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Lesson 2: Compare and reduce fractions

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compare fractions

In Introduction to Fractions, we learned that fractions are a way of representing a part of something. Fractions are useful because they tell us exactly how much we have of something. Some fractions are larger than others. For example, which is larger: 6/8ths of a pizza or 7/8ths of a pizza?

In this image we can see that 7/8 is larger. The figure makes it easy to compare these fractions. But how could we have done that without the pictures?

Click through the slideshow to learn how to compare fractions.

We have already seen that fractions have two parts.

One part is the top number or numerator.

The other is the bottom number or denominator.

The denominator tells us how many parts a whole has.

The counter tells us how many of these parts we have.

When fractions have the same denominator, it means they split into the same number of parts.

This means we can compare these fractions just by looking at the numerator.

Here 5 is more than 4…

Here 5 is more than 4… so we can say that 5/6 is more than 4/6.

Let’s look at another example. Which of these is bigger: 2/8 or 6/8?

If you thought 6/8 was bigger, you were right!

Both fractions have the same denominator.

So we compared the counters. 6 is greater than 2, so 6/8 is more than 2/8.

As you’ve seen, when two or more fractions have the same denominator, you can compare them by looking at their numerators. As you can see below, 3/4 is larger than 1/4. The larger the numerator, the larger the fraction.

Comparing fractions with different denominators

On the previous page we compared fractions that have the same lower numbers or denominators. But you know that fractions can have any number as a denominator. What if you need to compare fractions with different lower numbers?

For example, which of these is larger: 2/3 or 1/5? It’s hard to tell just by looking at her. After all, 2 is greater than 1, but the denominators are not equal.

If you look at the picture, the difference becomes clear: 2/3 is larger than 1/5. With an illustration it was easy to compare these fractions, but how could we have done that without the picture?

Click through the slideshow to learn how to compare fractions with different denominators.

Let’s compare these fractions: 5/8 and 4/6.

Before we compare them, we need to change both fractions so that they have the same denominator, or bottom number.

First we find the smallest number that can be divided by both denominators. This is what we call the lowest common denominator.

Our first step is to find numbers that are divisible by 8.

Using a multiplication table makes this easy. All numbers in the 8-series can be divided by 8 without a remainder.

Now let’s look at our second denominator: 6.

We can use the multiplication table again. All numbers in the 6-series can be divided by 6 without a remainder.

Let’s compare the two lines. It looks like there are some numbers that are divisible by both 6 and 8.

24 is the smallest number that occurs in both series, so the lowest common denominator.

Now let’s change our fractions so that they both have the same denominator: 24.

To do this, we need to change the numerators in the same way we changed the denominators.

Let’s look at 5/8 again. To change the denominator to 24…

Let’s look at 5/8 again. To change the denominator to 24…we had to multiply 8 by 3.

Since we multiplied the denominator by 3, we also multiply the numerator, or top number, by 3.

5 times 3 equals 15. So we changed 5/8 to 15/24.

We can because every number over itself is equal to 1.

So if we multiply 5/8 by 3/3…

So when we multiply 5/8 by 3/3, we’re really multiplying 5/8 by 1.

Since every number times 1 is equal to itself…

Since any number times 1 equals itself, we can say that 5/8 equals 15/24.

Now let’s do the same with our other fraction: 4/6. We also changed its denominator to 24.

Our old denominator was 6. To get 24, we multiplied 6 by 4.

So we also multiply the numerator by 4.

4 times 4 is 16. So 4/6 equals 16/24.

Now that the denominators are the same, we can compare the two fractions by looking at their numerators.

16/24 is greater than 15/24…

16/24 is greater than 15/24… so 4/6 is greater than 5/8.

reduce fractions

Which of these is bigger: 4/8 or 1/2?

If you did the math or just looked at the picture you might have been able to tell that they are the same. In other words, 4/8 and 1/2 mean the same thing, even though they’re spelled differently.

