5. Fractions

Lesson

If we can find the lowest common denominator , it will help us be able to see which fraction is smaller or larger. Let's try this problem to review.

Which fraction has a denominator that is a multiple of the denominator in \dfrac{2}{6}.

A

\dfrac{3}{5}

B

\dfrac{6}{9}

C

\dfrac{10}{12}

Worked Solution

Idea summary

Look for common multiples between the denominators of two different fractions as this will help us to find common denominators.

Let's look at how to benchmark fractions to 0,\dfrac{1}{2} or 1.

Consider the following fractions: \dfrac{3}{5},\,\dfrac{7}{8},\, \dfrac{1}{6}.

a

Which of these fractions is closest to 0?

A

\dfrac{3}{5}

B

\dfrac{7}{8}

C

\dfrac{1}{6}

Worked Solution

b

Which of these fractions is closest to 1?

A

\dfrac{7}{8}

B

\dfrac{3}{5}

C

\dfrac{1}{6}

Worked Solution

Idea summary

To order fractions we can compare them to the benchmarks 0, \, \dfrac{1}{2}, \, 1.

This video looks at comparing mixed numbers and improper fractions.

We wish to arrange the following in descending order: 4\dfrac{1}{2},\,\dfrac{31}{4},\, \dfrac{15}{2}.

a

Rewrite all 3 fractions as improper fractions with the lowest common denominator of 4.

Worked Solution

b

Which of the following lists the fractions in descending order?

A

\dfrac{15}{2},4\dfrac{1}{2},\dfrac{31}{4}

B

4\dfrac{1}{2},\dfrac{15}{2},\dfrac{31}{4}

C

4\dfrac{1}{2},\dfrac{31}{4}, \dfrac{15}{2}

D

\dfrac{31}{4},\dfrac{15}{2},4\dfrac{1}{2}

Worked Solution

Idea summary

In order to compare fractions, having the same denominator helps enormously, so you may need to find equivalent fractions if they are not the same.

Converting mixed numbers to improper fractions might be needed as well, so remember to think of which steps can help you achieve the same denominators.