Multiply Fraction 9/11 by Factor of 7: Step-by-Step Solution

Q: What does 'increase by a factor of 7' actually mean?

It means you're making the fraction 7 times larger. Think of it like having 7 copies of the original fraction $ \frac{9}{11} $.

Q: Why do I multiply both the top and bottom numbers?

To keep the fraction proportionally the same but scaled up! If you only multiply the numerator, you get a completely different fraction instead of 7 times the original.

Q: How can I check if 63/77 is really 7 times bigger than 9/11?

Divide your answer by 7: $ \frac{63}{77} ÷ 7 = \frac{63÷7}{77÷7} = \frac{9}{11} $. You should get back to the original fraction!

Fraction Scaling with Integer Multipliers

Increase the following fraction by a factor of 7:

$\frac{9}{11}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 7

00:04 Multiply the fraction by the given factor

00:07 Make sure to multiply both numerator and denominator

00:11 Calculate the multiplications

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Increase the following fraction by a factor of 7:

$\frac{9}{11}=$

Step-by-step solution

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

Step 1: Multiply the numerator of the fraction by the factor.
Step 2: Multiply the denominator of the fraction by the same factor.
Step 3: Write the new fraction.

Now, let's work through these steps:
Step 1: The numerator of the fraction is 9. We multiply it by 7, which gives us $9 \times 7 = 63$ .
Step 2: The denominator of the fraction is 11. We multiply it by 7, which gives us $11 \times 7 = 77$ .
Step 3: The resulting fraction is $\frac{63}{77}$ .

Therefore, the solution to the problem is $\frac{63}{77}$ .

Final Answer

$\frac{63}{77}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: For 9/11 × 7: calculate 9×7=63 and 11×7=77
Check: Verify 63/77 equals 7 times the original fraction 9/11 ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by the factor
Don't multiply just 9 by 7 to get 63/11 = wrong fraction! This changes the fraction's value instead of scaling it proportionally. Always multiply both the numerator AND denominator by the same factor.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

What does 'increase by a factor of 7' actually mean?

It means you're making the fraction 7 times larger. Think of it like having 7 copies of the original fraction $\frac{9}{11}$ .

Why do I multiply both the top and bottom numbers?

To keep the fraction proportionally the same but scaled up! If you only multiply the numerator, you get a completely different fraction instead of 7 times the original.

How can I check if 63/77 is really 7 times bigger than 9/11?

Divide your answer by 7: $\frac{63}{77} ÷ 7 = \frac{63÷7}{77÷7} = \frac{9}{11}$ . You should get back to the original fraction!

Do I need to simplify 63/77?

Not necessarily for this problem! The question asks for the fraction increased by factor 7, and $\frac{63}{77}$ shows that multiplication clearly. However, you can check if it simplifies further.

What if the factor was a fraction instead of 7?

The same rule applies! Multiply both numerator and denominator by that fraction. For example, to increase by factor $\frac{2}{3}$ , multiply: $\frac{9 \times 2}{11 \times 3} = \frac{18}{33}$ .

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