Fractions as parts of a whole and as points on a number line

Step 5 · Multiplication and first fractions topics

Read a fraction as equal parts of a whole, place fractions on a number line, and compare fractions with the same top or bottom number.

Equal parts of a whole

A fraction names equal parts of a whole. Cut a bar into 4 equal parts: each part is $\frac{1}{4}$ , one fourth. Shade 3 of them and you have $\frac{3}{4}$ , three fourths.

3/4

A bar cut into 4 equal parts with 3 shaded: three fourths.

The bottom number, the denominator, says how many equal parts the whole is cut into. The top number, the numerator, says how many of those parts you have.

Fractions on a number line

A fraction is also a number with its own place on the number line. Cut the stretch from 0 to 1 into 3 equal parts. The first mark is $\frac{1}{3}$ , the next is $\frac{2}{3}$ , and $\frac{3}{3}$ lands on 1.

0 to 1 cut into thirds: 1/3, 2/3, and 3/3 at 1.

Example: Placing a fraction

Where does $\frac{3}{4}$ go on a number line from 0 to 1?

Cut 0 to 1 into 4 equal parts.
Count 3 parts along from 0.

AnswerAt the third mark, one mark before 1.

Whole numbers can be written as fractions too. $\frac{4}{4}$ = 1, because 4 fourths fill the whole. $\frac{6}{3}$ = 2, because 6 thirds fill two wholes.

Comparing fractions

When two fractions have the same denominator, the parts are the same size, so more parts is more: $\frac{3}{6}$ is more than $\frac{2}{6}$ .

When they have the same numerator, look at the size of the parts. $\frac{1}{8}$ is smaller than $\frac{1}{4}$ , because cutting a whole into 8 parts makes smaller parts than cutting it into 4.

1/4

1/8

The same whole cut into 4 and into 8: one fourth is bigger than one eighth.

Example: Same numerator

Which is greater, $\frac{2}{3}$ or $\frac{2}{5}$ ?

Both are 2 parts.
Thirds are bigger than fifths.
So 2 thirds is more than 2 fifths.

Answer $\frac{2}{3}$

Try it yourself

Work each one on paper first, then open the answer to check.

A bar is cut into 6 equal parts and 5 are shaded. What fraction is shaded?
Show answer
$\frac{5}{6}$
How many eighths make one whole?
Show answer
8. $\frac{8}{8}$ = 1.
Which is greater, $\frac{3}{8}$ or $\frac{5}{8}$ ?
Show answer
$\frac{5}{8}$ . The parts are the same size, and 5 parts is more than 3.
Which is greater, $\frac{1}{2}$ or $\frac{1}{6}$ ?
Show answer
$\frac{1}{2}$ . Halves are bigger than sixths.
A number line from 0 to 1 is cut into fifths. What fraction is at the second mark?
Show answer
$\frac{2}{5}$