Question

Frankie solved the math problem below. Find the error in Frankie's work and explain it in words, using math language. 2 1/3 - 1 2/5 2 1/3 x 5/5 = 2 5/15 -1 2/5 x 3/3 = -1 6/15 = -1 1/15

Answer 1

Given:

The expression is

$2\dfrac{1}{3}-1\dfrac{2}{5}$

To find:

The error in Frankie's work.

Solution:

We need to simplify $2\dfrac{1}{3}-1\dfrac{2}{5}$, so

$2\dfrac{1}{3}=2\dfrac{1}{3}\times \dfrac{5}{5}$

$2\dfrac{1}{3}=2\dfrac{5}{15}$

and,

$1\dfrac{2}{5}=-1\dfrac{2}{5}\times \dfrac{3}{3}$

$1\dfrac{2}{5}=-1\dfrac{6}{15}$

Now,

$2\dfrac{1}{3}-1\dfrac{2}{5}=2\dfrac{5}{15}-1\dfrac{6}{15}$

$2\dfrac{1}{3}-1\dfrac{2}{5}=(2+\dfrac{5}{15})-(1+\dfrac{6}{15})$

$2\dfrac{1}{3}-1\dfrac{2}{5}=2+\dfrac{5}{15}-1-\dfrac{6}{15}$

$2\dfrac{1}{3}-1\dfrac{2}{5}=1-\dfrac{1}{15}$

$2\dfrac{1}{3}-1\dfrac{2}{5}=\dfrac{14}{15}$

Therefore, there is error in Frankie's last step. In that step, he did not subtract the mixed fraction correctly.