If 4/8 means the same as 1/2, why not just call it that? One half is easier to say than four eighths, and it’s also easier for most people to understand. After all, when dining out with a friend, split the bill in half, not eighths.

If you write 4/8 as 1/2, reduce it. When we shorten a fraction, we write it in a simpler form. Reduced fractions are always equal to the original fraction.

We have already reduced 4/8 to 1/2. If you look at the examples below, you can see that other numbers can be reduced to 1/2 as well. These fractions are all the same.

5/10 = 1/2

22.11 = 1/2

36/72 = 1/2

These fractions have also all been reduced to a simpler form.

4/12 = 1/3

14/21 = 2/3

35/50 = 7/10

Click through the slideshow to learn how to reduce fractions by dividing.

Let’s try to reduce this fraction: 16/20.

Since the numerator and denominator are even numbers, you can divide them by 2 to shorten the fraction.

First we divide the numerator by 2. 16 divided by 2 equals 8.

Next we divide the denominator by 2. 20 divided by 2 equals 10.

We reduced 16/20 to 8/10. We could also say that 16/20 equals 8/10.

If the numerator and denominator are still divisible by 2, we can further reduce the fraction.

8 divided by 2 is 4.

10 divided by 2 is 5.

Since there is no number by which 4 and 5 can be divided, we cannot reduce 4/5 any further.

This means that 4/5 is the simplest form of 16/20.

Let’s try reducing another fraction: 6/9.

While the numerator is even, the denominator is an odd number, so we can’t reduce by dividing by 2.

Instead, we need to find a number by which 6 and 9 can be divided. A multiplication table makes this number easy to find.

Let’s find 6 and 9 in the same row. As you can see, 6 and 9 can both be divided by 1 and 3.

Dividing by 1 doesn’t change these fractions, so we use the largest number that 6 and 9 can be divided by.

That’s 3. This is called the greatest common divisor, or gcd. (It can also be called the greatest common factor or GCF.)

3 is the gcd of 6 and 9 because it’s the largest number they can be divided by.

So we divide the numerator by 3. 6 divided by 3 is 2.

Then we divide the denominator by 3. 9 divided by 3 is 3.

Now we’ve reduced 6/9 to 2/3, which is the simplest form. We could also say that 6/9 equals 2/3.

Irreducible fractions

Not all fractions can be reduced. Some are already as simple as they can be. For example, you can’t cancel 1/2 because there is no number other than 1 that can divide both 1 and 2. (For this reason, you cannot reduce a fraction that has a numerator of 1.)

Also, some fractions with larger numbers cannot be reduced. For example, 17/36 cannot be reduced because there is no number by which both 17 and 36 can be divided. If you can’t find common multiples for the numbers in a fraction, it’s probably irreducible.

Try this!

Reduce each fraction to its simplest form.

Mixed numbers and improper fractions

In the previous lesson, you learned about mixed numbers. A mixed number has both a fraction and a whole number. An example is 1 2/3. You would read 1 2/3 like this: one and two thirds.

Another spelling would be 5/3 or five thirds. These two numbers look different but are actually the same. 5/3 is an improper fraction. It just means that the numerator is greater than the denominator.

There are times when you might prefer to use an improper fraction instead of a mixed number. It’s easy to convert a mixed number to an improper fraction. Let’s learn how:

Let’s convert 1 1/4 to an improper fraction.

First we need to figure out how many parts make up the whole number: 1 in this example.

To do this, we multiply the whole number , 1, by the denominator 4.

1 times 4 equals 4.

Now let’s add this number, 4, to the numerator 1.

4 plus 1 equals 5.

The denominator stays the same.

Our improper fraction is 5/4, or five quarters. So we could say that 1 1/4 equals 5/4.

This means that in 1 1/4 there are five 1/4s.

Let’s convert another mixed number: 2 2/5.

First we multiply the whole number by the denominator. 2 times 5 equals 10.

Next we add 10 to the numerator. 10 plus 2 equals 12.

The denominator remains the same as always.

So 2 2/5 equals 12/5.

Try this!

Try converting these mixed numbers to improper fractions.

