Fractions on a Number Line: Place on the axis

Let's first try to understand what numbers are greater and smaller than the number $\frac{6}{5}$.

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

\frac{?}{5}<\frac{6}{5}<\frac{?}{5}

Now let's complete the numerators with numbers that will help us reach whole numbers or half numbers in the fractions as follows:

\frac{5}{5}<\frac{6}{5}<\frac{7.5}{5}

Let's now simplify the fractions as follows:

$\frac{5:5}{5:5}=\frac{1}{1}=1$

$\frac{7.5:5}{5:5}=\frac{1.5}{1}=1.5=1\frac{1}{2}$

Therefore, the answer is:

1<\frac{6}{5}<1\frac{1}{2}

Since the denominator is 8, both the larger and smaller numbers will also have a denominator of 8:

\frac{?}{8}<\frac{7}{8}<\frac{?}{8}

Now let's complete the numerators with numbers that will help us reach whole numbers or half numbers in fractions as follows:

\frac{4}{8} < \frac{7}{8} < \frac{8}{8}

Next, we will simplify the fractions as follows:

$\frac{4:4}{8:4}=\frac{1}{2}$

$\frac{8:8}{8:8}=\frac{1}{1}=1$

Therefore, the answer is:

\frac{1}{2}<\frac{7}{8}<1

Let's try to understand what is bigger and what is smaller than the number $\frac{3}{5}$

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

\frac{?}{5}<\frac{3}{5}<\frac{?}{5}

Now let's complete the numerators with numbers that will help us reach whole numbers in fractions as follows:

\frac{0}{5}<\frac{3}{5}<\frac{5}{5}

Let's reduce the fractions as follows:

$\frac{0}{5}=0$

$\frac{5:5}{5:5}=\frac{1}{1}=1$

In other words, the fraction is between 0 and 1.

Let's try to find a smaller range, meaning consecutive numbers before and after the fraction's numerator as follows:

\frac{1}{5}<\frac{3}{4}<\frac{4}{5}

Let's try to understand what is bigger and what is smaller than the number $\frac{1}{4}$

Since the denominator is 4, both the larger and smaller numbers will have a denominator of 4:

\frac{?}{4}<\frac{1}{4}<\frac{?}{4}

Now let's complete the numerators with numbers that will help us reach whole numbers in fractions as follows:

\frac{0}{4}<-\frac{3}{4}<\frac{4}{4}

Let's proceed to reduce the fractions as follows:

$\frac{0}{4}=0$

$\frac{4:4}{4:4}=-\frac{1}{1}=1$

This means the fraction is between 0 and 1

But since the consecutive numbers for the fraction's numerator are:

\frac{0}{4} < \frac{1}{4} < \frac{2}{4}

\frac{0}{4} < \frac{1}{4} < \frac{3}{4}

We can see that all the answers are correct

Let's try to understand what is larger and what is smaller than the number $\frac{3}{4}$.

Since the denominator is 4, both the larger and smaller numbers will also have a denominator of 4:

\frac{?}{4} < \frac{3}{4} < \frac{?}{4}

Now let's complete the numerators with the numbers before and after 3 as follows:

\frac{2}{4} < \frac{3}{4} < \frac{4}{4}

Now we can simplify the fractions like this:

$\frac{2:2}{4:2}=\frac{1}{2}$

$\frac{4:4}{4:4}=\frac{1}{1}=1$

Therefore, the answer is:

\frac{1}{2} < \frac{3}{4} < 1

Let's first try to understand what is greater and smaller than the number $\frac{2}{4}$.

Since the denominator is 4, both the larger and smaller numbers will also have a denominator of 4:

\frac{?}{4}<\frac{2}{4}<\frac{?}{4}

Now let's complete the numerators with numbers that will help us reach whole numbers in fractions as follows:

\frac{0}{4}<\frac{2}{4}<\frac{4}{4}

Let's now simplify the fractions as follows:

$\frac{0}{4}=0$

$\frac{4:4}{4:4}=\frac{1}{1}=1$

Therefore, the answer is:

0<\frac{2}{4}<1

Let's first try to understand what is greater and what is smaller than the number $\frac{7}{5}$.

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

\frac{?}{5}<\frac{7}{5}<\frac{?}{5}

Now let's complete the numerators with numbers that will help us reach round numbers in fractions as follows:

\frac{5}{5}<\frac{7}{5}<\frac{10}{5}

We'll reduce the fractions as follows:

$\frac{5:5}{5:5}=\frac{1}{1}=1$

$\frac{10:5}{5:5}=\frac{2}{1}=2$

Therefore, the answer is:

1<\frac{7}{5}<2

Let's try to understand what is larger and what is smaller than the number $\frac{14}{5}$.

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

\frac{?}{5}<\frac{14}{5}<\frac{?}{5}

Now let's complete the numerators with numbers that will help us reach whole numbers in the fractions as follows:

\frac{10}{5}<\frac{14}{5}<\frac{15}{5}

Let's then simplify the fractions as follows:

$\frac{10:5}{5:5}=\frac{2}{1}=2$

$\frac{15:5}{5:5}=\frac{3}{1}=3$

Therefore, the answer is:

2<\frac{14}{5}<3

Let's first try to understand what is larger and what is smaller than the number $\frac{10}{3}$.

Since the denominator is 3, both the larger and smaller numbers will also have a denominator of 3:

\frac{?}{3}<\frac{10}{3}<\frac{?}{3}

Now let's complete the numerators with numbers that will help us reach round numbers in the fractions as follows:

\frac{9}{3}<\frac{10}{3}<\frac{12}{3}

We'll then reduce the fractions as follows:

$\frac{12:3}{3:3}=\frac{4}{1}=4$

$\frac{9:3}{3:3}=\frac{3}{1}=3$

Therefore, the answer is:

3<\frac{10}{3}<4

Let's try to understand what is larger and what is smaller than the number $-\frac{3}{4}$.

Since the denominator is 4, both the larger and smaller numbers will also have a denominator of 4:

-\frac{?}{4}<\frac{3}{4}<\frac{?}{4}

Now let's complete the numerators with numbers that will help us reach whole numbers in fractions as follows:

-\frac{4}{4}<-\frac{3}{4}<\frac{0}{4}

Let's then simplify the fractions as follows:

$\frac{0}{4}=0$

$-\frac{4:4}{4:4}=-\frac{1}{1}=-1$

Therefore, the answer is:

-1<-\frac{3}{4}<0