Question

Check the distributive property for the stated triples of rational numbers:
$\frac{3}{8},0,\frac{13}{7}$

Answer 1

We know that the distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together, that is, if $a,b$ and $c$ are three numbers, then $a(b+c)=ab+ac$.

Let $a=\frac{3}{8},b=0$ and$c=\frac{13}{7}$.

Let us first find $a(b+c)$ as follows:

$a(b+c)=\frac{3}{8}(0+\frac{13}{7})=\frac{3}{8}\times \frac{13}{7}=\frac{39}{56}........\left(1\right)$

Now, we find $ab+ac$ as follows:

$ab+ac=(\frac{3}{8}\times 0)+(\frac{3}{8}\times \frac{13}{7})=0+\frac{39}{56}=\frac{39}{56}.......\left(2\right)$

Since equation $\left(1\right)$ is equal to equation $\left(2\right)$,

$\therefore$ $a(b+c)=ab+ac$ i.e. $\frac{3}{8}(0+\frac{13}{7})=(\frac{3}{8}\times 0)+(\frac{3}{8}\times \frac{13}{7})$.

Hence, the given numbers $\frac{3}{8},0$ and $\frac{13}{7}$ satisfies the distributive property.