Convert improper fractions to mixed numbers

Improper fractions are useful for math problems that use fractions, as you’ll learn later. However, they are also more difficult to read and understand than mixed numbers. For example, it is much easier to visualize 2 4/7 in your head than 18/7.

Click through the slideshow to learn how to convert an improper fraction to a mixed number.

Let’s turn 10/4 into a mixed number.

You can think of every fraction as a division problem. Just treat the dash between the numbers like a division sign (/).

So we divide the numerator 10 by the denominator 4.

10 divided by 4 equals 2…

10 divided by 4 gives 2… with remainder 2.

The answer 2 becomes our integer because 10 can be divided by 4 twice.

And the remainder, 2, becomes the numerator of the fraction because we have 2 parts left.

The denominator stays the same.

So 10/4 equals 2 2/4.

Let’s try another example: 33/3.

We divide the numerator 33 by the denominator 3.

33 divided by 3…

33 divided by 3…is 11 with no remainder.

The answer, 11, becomes our integer.

There’s no remainder, so we can see that our improper fraction was actually an integer. 33/3 equals 11.

Try this!

Try converting these improper fractions into mixed numbers.

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We’re sorry

This answer is wrong.

The easiest way to solve this problem is to convert everything to the same shape. Either convert everything to a fraction or convert everything to percent.

Convert everything to a fraction:

12% is converted to 0.12 to get a decimal number.

.12 converts to 12/100 to turn it into a fraction. Fraction is not in the lowest terms.

Reducing the fraction 12/100 to the lowest terms gives the fraction 3/25.

You now need to compare it to 1/8.

To see if the fractions are equal, you need to change both to the same common denominator. The lowest common denominator for 25 and 8 is 200. To change 1/8 so that it has a denominator of 200, the numerator and denominator are multiplied by 1 in the form 25/25.

1/8 * 25/25 = 25/200

To change 3/25 so that it has a denominator of 200, the numerator and denominator are multiplied by 1 in the form 8/8.

3/25 * 8/8 = 24/200

You can now see that 25/200 does not equal 24/200, so the second choice is incorrect.

Convert everything to percent:

To convert 1/8 to a percentage, you must first convert it to a decimal.

To convert 1/8 to a decimal, divide the denominator by the numerator. 1 divided by 8 = 0.125

To convert the decimal 0.125 to a percentage, shift the decimal point to the right two places and add the percent sign.

12% is greater than 12.5%, making the second choice wrong.

Now let’s try another one.

Which statement is correct?

Share this reply link: Help Paste this link into email, text or social media.

Showing the work Using the given inputs: Rewriting these inputs as decimal numbers: Comparing the decimal values ​​we have: Hence the comparison shows:

use calculator

Compare fractions to find out which fraction is larger and which smaller. You can also use this calculator to compare mixed numbers, compare decimals, compare whole numbers, and compare improper fractions.

How to compare fractions

To compare fractions with different denominators, convert them into equivalent fractions with the same denominator.

If you have mixed numbers, convert them to improper fractions. Find the lowest common denominator (LCD) for the fractions. Convert each fraction to its equivalent using the LCD in the denominator. Compare fractions: If the denominators are the same, you can compare the numerators. The fraction with the larger numerator is the larger fraction.

Example:

Compare 5/6 and 3/8.

Find the LCD: The multiples of 6 are 6, 12, 18, 24, 30, etc. The multiples of 8 are 8, 16, 24, 32, etc. The least common multiple is 24, so we’ll use that as the least common multiple Denominator.

Convert each fraction to its corresponding fraction using the LCD.

For 5/6 numerator and denominator, multiply by 4 to have LCD = 24 in the denominator.

\( \dfrac{5}{6} \times \dfrac{4}{4} = \dfrac{20}{24} \)

For 3/8 numerator and denominator, multiply by 3 to have LCD = 24 in the denominator.

