When the bar fills up

Before you read anything

$\frac{3}{4} + \frac{3}{4}$. Count the quarters.

You get six of them, and only four fit in a bar. Say what you do with the other two before you read on.

Six quarters is more than a bar

Three quarters and three quarters is six quarters. Four of them fill one bar, and the other two start the next.

So $\frac{6}{4}$ is one whole and two quarters, and nothing new happened. Six quarters is six of the things called quarters, exactly as in lesson 11.1.

:x nutshell-more-than-one

A fraction whose top is bigger than its bottom. It is not a mistake — it is what happens when the counting fills the bar and keeps going.

You met this in module 7

Sixteen sweets between three children was five each and one over. This is that leftover in quarters: the bar fills, and what is left starts the next one.

A :top bigger than the bottom is an answer, not a mistake.

Nakato

wrote $\frac{6}{4}$ and crossed it out as impossible

Nakato had the right answer and did not trust it. Six quarters is a perfectly good amount — it is a bar and a half.

Both ways of saying it

$\frac{6}{4}$ and $1\frac{2}{4}$ are the same amount, the way $\frac{1}{2}$ and $\frac{3}{6}$ were. One counts quarters; the other counts whole bars first and quarters afterwards.

Check yourself

Six to try

None of these quite fills the bar. Get the counting right here — the two at the end are where it overflows.

1

$\frac{3}{8} + \frac{3}{8} = \frac{\square}{8}$. What goes in the box?

2

$\frac{1}{5} + \frac{3}{5} = \frac{\square}{5}$. What goes in the box?

3

$\frac{2}{5} + \frac{1}{5} = \frac{\square}{5}$. What goes in the box?

4

$\frac{2}{4} + \frac{2}{5}$. Cut both into $20$ths: $\frac{\square}{20}$. What goes in the box?

5

$\frac{1}{3} + \frac{2}{4}$. Cut both into $12$ths: $\frac{\square}{12}$. What goes in the box?

6

Zawadi drinks $\frac{3}{6}$ of a bottle in the morning and $\frac{2}{6}$ in the afternoon. How many $6$ths is that altogether?

Past the end of the bar · page 1 of 2 Print it

Past the end of the bar · page 2 of 2 Print it

The question this leaves you with

Amina has some mangoes. She gives a third of them away and has 12 left.

You have never been told how many she started with. But you have a bar, you know what one part is worth, and you have been finding unknown units since module 6.

Can you draw it? The picture that answers this is the last thing this course has to give you.

Show that you have it

Filling the bar and going past

Both go past one whole. Say the answer as whole bars and leftovers, and then say it again as a count of slices.

1

$\frac{9}{6}$ is the same as which of these?

2

$\frac{9}{8}$ is the same as which of these?

Check what stuck The whole thing on one page