Find the Opposite Number: Converting 7¼ to Its Negative Form

Question

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

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

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.

$\frac{4}{29}$