Question
Find five rational numbers between $\frac{3}{5}{\text{ and }}\frac{4}{5}$
✓
Answer
We know that there are infinite rational numbers between any two numbers.
A rational number is the one that can be written in the form of $\frac{p}{q}$
where $p$ and $q$ are Integers and $q \ne 0$ We know that the numbers $\frac{3}{5}{\text{ and }}\frac{4}{5}$
can also be written as.$0.6$ and $0.8$ or$\eqalign{ & {3 \over 5} = {3 \over 5} \times {{20} \over {20}} = {{60} \over {100}} \cr & {4 \over 5} = {4 \over 5} \times {{20} \over {20}} = {{80} \over {100}} \cr}$
We can conclude that the numbers all lie between We need to rewrite the numbers $0.61,0.62,0.63,0.64{\text{ and }}0.65$ in $\frac{p}{q}$ form to get the rational numbers between $\frac{3}{5}{\text{ and }}\frac{4}{5}$ .
So, after converting, we get $\frac{{61}}{{100}},\frac{{62}}{{100}},\frac{{63}}{{100}},\frac{{64}}{{100}}{\text{ and }}\frac{{65}}{{100}}$
We can further convert the rational numbers $\frac{{62}}{{100}},\frac{{64}}{{100}}{\text{ and }}\frac{{65}}{{100}}$ into lowest fractions.
On converting the fractions, we get $\frac{{31}}{{50}},\frac{{16}}{{25}}{\text{ and }}\frac{{13}}{{20}}$
Therefore, five rational numbers between $\frac{3}{5}{\text{ and }}\frac{4}{5}$are $\frac{{61}}{{100}},\frac{{31}}{{50}},\frac{{63}}{{100}},\frac{{16}}{{25}}{\text{ and }}\frac{{13}}{{50}}$
A rational number is the one that can be written in the form of $\frac{p}{q}$
where $p$ and $q$ are Integers and $q \ne 0$ We know that the numbers $\frac{3}{5}{\text{ and }}\frac{4}{5}$
can also be written as.$0.6$ and $0.8$ or$\eqalign{ & {3 \over 5} = {3 \over 5} \times {{20} \over {20}} = {{60} \over {100}} \cr & {4 \over 5} = {4 \over 5} \times {{20} \over {20}} = {{80} \over {100}} \cr}$
We can conclude that the numbers all lie between We need to rewrite the numbers $0.61,0.62,0.63,0.64{\text{ and }}0.65$ in $\frac{p}{q}$ form to get the rational numbers between $\frac{3}{5}{\text{ and }}\frac{4}{5}$ .
So, after converting, we get $\frac{{61}}{{100}},\frac{{62}}{{100}},\frac{{63}}{{100}},\frac{{64}}{{100}}{\text{ and }}\frac{{65}}{{100}}$
We can further convert the rational numbers $\frac{{62}}{{100}},\frac{{64}}{{100}}{\text{ and }}\frac{{65}}{{100}}$ into lowest fractions.
On converting the fractions, we get $\frac{{31}}{{50}},\frac{{16}}{{25}}{\text{ and }}\frac{{13}}{{20}}$
Therefore, five rational numbers between $\frac{3}{5}{\text{ and }}\frac{4}{5}$are $\frac{{61}}{{100}},\frac{{31}}{{50}},\frac{{63}}{{100}},\frac{{16}}{{25}}{\text{ and }}\frac{{13}}{{50}}$
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