# If 5 1 equals 5 1

### More or less?

Very important: on which tray is there more pizza to eat? :-)

Which fraction is greater? It is difficult to estimate with a sense of proportion. And you don't see straight away from the fraction which one is larger.

Now you are learning different methods of how you can calculate which fraction is larger. So you can **you compare and order fractions.**

First you compare **two** Fractions. However, the procedures work the same way with multiple breaks.

### Fractions with the same denominator

It's easy to compare fractions with the same denominator. You see which counter is larger. This break is the bigger one.

**Example: Compare $$ 6/7 $$ and $$ 4/7 $$.**

$$6/7 > 4/7$$

That means: $$ 6/7 $$ is greater than $$ 4/7 $$.

Figuratively it looks like this:

$$6/7$$ $$>$$ $$4/7$$

There are signs for comparing numbers

$$ <$$ less than

$$> $$ greater than

$$ = $$ equal

"Smaller" and you can easily remember:

A fraction means: divide the whole into as many parts as the denominator suggests. Take as many parts from it as the meter says.

Example:

Divide the whole thing into FOUR parts. Take THREE of them.

### Fractions with the same numerator

You can also compare fractions with the same numerator at a glance.

**Example: Compare $$ 4/5 $$ and $$ 4/6 $$.**

$$4/5>4/6$$

You can see that in the picture.

$$4/5$$ $$>$$ $$4/6$$

$$ 4/5 $$ are more because the whole is divided into fewer parts. If the numerators are equal, the fraction with the larger denominator is the smaller.

*kapiert.de*can do more:

- interactive exercises

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### Any fractions

But what about fractions where the numerator and denominator are different?

**Example: Compare $$ 9/20 $$ and $$ 23/50 $$.**

Proceed like this:

**1. Find the same denominator:**

You bring up the fractions that you want to sort out **same denominator.**

Find a number that occurs both in the multiple series of $$ 20 $$ and in the multiple series of $$ 50 $$.

$$20, 40, 60, 80, 100, 120, …$$

$$50, 100, 150, …$$

You can see that the $$ 100 $$ occurs in both multiple series.

**2. Determine extension numbers:**

$$ 100: 20 = 5 $$. The $$ 100 $$ is in the 5th position in the multiple series.

$$ 100: 50 = 2 $$. The $$ 100 $$ is in the 2nd position of the multiple series.

**3. Expand:**

Expand $$ 9/20 $$ so that the denominator contains $$ 100 $$.

Now you expand $$ 23/50 $$ so that 100 is in the denominator.

**4. Compare:**

Now you compare the two counters. The fraction with the larger numerator is the larger fraction.

$$46/100 > 45/100$$

So $$ 23/50> 9/20 $$.

You compare fractions with different numerators and denominators by bringing them to the same denominator.

This is how you do it:

- Looking for the same denominator
- Determine expansion numbers
- Expand
- to compare

Now, if you're wondering if you couldn't put the fractions on the same count, the answer is YES.

However, very few people put fractions on the same counter. But it is mathematically correct.

### Pizza!!

Which tray is there more pizza on?

**1. Find the same denominator:**

$$15 \ \ 30 \ \ 45 \ \ 60 \ \ 75$$

$$ 12 \ \ 24 \ \ 36 \ \ 48 \ \ 60 $$ - ah, the $$ 60 $$!

**2. Determine extension numbers:**

$$60 : 15 = 4$$

$$60 : 12 = 5$$

**3. Expand:**

$$ 8/15 stackrel (4) = 32/60 $$

$$ 7/12 stackrel (5) = 35/60 $$

**4. Compare:**

$$32/60<35/60$$

So: $$ 8/15 <7/12 $$

Grab the second pizza tray. :-)

### If you already know decimal fractions

You convert the fractions to be ordered into a decimal number. Then you can just compare them.

**Example: Compare $$ 9/20 $$ and $$ 23/50 $$.**

$$9/20 = 9 : 20 = 0,45$$

$$- 0$$

$$ bar 90 $$

$$-80$$

$$ bar 100 $$

$$ - ul 100 $$

$$0$$

$$23/50 = 23 : 50 = 0,46$$

$$-$$ $$0$$

$$ bar 230 $$

$$-200$$

$$ bar 300 $$

$$ - ul 300 $$

$$0$$

If you compare $$ 0.45 $$ and $$ 0.46 $$, you can see that $$ 0.46 $$ is the larger number. ($$ 6 $$ is more than $$ 5 $$.)

If you put the two fractions in the calculator, you'll get those decimal numbers too.

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

### Improper fractions

For fractions greater than 1, the sorting works the same as for real fractions. However, there is the case that you don't have to calculate at all if you can see at first glance which fraction is larger.

**Example: which fraction is larger? $$ 2/3 $$ or $$ 6/5 $$?**

$$ 2/3 $$ is less than a whole. You can tell by the fact that the numerator has a smaller number than the denominator. $$ 6/5 $$ is greater than a whole. You could also write $$ 1 1/5 $$ for it.

So you know right away: $$ 6/5> 2/3 $$

### Trick: Break size $$ 1/2 $$

If you've given two fractions where one is greater than $$ 1/2 $$ and one less than $$ 1/2 $$, you can save yourself the math.

**Example: which fraction is larger? $$ 2/3 $$ or $$ 3/7 $$**

$$ 2/3 $$ is more than $$ 1/2 $$.

$$ 3/7 $$ is less than $$ 1/2 $$.

Now you can specify:

$$2/3 >3/7$$

Or

$$3/7<2/3$$

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