MHB How do we expand fractions to make their denominators the same for subtraction?

  • Thread starter Thread starter bobisaka
  • Start date Start date
AI Thread Summary
To expand fractions for subtraction, it is essential to have a common denominator. The denominators of the fractions in question are 6 and 9, with the least common denominator being 18. The first fraction, $\frac{11}{6}$, is expanded by multiplying by 3 to become $\frac{33}{18}$, while the second fraction, $\frac{7}{9}$, is expanded by multiplying by 2 to become $\frac{14}{18}$. This allows for the subtraction of the numerators, resulting in $\frac{19}{18}$. Understanding this process is crucial for performing operations with fractions effectively.
bobisaka
Messages
3
Reaction score
0
In step 3, how did the fractions come to multiplying with those particular numbers?

View attachment 9462
 

Attachments

  • math.png
    math.png
    12.5 KB · Views: 120
Mathematics news on Phys.org
We expand the fractions in that way so that the two fractions get the same denominator, in order to be able to calculate the subtraction, since it is not possible to subtract fractions with different denominators.

The denominator of the first fraction is $6$ and the of the second one it is $9$. We expand both fractions to make their denominators the same as the least common denominator.

The Least Common Multiple of $6$ and $9$ is $18$. It holds that $6\cdot 3=18$ and $9\cdot 2=18$. Therefore we expand the first fraction by $3$ : $\frac{11}{6}=\frac{11\cdot 3}{6\cdot 3}=\frac{33}{18}$ and the second fraction by $2$: $\frac{7}{9}=\frac{7\cdot 2}{9\cdot 2}=\frac{14}{18}$.

Now we can do the subtraction by subtracting the numerators: $$\frac{11}{6}-\frac{7}{9}=\frac{33}{18}-\frac{14}{18}=\frac{19}{18}$$
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top