given that a/b=c/d, decide whether it is true or not that a/c=b/d.
and how can i explain my reasoning?
given that a/b = c/d
then ad = bc
now divide both sides by cd to get
a/c = b/d as required
or
if we cross - multiply the first we had ad = bc
if we cross-multiply a/c = b/d we also get ad = bc
so it it true.
thank you
To determine whether the statement "a/c = b/d" is true or not, we can apply cross multiplication. Here's how you can explain your reasoning:
1. Start by writing the equation "a/b = c/d."
2. Cross multiply by multiplying the numerator of the first fraction with the denominator of the second fraction, and vice versa. This yields two new equations:
- First equation: a * d = b * c
- Second equation: b * c = a * d
3. Now, let's compare the second equation with the statement we want to evaluate, which is "a/c = b/d."
4. Observe that both equations have the same terms on either side of the equal sign, which means that a/c = b/d is true.
5. You can explain your reasoning by stating that since the cross multiplication of a/b = c/d yields the equation b * c = a * d, and this equation has the same terms on both sides as the statement a/c = b/d, we can conclude that the statement is true.
Therefore, according to the given equation a/b = c/d, it is true that a/c = b/d.