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Ruler Arithmetic
By Charles Williams
Ruler Arithmetic explains how to read a ruler.
Look at one inch on your ruler. Sometimes one inch can be divided with two marks. Count the marks. Are there two? Then study the "2 Marks" section.
Look at one inch on your ruler. Maybe one inch can be divided with four marks? Count the marks. Are there four? Then study the "4 Marks" section.
Look at one inch on your ruler. Can it be divided with eight marks? Count the marks. Are there eight? Then study the "8 Marks" section.
Usually one inch is divided with sixteen marks. Are there sixteen marks? Study the "16 Marks" section.
Most rulers combine the marks. Practice reading a ruler using sixteenths, eighths, quarters, and halves here.
Do you need to learn how to read a ruler the right way? Begin with the next section and study straight-thru to the end of this page.
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.
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.
- Adding one-fourth plus two-fourths is three-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" - You can only add fractions when all the denominators are the same.
- "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. (In this practice you must reduce two-fourths. Every time you see "two-fourths" you must reduce it to "one-half" .)
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.
- Adding one-eighth plus two-eighths is three-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 with eighths now.
Every answer, when possible, must be "reduced".
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 goes 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?
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.
Exercise: Fraction Addition and Fraction Subtraction
Want to get good at something? Practice it all the time.
The same holds true for Ruler Arithmetic. Print these Ruler Arithmetic problems now. Remember: The answer is always "reduced" -- if possible.
Quick: Which one is the "denominator", the bottom or top? Print these "denominator" problems. Solving these problems takes a few steps. First, change the problem so both denominators are the same. Then add or subtract. Finally, if necessary, "reduce".
- Review: Step-by-Step
- Both demoninators must be the same: Let's add 1/2 + 1/16.
- Making both denominators the same: Multiply the top and bottom of 1/2 by the same number, like this: 1/2 X 8/8 = 8/16.
- Both denominators are the same now: 8/16 + 1/16.
- Do the arithmetic: 8/16 + 1/16 = 9/16.
- Can 9/16 be "reduced"? No. End of problem!
Practice: Read a Ruler
Most rulers combine sixteenths, eighths, quarters and halves.
To complete the Read a Ruler exercise, you must already be good at reading -- and "reducing" -- the marks for sixteenths, eighths, quarters and halves.
- Are you good at sixteenths?
- Are you good at eighths?
- Are you good at quarters?
- Are you good at halves?
Let's see how good you are! In the Read a Ruler exercise, count how many marks the thick blue line covers. Follow these instructions:
- Count how many marks the thick blue line covers.
- Did it pass the one inch mark? Two inches? Three? Type 1, 2 or 3 in the "inches" box.
- Is the thick blue line on a sixteenth mark? eighth mark? quarter mark? half mark? Type the correct number in the appropriate box.
- Click "Submit" and then see whether you are "Correct!" or not.
- Click "Next"
We have now put all the pieces together. Congratulations!
Now you must practice these steps all the time and get really, really good at reading the ruler. Good luck!