We can use models to help us identify the size of our fraction. This will help us be able to order fractions in this lesson. Let's try a practice problem now.

Examples

Example 1

Below is a fraction bar.

A fraction bar divided into 3 equal parts with 1 shaded part.

What is the fraction of the coloured piece?

\dfrac{2}{3}

\dfrac{3}{4}

\dfrac{1}{4}

\dfrac{1}{3}

Worked Solution

Create a strategy

Write the fraction as: \,\, \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}.

Apply the idea

There is 1 shaded part and 3 total parts in the fraction bar. So the fraction is \dfrac{1}{3}.

The correct option is D.

Idea summary

To represent a fraction with a fraction model:

The numerator tells us how many parts should be shaded in. The denominator tells us how many parts to divide the shape into.

Order and count fractions up to tenths

This video covers counting and ordering fractions in words, symbols and pictures.

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Exploration

Using the geogebra applet, slide the slider to see an area model for each fraction.

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The number of eighths is equal to the number of squares shaded.

Examples

Example 2

Danielle was counting fractions in the eighths. Fill in the missing numbers in the fractions.

An image showing 9 rectangles that represent different fractions. Ask your teacher for more information.

Worked Solution

Create a strategy

Write each fraction as:

A fraction with parts explained. Ask your teacher for more information.

Apply the idea

Each rectangle is divided into 8 parts so all the denominators should be 8. To fill in each numerator, count the number of shaded squares.

Idea summary

Remember to count up all the pieces to find the denominator, not just the unshaded ones.

Order and count improper and mixed fractions

Watch this video to learn about improper fractions and mixed numbers.

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Examples

Example 3

Complete the table to complete the conversions.

Mixed Number	Improper fraction
1\dfrac{2}{3}	\dfrac{5}{3}
	\dfrac{3}{2}
1\dfrac{3}{4}
2\dfrac{2}{3}
	\dfrac{9}{4}

Worked Solution

Create a strategy

To find the improper fraction, multiply the whole number by the denominator, then add the numerator.

To find the mixed number, divide the numerator by the denominator.

Apply the idea

For the second row:

\displaystyle \dfrac{3}{2}	\displaystyle =	\displaystyle 3 \div 2	Divide the numerator by denominator
	\displaystyle =	\displaystyle 1 \text{ remainder } 1	Write the result and remainder
	\displaystyle =	\displaystyle 1 \dfrac{1}{2}	Write as a mixed number

For the third row:

\displaystyle 1\dfrac{3}{4}	\displaystyle =	\displaystyle \dfrac{1\times 4 + 3}{4}	Multiply the denominator and whole number
	\displaystyle =	\displaystyle \dfrac{4+3}{4}	Add the numerator
	\displaystyle =	\displaystyle \dfrac{7}{4}

Similarly doing this for the other rows gives us the completed table:

Mixed Number	Improper fraction
1\dfrac{2}{3}	\dfrac{5}{3}
1\dfrac{1}{2}	\dfrac{3}{2}
1\dfrac{3}{4}	\dfrac{7}{4}
2\dfrac{2}{3}	\dfrac{8}{3}
2\dfrac{1}{4}	\dfrac{9}{4}

Idea summary

An improper fraction has a numerator greater than or equal to the denominator. A mixed number has a whole number and a fraction part.

To convert a mixed numer to an improper fraction, multiply the whole number by the denominator, then add the numerator.

To convert an improper fraction to a mixed numer, divide the numerator by the denominator. The quotient will be the whole part and the remainder will be the numerator.

Outcomes

ACMNA078

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

5.05 Order fractions

Ideas

Are you ready?

Examples

Example 1

Order and count fractions up to tenths

Exploration

Examples

Example 2

Order and count improper and mixed fractions

Examples

Example 3

Outcomes

ACMNA078

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