\( \dfrac{3}{8} \times \dfrac{3}{3} = \dfrac{9}{24} \)

Compare the fractions. Since there are equal denominators, you can compare the numerators. 20 is greater than 9, so:

Since \( \dfrac{20}{24} > \dfrac{9}{24} \) we conclude \( \dfrac{5}{6} > \dfrac{3}{8} \)

For more help with fractions, see our Fractions Calculator, Simplified Fractions Calculator, and Mixed Numbers Calculator.

References: Help with Fractions Finding the lowest common denominator.

A tape measure, sometimes called a tape measure, is a roll of metal tape with evenly graduated markings used for measuring. The ribbon is often yellow and rolled in a plastic sleeve.

Measuring tapes are widely used in construction, architecture, building, home projects, crafts and woodworking fields. They usually come in lengths ranging from 6 feet to 35 feet long.

Tape measures can have measurements in imperial and metric, imperial only, or metric only.

How to read an imperial tape measure

On an imperial tape measure, the markings represent lengths in inches and fractions of an inch.

Each major line represents one inch (1″), and the lines in between represent the following fractions: 1⁄ 16″, 1⁄ 8″, 3⁄ 16″, 1⁄ 4″, 5⁄ 16″, 3⁄ 8 “, 7⁄ 16″, 1⁄ 2″, 9⁄ 16″, 5⁄ 8″, 11⁄ 16″, 3⁄ 4″, 13⁄ 16″, 7⁄ 8″, and 15⁄ 16″.

To read a tape measure, find the number next to the large tick and then find out how many small ticks behind it the measurement is. Add the number next to the big tick with the fraction to get the measurement. For example, if your five ticks extend past the tick of the number 4, then the measurement is 4 5⁄16”.

Reading a tape measure is like reading a ruler.

What do all the markings mean?

In order to read a tape measure, you need to understand what all the markings mean. The large ticks are 1″ apart, and the small ticks are fractions of an inch. The numbers next to the large ticks indicate the distance in inches from the end of the belt.

The ticks in the middle of the inch marks are half inch marks and there is 1⁄2 inch between each inch mark and the half inch mark.

The lines between the inch marks and the half-inch marks are quarter-inch marks. There is 1⁄4 inch between the one inch mark and the quarter inch mark. There is a 1⁄4 inch gap between each quarter inch mark and the half inch mark.

The second smallest ticks are eighth-inch marks, and there are 1⁄8 inches between the eighth-inch marks and the quarter-inch marks and the one-inch marks.

The smallest lines on a tape measure are sixteenth inch marks. Between each mark on the tape measure is 1⁄16 inches.

Fractional customs for each brand

Look at the decimal equivalents for all fractions on a tape measure. You may also like our Fractional Inches Calculator, which allows you to convert between decimal fractions and fractional inches and get decimal equivalents.

Fractional inches, decimal and millimeter equivalents

Chart showing equivalent fraction, decimal and millimeter measurements Fraction -Decimal millimeter 1⁄ 16” 0.0625 1.5875 1⁄ 8” 0.125 3.175 3⁄ 16” 0.1875 4.7625 1⁄ 4” 0.25 6.35 5⁄ 16” 0.3125 7.9375 3⁄8” 0.375 9.525 7.3125 ⁄16” 0.4375 11.1125 1⁄2” 0.5 12.7 9⁄16” 0.5625 14.2875 5⁄8” 0.625 15.875 15.875 16 ”0.6875 17.4625 3⁄ 4” 0.75 19.05 13ression ”0.8125 7⁄ 8” 0.875 1555 20.6375 7⁄ 8 ”0.875 1555 20.6375 22.225 1555 20.6375 7⁄ 8” 0.875 22.225 1555 20.6375 7⁄8” 0.875 22.225 1555 20.6375 7⁄8”0.875 22.225 1555 20.6375 7⁄8” 0.875 22.225 1555 8 7⁄37”. ” 0.9375 23.8125 1″ 1 25.4

How to read a metric tape measure

Metric tape measures have markings similar to imperial models, but the markings represent centimeters and millimeters. The larger markings on a tape measure with numbers are the centimeters and the smaller markings are millimeters.

