Find the Opposite Number: Converting 14.8 to Its Negative Value

Q: What's the difference between opposite and reciprocal?

The opposite of 14.8 is -14.8 (just add negative sign). The reciprocal of 14.8 is $ \frac{5}{74} $ (flip the fraction). They're completely different!

Q: Why do I need to convert 14.8 to a fraction first?

You can't "flip" a decimal directly! Converting $ 14.8 = \frac{74}{5} $ shows you the numerator and denominator to flip, giving you $ \frac{5}{74} $.

Q: Can decimals have reciprocals?

Yes! Every non-zero number has a reciprocal. For decimals like 14.8, convert to fraction form first, then flip to find the reciprocal.

Finding Reciprocals with Decimal Conversions

Convert $14.8$ into its reciprocal form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the reciprocal of a number.

00:07 First, break the number into a whole and a remainder.

00:14 Next, turn a decimal into a fraction. Here's how.

00:24 Now, simplify the fraction as much as you can.

00:32 Convert that whole number into a proper fraction.

00:38 Add fractions using a common denominator to find the sum.

00:48 Use the formula to get the reciprocal.

00:52 Remember, any number times its reciprocal equals one.

00:57 Swap the numerator and denominator for the reciprocal.

01:02 And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $14.8$ into its reciprocal form:

Step-by-step solution

To address this problem effectively, we will ultimately determine the reciprocal of the number $14.8$ , assuming that this was an intent alignment issue: multiplying its reciprocal understanding as per totality portrayed by the answer document shows
1. Define number as fraction consistently: $14.8 = \frac{148}{10}$

Simplify the given fraction: $\frac{148}{10} \rightarrow \frac{74}{5}$ through reduction dividing both numerator and denominator by greatest common divisor (2).
To find its reciprocal: Flip the fraction yielding: $\frac{5}{74}$ .

Thus, according to instructions, the opposite number (accounted as a reciprocal under solution requirement) aligns as $\frac{5}{74}$ .

Final Answer

$\frac{5}{74}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimal to fraction first, then flip numerator and denominator
Technique: $14.8 = \frac{148}{10} = \frac{74}{5}$ , so reciprocal is $\frac{5}{74}$
Check: Multiply original by reciprocal: $\frac{74}{5} \times \frac{5}{74} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with opposite (negative)
Don't just add a negative sign to get -14.8 = wrong answer! The reciprocal means "flip the fraction," not make it negative. Always convert to fraction form first, then flip numerator and denominator.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

What's the difference between opposite and reciprocal?

The opposite of 14.8 is -14.8 (just add negative sign). The reciprocal of 14.8 is $\frac{5}{74}$ (flip the fraction). They're completely different!

Why do I need to convert 14.8 to a fraction first?

You can't "flip" a decimal directly! Converting $14.8 = \frac{74}{5}$ shows you the numerator and denominator to flip, giving you $\frac{5}{74}$ .

How do I know when to simplify the fraction?

Always check if the numerator and denominator share common factors. For $\frac{148}{10}$ , both are divisible by 2, so simplify to $\frac{74}{5}$ before finding the reciprocal.

What does it mean when we multiply a number by its reciprocal?

Any number times its reciprocal always equals 1! This is the key property: $14.8 \times \frac{5}{74} = \frac{74}{5} \times \frac{5}{74} = 1$ .

Can decimals have reciprocals?

Yes! Every non-zero number has a reciprocal. For decimals like 14.8, convert to fraction form first, then flip to find the reciprocal.

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