Question

2 find two different ways to show that $\frac{1}{3}+\frac{1}{4}$ is not equal to $\frac{2}{7}$. you can use numbers, words, or labeled sketches.

Explanation:

Step1: Calculate the sum of $\frac{1}{3}+\frac{1}{4}$

Find a common - denominator. The common denominator of 3 and 4 is 12. So $\frac{1}{3}+\frac{1}{4}=\frac{4}{12}+\frac{3}{12}=\frac{4 + 3}{12}=\frac{7}{12}$.

Step2: Compare $\frac{7}{12}$ and $\frac{2}{7}$

Cross - multiply. $7\times7 = 49$ and $12\times2=24$. Since $49
eq24$, $\frac{7}{12}
eq\frac{2}{7}$, so $\frac{1}{3}+\frac{1}{4}
eq\frac{2}{7}$.

Step3: Another way: convert to decimals

$\frac{1}{3}\approx0.333$, $\frac{1}{4}=0.25$, so $\frac{1}{3}+\frac{1}{4}=0.333 + 0.25=0.583$. And $\frac{2}{7}\approx0.286$. Since $0.583
eq0.286$, $\frac{1}{3}+\frac{1}{4}
eq\frac{2}{7}$.

Answer:

The sum of $\frac{1}{3}+\frac{1}{4}=\frac{7}{12}
eq\frac{2}{7}$ (by common - denominator method) and $\frac{1}{3}+\frac{1}{4}\approx0.583
eq0.286\approx\frac{2}{7}$ (by decimal conversion method)