Since a centimeter is 10 millimeters, there are 9 millimeter divisions between each centimeter on the tape.

On a metric tape measure, there is 1 cm between each large numbered line and 1 mm between each smaller line that is not numbered.

How to use a tape measure

Get the most out of your tape measure with the following usage tips.

How to use Bandstop

Almost all tape measures have a lock that prevents the tape from rewinding. This is useful when you need to take some weight off the tape measure or put the tape down while it is extended.

On this Stanley FatMax model, the slide lock is the large black button at the top. Sliding these down locks the strap open to prevent recoil.

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How to use the sliding hook

A distinctive feature of a tape measure is the hook at the end of the tape. This serves a dual purpose of preventing the tape from rolling into the housing and to allow hooking onto the end of items being measured.

You may notice that the end hook slides or moves just a little. This is intentional to allow for the thickness of the hook, making the tape measure accurate when hooked to a surface and also when the end butts against a surface.

Watch out for measuring tapes without sliding hooks, as these are not as accurate.

How to use the frame bolt notes

Most tape measures have red markings at specific intervals: 16″, 32″, 48″, 64″ and so on. These numbers are significant in that they indicate the center of a 16″ stud on the midframe.

Some tape measures also feature intervals with a black diamond symbol that are 19.2″ apart. These diamonds are also used to indicate frame spacing for wider stud or beam spacing.

How to use the nail gripper

The hook on a tape measure often has a small hole or groove in it. This is actually used to hook the hook onto a nail or screw to keep it from slipping off during long measurements.

This is particularly useful for longer measurements, such as B. measuring the length of a room or terrace.

The oval recess on the upper hook is used for hanging a nail or screw.

Use the sides of the hook

Some tape measures, especially frame tapes, have large hooks that can be used to grip surfaces on the side of the hook. Using these can improve the gripping ability of the hook and improve the accuracy of measurements as there is no need to rotate the tape measure to read the markings.

How to choose the right tape measure

There are many tape measures on the market and many serve very different purposes. When choosing the device that’s right for you, consider what you plan to use it for, how long you’ll need it, and how much you’re willing to spend.

When choosing a tape measure, consider the following characteristics to find a tape measure that is right for you and your needs.

Size and legibility of the markers

Imperial or metric markings

length of the band

Physical size of the tape

Outstanding length for measuring longer lengths

locking functions

durability

Price

Check out our best tape measure rating to find out which tape measure we think is the best and for reviews of several leading tape measures on the market. In a pinch, you can even print out a tape measure to save yourself a trip to the store.

What is a ruler

A ruler is a device with measurement markings on it that is used to measure straight lines. Students, engineers, contractors, and makers use rulers for math, construction, architecture, sewing, landscaping, and more.

According to Dictionary.com, a ruler is a straight-edged strip of wood, metal, or other material, usually marked in inches or centimeters, used for drawing lines, measuring, etc.[1]

Different types of rulers include wooden or metal rulers, rulers, tape measures, tape measures, carpenter’s rules, and architect’s scales.

Rulers have measurements in imperial and metric, imperial only, or metric only. Get more information about rulers, including different types and uses, or download and print one of our free printable rulers.

How to Use a Ruler – Standard Imperial Measurements

The markings on a standard ruler represent fractions of an inch. The marks on a ruler from the beginning to the 1″ mark are: 1⁄ 16”, 1⁄ 8”, 3⁄ 16”, 1⁄ 4”, 5⁄ 16”, 3⁄ 8”, 7⁄ 16”, 1⁄ 2″, 9⁄ 16″, 5⁄ 8″, 11⁄ 16″, 3⁄ 4″, 13⁄ 16″, 7⁄ 8″, 15⁄ 16″ and 1″. If the measurement is over 1 inch, simply use the number on the ruler and add the fraction. For example, if you are two ticks past tick number 3, then the measurement is 3 1⁄8″.

What do the markings on a ruler mean?

Reading a ruler starts with understanding what all the ticks mean. The largest dashes on a ruler represent a full inch, and the space between each large dash is 1″.

