Lesson

Do you remember how to name a fraction using a model?

Which of the following shows \dfrac{1}{10} of the area of the shape shaded?

A

B

C

D

Worked Solution

Idea summary

The

**numerator**(top number) is the number of parts shaded to represent the fraction.The

**denominator**(bottom number) is the number of equal parts the shape is divided into.

Benchmarks are numbers that we use to make things easier, with fractions we often benchmark with the numbers 0, \, \dfrac{1}{2} or 1. This video shows how to see if fractions are closer to 0, \, \dfrac{1}{2} or 1.

Is the fraction \dfrac{1}{4} closer to 0 or 1?

Worked Solution

Idea summary

Fractions are often benchmarked with the numbers 0, \, \dfrac{1}{2} or 1.

The halfway point between 0 and 1 is \dfrac{1}{2}.

If the fraction is less than halfway, then it is closer 0.

If the fraction is more than halfway, then it is closer to 1.

Now that you have seen how to benchmark fractions, let's see how to use benchmarks to help us compare fraction sizes.

Let's compare the fractions \dfrac{2}{5} and \dfrac{3}{4}.

a

Is the fraction \dfrac{2}{5} closer to 0 or 1?

Worked Solution

b

Is the fraction \dfrac{3}{4} closer to 0 or 1?

Worked Solution

c

Use greater than (\gt) or less than (\lt) symbol in the box to make this number sentence true:\dfrac{2}{5} \, ⬚ \, \dfrac{3}{4}

Worked Solution

Idea summary

When comparing fractions, if the denominator is the same, then we compare the numerator.

The denominator tells us how many parts make up one whole.

We can use the benchmarks of 0 and 1 to compare fractions.

What if the denominator of the fraction makes it hard to know how big it is? Benchmarking can help us with that as well.

Is the fraction \dfrac{9}{32} closer to 0 or \dfrac{1}{2}?

Worked Solution

Idea summary

We can plot a given fraction and the benchmarks 0, \, \dfrac{1}{2} and 1 on a number line to see which benchmark the fraction is closest to.

Compare and order common unit fractions and locate and represent them on a number line