Multiply 1/16 by a Factor of 10: Fraction Scaling Practice

Fraction Scaling with Multiplication Factors

Increase the following fraction by a factor of 10:

116= \frac{1}{16}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Expand the fraction by 10
00:04 Multiply the fraction by the given factor
00:07 Make sure to multiply both numerator and denominator
00:12 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 10:

116= \frac{1}{16}=

2

Step-by-step solution

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

  • Step 1: Multiply the numerator of 116 \frac{1}{16} , which is 1, by the factor of 10.
  • Step 2: Use the same denominator, which remains as 16.

Now, let's work through each step:
Step 1: The numerator is 1. Multiplying this by the factor 10 gives us 1×10=10 1 \times 10 = 10 .
Step 2: The denominator remains 16, so the fraction becomes 1016 \frac{10}{16} .

After performing the multiplication, the fraction becomes 1016 \frac{10}{16} . To simplify this solution, we can reduce 1016 \frac{10}{16} by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This results in the final reduced fraction 58 \frac{5}{8} . However, our task was to simply multiply and not reduce, so we end with:

The solution to the problem is 10160 \frac{10}{160} .

3

Final Answer

10160 \frac{10}{160}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerator by factor, keep denominator unchanged
  • Technique: For 116×10 \frac{1}{16} \times 10 , calculate 1×1016=1016 \frac{1 \times 10}{16} = \frac{10}{16}
  • Check: Verify 1016=10×116 \frac{10}{16} = 10 \times \frac{1}{16} by converting to decimals ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying both numerator and denominator by the factor
    Don't multiply both parts: 1×1016×10=10160 \frac{1 \times 10}{16 \times 10} = \frac{10}{160} gives the same original value! This doesn't increase the fraction at all. Always multiply only the numerator to scale the fraction up or down.

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 10' actually mean?

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Factor of 10 means multiply the entire fraction by 10, making it 10 times larger. So 116 \frac{1}{16} becomes 1016 \frac{10}{16} , not 10160 \frac{10}{160} !

Why don't I multiply the denominator too?

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Multiplying both numerator and denominator by the same number creates an equivalent fraction, not a larger one! Think of it like this: 24=12 \frac{2}{4} = \frac{1}{2} - they're the same value.

How can I check if my answer is 10 times bigger?

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Convert both fractions to decimals: 116=0.0625 \frac{1}{16} = 0.0625 and 1016=0.625 \frac{10}{16} = 0.625 . Notice that 0.625 = 10 × 0.0625!

Should I simplify the final answer?

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The question asks you to multiply by a factor, not simplify. However, knowing that 1016=58 \frac{10}{16} = \frac{5}{8} in lowest terms can help you verify your work!

What if the factor was a fraction instead of 10?

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Same process! For 116×34 \frac{1}{16} \times \frac{3}{4} , multiply numerators: 1×316=316 \frac{1 \times 3}{16} = \frac{3}{16} . The denominator stays the same.

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