The large lines between the inch marks are half-inch marks, and the distance between an inch line and a half-inch line is 1⁄2 inch.

The middle sized ticks between the inch ticks and the half inch ticks are the quarter inch ticks. The distance between a quarter inch tick and an inch tick or a half inch tick is 1⁄ 4″.

The smaller dashes are the eighths of an inch dashes and may be the smallest or second smallest marks on the ruler. The distance between an eighth of an inch tick and the other larger ticks is 1⁄8″.

The smallest ticks on a ruler are the sixteenths of an inch ticks. The distance between a sixteenth of an inch tick and the other larger ticks is 1⁄ 16″.

How to Use a Metric Ruler – Metric Measurements

Metric rulers have centimeter and millimeter markings. The larger markings represent one centimeter.

The smaller lines on a metric ruler represent one millimeter. A centimeter is 10 millimeters, so there are 9 millimeter ticks between each centimeter tick.

More information on reading a ruler can be found here

Ruler Measurements: Fractional inches on a ruler

These are the measurements and fractions that appear on a ruler and the decimal and millimeter equivalents. If you need to convert larger fractions of inches to decimal or metric, use our fractional inches calculator.

Fractional, decimal and millimeter equivalent measurements

Millimeters to inches converter

From millimeter (mm) centimeter (cm) meter (m) kilometer (km) inch (in) foot (ft) yard (yd) mile (mi) to millimeter (mm) centimeter (cm) meter (m) kilometer (km) Inch (in) Feet (ft) Yard (yd) Mile (mi) Millimeter mm = Convert × Reset Swap inches (dec) to inches (frac) to feet+inch ft in calculation view on inch ruler Divide

inches to mm ►

* The fractional inch result is rounded to the nearest 1/64th fraction.

How do you convert millimeters to inches

1 millimeter equals 0.03937007874 inches:

1mm = (1/25.4)″ = 0.03937007874″

The distance d in inches (″) is equal to the distance d in millimeters (mm) divided by 25.4:

d(″) = d(mm) / 25.4

example

Convert 20 mm to inches:

d (″) = 20mm / 25.4 = 0.7874″

How many inches in a millimeter

One millimeter equals 0.03937 inches:

1mm = 1mm / 25.4mm/inch = 0.03937 inch

How many millimeters is in an inch

One inch equals 25.4 millimeters:

1 inch = 25.4mm/inch × 1 inch = 25.4mm

How do you convert 10mm to inches?

Divide 10 millimeters by 25.4 to get inches:

10mm = 10mm / 25.4mm/inch = 0.3937 inch

Millimeters to inches conversion table

Fractional inches are rounded to a resolution of 1/64.

millimeters (mm) inches (“)

(decimal) inches (“)

(fraction) 0.01mm 0.0004″0″ 0.1mm 0.0039″0″ 1mm 0.0394″ 3/64″ 2mm 0.0787″ 5/64″ 3mm 0.1181″1 /8″ 4mm 0.1575″ 5/32″ 5mm 0.1969969” “13/64″ 6mm 0.2362″ 15/64″ 7mm 0.2756″ 9/32″ 8mm 0.3150″ 5/16″ 9mm 0.3543″ 23/64” 10mm 0.3937″ 25/64″ 20mm 0.7874″ 25 2574″ 257474″ 257474″ 257474″ 25.2010 /32″ 1/1. 16 ″ 40 mm 1.5784 ″ 1 37/64 ″ 1.9685 ″ 1 31/3622 ″ 2 23/64 ″ 70 mm 2.75 3 ″ 2.7555 ″ 3.1496 ″ 35/32 ″ 3.5433 ″ 3 35/ 64″ 100mm 3.9370″ 3 15/16″

inches to mm ►

See also

3/8 as a decimal is 0.375.

