Equivalent fractions

Half a pizza cut into 2 slices or into 8: the same amount to eat. The numbers change; the amount does not.

A fraction names an amount:

\tfrac{2}{3}

is 2 of 3 equal parts. The top number is the numerator (how many parts) and the bottom number the denominator (how many equal parts in the whole); this lesson calls them the top and the bottom. The same amount can be cut into more parts, or fewer, and named by a different fraction. Fractions that name the same amount are equivalent.

In this lesson you find equivalent fractions on fraction bars, then write a fraction in its simplest form.

PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.

The same as 2/3

Picture the bar split into 3 parts. What happens if each part is cut in half?

Which fraction is the same amount as

\tfrac{2}{3}

\tfrac{4}{5}

\tfrac{3}{4}

\tfrac{2}{6}

\tfrac{4}{6}

TryTry it on the board and compare the result with your prediction.

Match the bars

$d$ is the number of parts in the orange bar and $c$ the number shaded. The board says when the two shade the same amount.

Try it yourselfYour edits are saved in this browser.

The top bar is $\tfrac{2}{3}$ . Set the orange bar to 6 parts ( $d = 6$ ) and shade the same amount. Was your prediction right?

Use the board. This ticks when you get there.

InvestigateWork out why it happens, one step at a time.

Multiply or divide both

Here is how to find equivalent fractions, and the simplest one.

Worked exampleBefore each step, say what you think comes next.

$\tfrac{2}{3} = \tfrac{2 \times 4}{3 \times 4} = \tfrac{8}{12}$ Split each part into 4: multiply the top and the bottom by 4.
$\tfrac{12}{18} = \tfrac{12 \div 2}{18 \div 2} = \tfrac{6}{9}$ Join parts: divide the top and the bottom by a common factor.
$\tfrac{6}{9} = \tfrac{6 \div 3}{9 \div 3} = \tfrac{2}{3}$ 6 and 9 still share 3, so divide again.
$\tfrac{12}{18} = \tfrac{12 \div 6}{18 \div 6} = \tfrac{2}{3}$ Or in one step: divide by the highest common factor, 6.

A fraction is in simplest form (lowest terms) when the top and the bottom have no common factor but 1. Try one: simplify $\tfrac{12}{18}$ .

Read Lily's working. What does "the same" have to mean?

Write $\tfrac{12}{18}$ in its simplest form.

Lily looks for a fraction equal to $\tfrac{2}{3}$ . Click the line where her working goes wrong.

Why is

\tfrac{2}{3} = \tfrac{8}{12}

?8 − 2 = 6 and 12 − 3 = 98 and 12 are both evenEach third is split into 4 twelfths, so 2 thirds are 8 twelfths

ModifyChange the problem on purpose and see what happens.

One change at a time

Each task changes one thing.

Need a hint?

Each quarter split into 3 makes twelfths.

Need a hint?

Make d smaller: try 6 parts, then 3.

Another hint

Keep the same amount shaded.

Try it yourselfYour edits are saved in this browser.

The top bar is $\tfrac{3}{4}$ . Make the orange bar an equal fraction with 12 parts.

Use the board. This ticks when you get there.

Fill the gap: $\tfrac{3}{5} = \tfrac{?}{20}$ .

Write $\tfrac{15}{25}$ in its simplest form.

The top bar is $\tfrac{8}{12}$ . Make the orange bar the same amount with as few parts as possible.

Use the board. This ticks when you get there.

Edge case: can

\tfrac{7}{9}

be simplified?Yes: divide both by 7No: 7 and 9 have no common factor but 1Yes: 7/9 = 1/2

PractiseA few on your own, to check you have it.

Equal fractions

Write $\tfrac{18}{24}$ in its simplest form.

Fill the gap: $\tfrac{5}{8} = \tfrac{15}{?}$ .

Which is bigger,

\tfrac{2}{3}

\tfrac{3}{5}

? Write both with 15 parts.3/5 (it has bigger numbers)They are equal2/3 (10/15 is more than 9/15)

Review: work out $-3 + 5$ .

MakeMake your own problem using what you have learned. Expect a few tries; that is normal.

Neither in lowest terms

Then: what is the simplest form of both your fractions?

Try it yourselfYour edits are saved in this browser.

Need a hint?

Start with a simple fraction such as 1/2 and multiply its top and bottom by 2 for one bar.

Another hint

Multiply by 3 for the other bar.

Make the two bars equal, with neither fraction in lowest terms.

Use the board. This ticks when you get there.

Equivalent fractions

The same as 2/3

Match the bars

Multiply or divide both

One change at a time

Equal fractions

Neither in lowest terms

Students will be able to

Before class

Running the lesson

When students get stuck

Stretch and support

Where it leads

What each step is for