What number comes after the given number? How is the next number found? How do you read it?

Here are the answers to the questions from the image:

1. How many parts is one whole divided into for the given number?
When a whole is divided into equal parts, the number of parts represents the denominator of a fraction.

2. How is the part/shaded parts from the whole written?
The part or shaded parts from the whole are written as a fraction, where the number of parts chosen (shaded) is the numerator and the total number of equal parts in the whole is the denominator. For example, if 3 parts out of 4 are shaded, it is written as $\frac{3}{4}$.

Use these number lines to answer the questions:

a) Number line divided into 4 equal parts between 0 and 1:

i) What do the marks on the number line between 0 and 1 show?
The marks show:

• $\frac{1}{4}$
• $\frac{2}{4}$ (which simplifies to $\frac{1}{2}$)
• $\frac{3}{4}$

ii) How did you work it out?
I worked it out by counting the 4 equal divisions between 0 and 1, which means each division represents one-fourth of the whole.

iii) What will the next mark be between 1 and 2? How would you show it?
The next mark between 1 and 2 will be $1\frac{1}{4}$ or $\frac{5}{4}$.

$$\boxed{\frac{5}{4}}$$

b) Number line divided into 2 equal parts between 0 and 1:

i) What do the marks on the number line between 0 and 1 show?
The mark shows:

• $\frac{1}{2}$

ii) How did you work it out?
I worked it out by counting the 2 equal divisions between 0 and 1, which means each division represents one-half of the whole.

iii) What will the next mark be between 1 and 2? How would you show it?
The next mark between 1 and 2 will be $1\frac{1}{2}$ or $\frac{3}{2}$.

$$\boxed{\frac{3}{2}}$$

c) Number line divided into 8 equal parts between 0 and 1:

i) What do the marks on the number line between 0 and 1 show?
The marks show:

• $\frac{1}{8}$
• $\frac{2}{8}$ (which simplifies to $\frac{1}{4}$)
• $\frac{3}{8}$
• $\frac{4}{8}$ (which simplifies to $\frac{1}{2}$)
• $\frac{5}{8}$
• $\frac{6}{8}$ (which simplifies to $\frac{3}{4}$)
• $\frac{7}{8}$

ii) How did you work it out?
I worked it out by counting the 8 equal divisions between 0 and 1, which means each division represents one-eighth of the whole.

iii) What will the next mark be between 1 and 2? How would you show it?
The next mark between 1 and 2 will be $1\frac{1}{8}$ or $\frac{9}{8}$.

$$\boxed{\frac{9}{8}}$$