Watch video guide

Work out

Question 1 In the fraction 3/8, the number 8 is the numerator

denominator

Decimal

Fraction Show the answer answer denominator

Question 2 In the fraction 3/8, the number 3 is the numerator

denominator

Decimal

Fraction Show the answer answer numerator

Question 3 What is the equivalent fraction to 3/8? 16.06

17.6

15.06

9/36 Show the answer Answer 6/16

Question 4 What is the equivalent fraction to 3/8? 16.06

9/32

32/9

9/36 Show the answer Answer 9/32

Question 5 What is the equivalent fraction to 3/8? 300/808

301/808

300/800

None Show the answer Answer 300/800

How is the long division method performed?

To convert the fraction to decimal, write the numbers in long division with 3 as the dividend and 8 as the divisor.

Since 3 cannot be divided by 8, we can add 0 to 3 to make it 30 and put a decimal point in the quotient.

Keep dividing, if you get a remainder less than 8, you can add 0 to make it divisible by 8.

Do the division until you get the remainder 0 or until the remainder is repeated.

Here we did the division until we got 0 as the remainder. Since we cannot divide further, the answer would be the quotient we get from this division, 0.375.

Remember

Here are some common terms you should be familiar with. In the fraction $$\frac38$$ the number 3 is the dividend ( our numerator )

The number 8 is our divisor (our denominator).

You may be interested in what 1/3 is as a decimal fraction?

Find more fractions in decimals

What is a ruler

A ruler is a device with measurement markings on it that is used to measure straight lines. Students, engineers, contractors, and makers use rulers for math, construction, architecture, sewing, landscaping, and more.

According to Dictionary.com, a ruler is a straight-edged strip of wood, metal, or other material, usually marked in inches or centimeters, used for drawing lines, measuring, etc.[1]

Different types of rulers include wooden or metal rulers, rulers, tape measures, tape measures, carpenter’s rules, and architect’s scales.

Rulers have measurements in imperial and metric, imperial only, or metric only. Get more information about rulers, including different types and uses, or download and print one of our free printable rulers.

How to Use a Ruler – Standard Imperial Measurements

The markings on a standard ruler represent fractions of an inch. The marks on a ruler from the beginning to the 1″ mark are: 1⁄ 16”, 1⁄ 8”, 3⁄ 16”, 1⁄ 4”, 5⁄ 16”, 3⁄ 8”, 7⁄ 16”, 1⁄ 2″, 9⁄ 16″, 5⁄ 8″, 11⁄ 16″, 3⁄ 4″, 13⁄ 16″, 7⁄ 8″, 15⁄ 16″ and 1″. If the measurement is over 1 inch, simply use the number on the ruler and add the fraction. For example, if you are two ticks past tick number 3, then the measurement is 3 1⁄8″.

What do the markings on a ruler mean?

Reading a ruler starts with understanding what all the ticks mean. The largest dashes on a ruler represent a full inch, and the space between each large dash is 1″.

The large lines between the inch marks are half-inch marks, and the distance between an inch line and a half-inch line is 1⁄2 inch.

The middle sized ticks between the inch ticks and the half inch ticks are the quarter inch ticks. The distance between a quarter inch tick and an inch tick or a half inch tick is 1⁄ 4″.

The smaller dashes are the eighths of an inch dashes and may be the smallest or second smallest marks on the ruler. The distance between an eighth of an inch tick and the other larger ticks is 1⁄8″.

The smallest ticks on a ruler are the sixteenths of an inch ticks. The distance between a sixteenth of an inch tick and the other larger ticks is 1⁄ 16″.

How to Use a Metric Ruler – Metric Measurements

Metric rulers have centimeter and millimeter markings. The larger markings represent one centimeter.

The smaller lines on a metric ruler represent one millimeter. A centimeter is 10 millimeters, so there are 9 millimeter ticks between each centimeter tick.

More information on reading a ruler can be found here

Ruler Measurements: Fractional inches on a ruler

These are the measurements and fractions that appear on a ruler and the decimal and millimeter equivalents. If you need to convert larger fractions of inches to decimal or metric, use our fractional inches calculator.

Fractional, decimal and millimeter equivalent measurements