction to find the part of the whole.

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 do I multiply 56 by 3 instead of dividing by 7 first?

You can do either! 56 × 3 ÷ 7 = 168 ÷ 7 = 24 or 56 ÷ 7 × 3 = 8 × 3 = 24. Both methods work because multiplication and division can be done in any order.

How do I know if 3/7 means 'multiply' and not 'divide'?

The phrase '3/7 of them are girls' means you want part of the whole group. 'Of' in math problems usually means multiply, so $\frac{3}{7} \times 56$ gives you the number of girls.

What if I get a decimal or fraction as my answer?

In this problem, you should get a whole number because you can't have part of a student! If you get 24.5 girls, double-check your calculation - the answer should be exactly 24.

How can I check if 24 is the right answer?

Ask yourself: If 24 out of 56 students are girls, is that really 3/7? Calculate $\frac{24}{56} = \frac{3}{7}$ by dividing both by 8. Yes, it checks out!

Why does 56 divide evenly by 7?

This problem was designed so the answer is a whole number! 56 ÷ 7 = 8, which means 56 is a multiple of 7. Not all fraction problems work out this neatly in real life.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime