Multiply 6/7 by a Factor of 5: Fraction Scaling Practice

Fraction Scaling with Equivalent Fractions

Increase the following fraction by a factor of 5:

67= \frac{6}{7}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Expand the fraction by 5
00:03 Multiply the fraction by the given factor
00:06 Make sure to multiply both numerator and denominator
00:09 Calculate the multiplications
00:15 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

Increase the following fraction by a factor of 5:

67= \frac{6}{7}=

2

Step-by-step solution

To solve the problem, we need to increase the fraction 67 \frac{6}{7} by a factor of 5. This involves multiplying both the numerator and denominator by 5.

  • Step 1: Multiply the numerator of the fraction: 6×5=30 6 \times 5 = 30 .
  • Step 2: Multiply the denominator of the fraction: 7×5=35 7 \times 5 = 35 .
  • Step 3: Form the new fraction: 3035 \frac{30}{35} .

Thus, when you increase the fraction 67 \frac{6}{7} by a factor of 5, the result is 3035 \frac{30}{35} .

3

Final Answer

3035 \frac{30}{35}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply both numerator and denominator by the same factor
  • Technique: Scale by 5 means 67×55=3035 \frac{6}{7} \times \frac{5}{5} = \frac{30}{35}
  • Check: Verify 3035=67 \frac{30}{35} = \frac{6}{7} by simplifying back to original ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying only the numerator by the scaling factor
    Don't multiply just 6 by 5 to get 307 \frac{30}{7} = wrong answer! This changes the fraction's value instead of creating an equivalent fraction. Always multiply both numerator and denominator by the same factor.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

\( \frac{4}{8}= \)

FAQ

Everything you need to know about this question

What does 'increase by a factor of 5' actually mean?

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It means to create an equivalent fraction where both the numerator and denominator are 5 times larger. Think of it as making the fraction pieces smaller but having more of them!

Why do I multiply both parts instead of just adding 5?

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Scaling means proportional growth, not addition. If you just add 5 to get 1112 \frac{11}{12} , you get a completely different value than 67 \frac{6}{7} !

Is 3035 \frac{30}{35} the same value as 67 \frac{6}{7} ?

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Yes! They're equivalent fractions. You can verify this by dividing: 30 ÷ 35 = 0.857... and 6 ÷ 7 = 0.857... Both give the same decimal value.

Should I simplify 3035 \frac{30}{35} to 67 \frac{6}{7} ?

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The question asks for the scaled fraction, so 3035 \frac{30}{35} is the correct answer. Simplifying would take you back to where you started!

How can I check my work quickly?

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Use cross multiplication: 6 × 35 should equal 7 × 30. Since 210 = 210, your fractions are equivalent! ✓

What if the scaling factor was a different number?

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Same process! For factor 3: 67 \frac{6}{7} becomes 1821 \frac{18}{21} . For factor 10: it becomes 6070 \frac{60}{70} . Always multiply both parts by the same number!

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