Question

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

Answer 1

Answer: I don't think so because 1 2/5-3/4 equals 13/20

Answer 2

Answer: Yes, it's true.

Step-by-step explanation:

The first step is to convert the mixed number $1\frac{2}{5}$ to a fraction. The procedure for this is:

1. Multiply the whole number 1 by the denominator 5.
2. Add the product obtained and the numerator 2 (This will be the numerator of the fraction).
3. The denominator does not change. It will be 5.

Then:

$1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{7}{5}$

Rewrite the equation:

$\frac{7}{5}-\frac{3}{4}=\frac{1}{4}+\frac{2}{5}$

Notice that the denominators on the left side are 4 and 5 and the denominator on the right side are also 4 and 5.

Then, the Least Common Denominator (LCD) on both sides is:

$5=5\\\\4=2*2=2^2$

$LCD=5*2^2=20$

Now we can solve the subtraction on the left side of the equation and the addition on the righ side:

$\frac{(7*4)-(3*5)}{20}=\frac{(1*5)+(2*4)}{20}\\\\\frac{13}{20}=\frac{13}{20}$

Therefore:

$1\frac{2}{5}-\frac{3}{4}=\frac{1}{4}+\frac{2}{5}$  (IT'S TRUE)