Find the Opposite Number: Converting 7¼ to Its Negative Form

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

Great question! The opposite of a number changes its sign (positive to negative), while the reciprocal flips the fraction. For $ 7\frac{1}{4} $: opposite is $ -7\frac{1}{4} $, reciprocal is $ \frac{4}{29} $.

Q: Why do I need to convert the mixed number first?

Mixed numbers like $ 7\frac{1}{4} $ aren't single fractions - they're addition problems! You can't flip them directly. Converting to $ \frac{29}{4} $ gives you one fraction that you can properly flip.

Q: How do I convert a mixed number to improper fraction?

Use this formula: multiply whole number by denominator, then add numerator. For $ 7\frac{1}{4} $: (7×4) + 1 = 28 + 1 = 29, so you get $ \frac{29}{4} $.

Q: What does it mean to 'flip' a fraction?

Flipping means switching the numerator and denominator. So $ \frac{29}{4} $ becomes $ \frac{4}{29} $. This gives you the reciprocal!

Reciprocal Operations with Mixed Numbers

Convert $7\frac{1}{4}$ into its reciprocal form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the reciprocal number

00:04 Break down the number into whole number and remainder

00:10 Convert from whole number to whole fraction

00:15 Add the fractions under a common denominator

00:29 Use the formula to find the reciprocal number

00:33 Any number multiplied by its reciprocal always equals 1

00:39 Switch between numerator and denominator to get the reciprocal number

00:42 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

Convert $7\frac{1}{4}$ into its reciprocal form:

Step-by-step solution

To find the opposite number of $7\frac{1}{4}$ in the form of a reciprocal, follow these steps:

Step 1: Convert the mixed number $7\frac{1}{4}$ into an improper fraction.
This involves multiplying the whole number $7$ by the denominator $4$ and adding the numerator $1$ :
$7 \times 4 + 1 = 28 + 1 = 29$
This gives us the improper fraction $\frac{29}{4}$ .
Step 2: Find the reciprocal of $\frac{29}{4}$ .
The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$ :
$\text{Reciprocal of } \frac{29}{4} = \frac{4}{29}$

Therefore, the opposite number of $7\frac{1}{4}$ in terms of a reciprocal is $\frac{4}{29}$ .

The correct answer is $\frac{4}{29}$ , which corresponds to choice 2.

Final Answer

$\frac{4}{29}$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert mixed numbers to improper fractions first
Technique: For $7\frac{1}{4}$ : 7×4+1 = 29, giving $\frac{29}{4}$
Check: Multiply reciprocals: $\frac{29}{4} \times \frac{4}{29} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Finding reciprocal of mixed number without converting
Don't flip $7\frac{1}{4}$ to get $\frac{1}{4}7$ = nonsense! This creates an invalid expression because mixed numbers aren't proper fractions. Always convert to improper fraction first: $\frac{29}{4}$ , then flip to $\frac{4}{29}$ .

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?

Great question! The opposite of a number changes its sign (positive to negative), while the reciprocal flips the fraction. For $7\frac{1}{4}$ : opposite is $-7\frac{1}{4}$ , reciprocal is $\frac{4}{29}$ .

Why do I need to convert the mixed number first?

Mixed numbers like $7\frac{1}{4}$ aren't single fractions - they're addition problems! You can't flip them directly. Converting to $\frac{29}{4}$ gives you one fraction that you can properly flip.

How do I convert a mixed number to improper fraction?

Use this formula: multiply whole number by denominator, then add numerator. For $7\frac{1}{4}$ : (7×4) + 1 = 28 + 1 = 29, so you get $\frac{29}{4}$ .

What does it mean to 'flip' a fraction?

Flipping means switching the numerator and denominator. So $\frac{29}{4}$ becomes $\frac{4}{29}$ . This gives you the reciprocal!

How can I check if my reciprocal is correct?

Multiply your original number by its reciprocal - you should always get 1! Try it: $\frac{29}{4} \times \frac{4}{29} = \frac{29 \times 4}{4 \times 29} = \frac{116}{116} = 1$ ✓

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