Given:
Equations using properties.
To find:
The equation which use the inverse property of multiplication.
Solution:
Inverse property of multiplication:
The product of any number and its reciprocal is always 1.
Let us select the option which uses inverse property of multiplication.
Option A: [tex]\left(\frac{3}{4} \cdot \frac{4}{3}\right)+7=8[/tex]
Inverse of [tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]. Their product is 1.
[tex]$\frac{3}{4} \cdot \frac{4}{3}=1[/tex]
This equation uses the inverse property of multiplication.
Option B: [tex]\left(-\frac{7}{8}+\frac{7}{8}\right)+4=4[/tex]
Inverse of [tex]\frac{-7}{8}[/tex] is [tex]\frac{8}{-7}[/tex]
So, it is not true equation.
Option C: [tex](-5 \cdot 0)-9=-9[/tex]
Inverse of [tex]-5[/tex] is [tex]-\frac{1}{5}[/tex].
So, it is not true equation.
Option D: [tex]\left[7 \cdot\left(\frac{5}{7}-\frac{4}{7}\right)\right]+8=9[/tex]
Here also inverse property is not used.
So, it is not true equation.
Hence the equation use the inverse property of multiplication is
[tex]$\left(\frac{3}{4} \cdot \frac{4}{3}\right)+7=8[/tex].
