Question

Is it true that 4 3/5 - 3 2/3 = 1 + 3/5 + 2/3? Prove your answer.

Answer 1

Answer:

Not true.

Step-by-step explanation:

We are asked to prove the given equation.

$4\frac{3}{5}-3\frac{2}{3}=1+\frac{3}{5}+\frac{2}{3}$

Convert mixed fraction into improper fraction:

$4\frac{3}{5}\Rightarrow \frac{4\times 5+3}{5}=\frac{20+3}{5}=\frac{23}{5}$

$3\frac{2}{3}\Rightarrow \frac{3\times 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}$

$\frac{23}{5}-\frac{11}{3}=1+\frac{3}{5}+\frac{2}{3}$

Make a common denominator:

$\frac{23*3}{5*3}-\frac{11*5}{3*5}=\frac{1*15}{15}+\frac{3*3}{5*3}+\frac{2*5}{3*5}$

$\frac{69}{15}-\frac{55}{15}=\frac{15}{15}+\frac{9}{15}+\frac{10}{15}$

Combine numerators:

$\frac{69-55}{15}=\frac{15+9+10}{15}$

$\frac{14}{15}=\frac{34}{15}$

Since both sides of the equation are not equal, therefore, the given equation is not true.