Pre-Algebra Mnemonics and Songs

Pre-Algebra

Arithmetic (Spelling)
Spelling of Arithmetic:
A Rat In The House May Eat The Ice-Cream.

Arithmetic Properties

Commutative Property
The commuting distance is the same in either direction, from home to work or work to home.

The Commutative Property tells us that: a + b = b + a or a × b = b × a

Associative Property
To associate with people is to group up with them.

The Associative Property are about grouping:
(a + b) + c = a + (b + c), or (a × b) × c = a × (b × c)

Distributive Property
To distribute something is to give it to everyone.

The Distributive Property “gives” whatever’s outside the parentheses to everything inside: a (b + c)=ab + ac

A video rap to help you remember the number properties - associative, commutative, distributive and identity

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Which is the Numerator, which is the Denominator?

Think “Notre Dame” (N before D)

nUmerator Up, Denominator Down

Nice Dog (N before D)

NUmerator is Never Under, Denominator is Down

This song will help you remember the difference between the numerators and denominators in fractions

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Dividing One Fraction With Another

Keep the first fraction, Change the sign from divide to multiply, Flip the last fraction.

Kentucky Chicken Fried
Kangaroo Candy Flowers
Koalas Chasing Ferrets

A song to help you remember how to divide fractions

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A song to help you remember how to add and subtract fractions.

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Division Algorithm (How To Do Long Division)

Divide - Multiply - Subtract - Compare - Bring Down

Does McDonalds Serve Cheese Burgers?

Does My Sister Cook Bananas?

Divide - Multiply - Subtract -Compare -Remainder

Does McDonald's Sell Cheeseburgers Raw?

Feet in a Mile

5280 feet = 1 mile
5 Tomatoes
5 to (m)ate oe(s)
5 2 8 0 -- or 5,280 feet in a mile

Greater Than or Less Than?
< or > ?
Which means greater than? Which means less than? How can you tell?
The alligator has to open its mouth wider for the larger number.

The following video shows how to remember which symbol to use.

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Metric Unit Prefixes
Metric Units of Measure in Order

* Kilo
* Hecto
* Deca
* Units [meter, liter, gram]
* Deci
* Centi
* Milli

King Hector Doesn't Usually Drink Cold Milk.

King Henry Danced [Merrily / Lazily / Grandly] Drinking Chocolate Milk.

For the standard units you can insert [Merrily] for meter, [Lazily] for liter, or [Grandly] for gram

A song to help you remember the metric system

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Mode & Median
Mode
The mode is the value there are the most of.

“MOde” and “MOst” have the same starting 2 letters.

The mode is the Most Occuring Data Entity.

Median
The median splits the data down the middle, like the median strip in a road.

A song to help you remember mean, median and mode

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Multiplying Signed Numbers
Analogies can help here.

From sports:
we = pos, win = pos, they = neg, lose = neg, good = pos, bad = neg
  we win = good (pos × pos = pos)
  we lose = bad (pos × neg = neg)
  they win = bad (neg × pos = neg)
  they lose = good (neg × neg = pos)

From friendship:
friend = pos, enemy = neg
  My friend's friend is my friend (pos × pos = pos)
  My friend's enemy is my enemy (pos × neg = neg)
  My enemy's friend is my enemy (neg × pos = neg)
  My enemy's enemy is my friend (neg× neg = pos)

From life:
good = pos, bad = neg
   A good thing happening to a good person is good. (pos × pos = pos)
   A good thing happening to a bad person is bad. (pos × neg = neg)
   A bad thing happening to a good person is bad. (neg × pos = neg)
   A bad thing happening to a bad person is good. (neg× neg = pos

A song to help you remember how to multiply signed numbers.

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Order of Operations

The order of mathematical operations:
* Parentheses
* Exponents
* Multiplication/Division (left to right)
* Addition/Subtraction (left to right).

PEMDAS Mnemonics
1. Please
  Excuse
  My Dear
  Aunt Sally

2. Please
  Educate
  My Daughters
  And Sons

3. Pursuing
  Education
  Means Dedication
  And Study

A music video about PEMDAS, the order of operations- this one has a PEMDAS lesson with examples in the middle of the song.

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Place Value and Decimals

A song to help you remember place value in decimals

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Roman numerals

Roman numerals: I =1, V = 5, and X = 10.
I View Xrays.

Roman Numerals: I = 1, V = 5, X = 10, L = 50 , C = 100 , D = 500 and M = 1000.

I Viewed Xerxes Loping Carelessly Down Mountains.
I Value Xylophones Like Cows Dig Milk

Roman numerals: L = 50 , C = 100 , D = 500 and M = 1000.
Lucy Can't Drink Milk.

Song about roman numerals.

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Use the first letter of each word to help you remember the integers zero through ten.

"Zowie! Only time travelers forge forward." said Sam, entering next Tuesday.

(Thanks Amy for the contribution)

Speed, Distance and Time

The following diagram shows the speed-distance-time triangle. Scroll down the page for more examples and solutions on how to use the speed-distance-time triangle.

Speed Distance Time Triangle

D = distance traveled
S = Average speed
T = Time taken

You can use the formula triangle in the following way:
If you need to find D, cover up D in the triangle and you get S × T

If you need to find S, cover up S in the triangle and you get

If you need to find T, cover up T in the triangle and you get

Speed-Distance-Time triangle

This video shows how to use the Speed-Distance-Time Triangle to solve some word problems.

Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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