Ruler Arithmetic

Sometimes one inch is divided with 2 marks

Each mark is called a half.

Let's count the marks together, OK?

one-half

two-halves

Two-halves is one inch.

Now let's practice our addition:

Adding one-half plus one-half is two-halves.

1/2" + 1/2"

2/2"

"Reduce" means make smaller!

When possible, please "reduce" the answer.

2/2 "reduces" to: 1

Practice reading a ruler with halves now.

Top

Sometimes one inch is divided with 4 marks

Each mark on the ruler is a fraction.

The bottom number of a fraction is called the "denominator".

Take a cake break! Here the bottom number (the "denominator") tells how many pieces of cake makes one whole cake.

Now back to our ruler: the "denominator" tells how many marks it takes to make one inch.

Each mark is called a fourth.

Let's count the marks together, OK?

one-fourth

two-fourths

three-fourths

four-fourths

Four-fourths is one inch.

It is easy to "reduce" this: 4/4 = 1

Now let's practice our addition:

Adding one-fourth plus one-fourth is two-fourths.

Adding one-fourth plus two-fourths is three-fourths.

Adding one-fourth plus three-fourths is four-fourths.

Important:

The bottom number is called the "denominator".

You can only add fractions when all the denominators are the same.

1/4" + 1/4"	1/4" + 2/4"	1/4" + 3/4"
2/4"	3/4"	4/4"

"Reduce" means make smaller!

If possible, a fraction must be made smaller. It must be "reduced".

"Reducing" 4/4 to 1 is easy.

Some fractions cannot be "reduced" and must be left alone. Some fractions are already as small as they can get!

Here, just one fraction can be reduced. But how?

Divide the top number by 2. Divide the bottom number by 2.

Practice with fourths now.

Top

Sometimes one inch is divided with 8 marks

Each mark is called an eighth.

Let's count the marks together, OK?

one-eighth this is the very short mark way on the left

two-eighths

three-eighths

four-eighths

five-eighths

six-eighths

seven-eighths

eight-eighths this is the very long mark with the number "1" hanging off the bottom

This is how to add fractions:

Adding one-eighth plus one-eighth is two-eighths.

Adding one-eighth plus two-eighths is three-eighths.

Adding one-eighth plus three-eighths is four-eighths.

Adding one-eighth plus four-eighths is five-eighths.

Adding one-eighth plus five-eighths is six-eighths.

Adding one-eighth plus six-eighths is seven-eighths.

Adding one-eighth plus seven-eighths is eight-eighths.

Eight-eighths is one inch.

Add the fractions yourself:

1/8" + 1/8"	1/8" + 2/8"	1/8" + 3/8"	1/8" + 4/8"	1/8" + 5/8"	1/8" + 6/8"	1/8" + 7/8"

Next:

Which fractions can be reduced?

2/8 can be reduced to 1/4
4/8 can be reduced to 1/2
6/8 can be reduced to 3/4
8/8 can be reduced to 1

Practice reading a ruler with eighths now.
Every answer, when possible, must be "reduced".

Top

Sometimes one inch is divided with 16 marks

Each mark is called a sixteenth.

Let's count the marks together, OK?

one-sixteenth this is the very short mark way on the left

two-sixteenths

three-sixteenths

four-sixteenths

five-sixteenths

six-sixteenths

seven-sixteenths

eight-sixteenths

nine-sixteenths

ten-sixteenths

eleven-sixteenths

twelve-sixteenths

thirteen-sixteenths

fourteen-sixteenths

fifteen-sixteenths

sixteen-sixteenths this is the very long mark with the number "1" hanging off the bottom

"Reduce" means make smaller!

Fractions, if possible, must be made smaller. They must be "reduced". "Reducing" 16/16 to 1 is easy.

Some fractions cannot be "reduced". 1/16 cannot be "reduced".

Print this worksheet and practice your arithmetic by "reducing" the fractions.

Adding fractions

In fractions, the bottom number is the "denominator". To add fractions, the "denominator" must be the same in each fraction.

Adding one-sixteenth plus one-sixteenth is two-sixteenths.

Adding one-sixteenth plus two-sixteenths is three-sixteenths.

Adding one-sixteenth plus three-sixteenths is four-sixteenths.

Adding one-sixteenth plus four-sixteenths is five-sixteenths.

Adding one-sixteenth plus five-sixteenths is six-sixteenths.

Adding one-sixteenth plus six-sixteenths is seven-sixteenths.

Adding one-sixteenth plus seven-sixteenths is eight-sixteenths.

Adding one-sixteenth plus eight-sixteenths is nine-sixteenths.

Adding one-sixteenth plus nine-sixteenths is ten-sixteenths.

Adding one-sixteenth plus ten-sixteenths is eleven-sixteenths.

Adding one-sixteenth plus eleven-sixteenths is twelve-sixteenths.

Adding one-sixteenth plus twelve-sixteenths is thirteen-sixteenths.

Adding one-sixteenth plus thirteen-sixteenths is fourteen-sixteenths.

Adding one-sixteenth plus fourteen-sixteenths is fifteen-sixteenths.

Adding one-sixteenth plus fifteen-sixteenths is sixteen-sixteenths.

Practice your Ruler Arithmetic

5/16" + 5/16"	4/16" + 6/16"	5/16" + 7/16"	6/16" + 8/16"	1/16" + 15/16"
5/16" — 5/16"	14/16" — 6/16"	15/16" — 7/16"	6/16" — 3/16"	16/16" — 15/16"
9-5/16" + 5/16"	2-4/16" + 12/16"	3-5/16" + 7/16"	1-6/16" + 8-8/16"	1/16" + 15/16"
1-5/16" — 5/16"	14/16" — 3-6/16"	2-15/16" — 7/16"	6/16" — 3/16"	11-16/16" — 9-15/16"

It's a little confusing, but for some reason this is how it's done. When you want to write "Nine and five-sixteenth inches" you do it like you see above.

The same goes for "two and four-sixteenth inches".

The same goes for "three and five-sixteenth inches".

The same for "one and six-sixteenth inches".

It would be easier if they just said "one inch and then six-sixteenths of another inch". BUT THEY DON'T SAY IT THAT WAY!

Always "reduce".

Every fraction that can be made smaller must be "reduced". Did you "reduce" the sixteenth answers, above?

Practice reading a ruler with sixteenths now.
Every answer, when possible, must be "reduced".

Since the ruler we use can only be divided with two, four, eight or sixteen marks, we have finished learning about the marks on the ruler.