"Key Words and Catch Phrases" for Word ProblemsAddition Words1. Add2. Altogether3. Both4. In all5. Sum6. TotalSubtraction Words1. Difference2. Fewer3. How many more4. How much more5. Left6. Less: Debra bought apples for $3.20 and oranges for $4.23. How muchlessdid the apples cost?7. Minus8. Need to9. Remains10. Subtract10. Words ending with "er"; higher, longer, faster, heavier, larger, shorter, slower, farther, etc. Example: Jean's apple weighs 100 grams, and Karen's apple weighs 80 grams. How muchheavieris Jean's apple?Multiplication Words1. Times:Maria ran around the track 5times.It took her 5 minutes to run around the track. How many minutes did she run?2. Every:Kim buys 2 appleseveryday. How many apples does she buy in a week?3. At this rate:Ed reads 25 words per minute.At this rate, how many words does he read in one hour?Division Words1. Each: Ken has 75 pencils and 15 boxes. How many pencils should he pack ineachbox so each customer gets the same number of pencils?Terms Used in Equations

Here are the terms used in equations for addition, subtraction, multiplication, and division. These terms include augend, addend, sum, subrahend, minuend, difference, multiplicand, multiplier, product, factors, dividend, divisor, quotient, and remainder.

Addition

In addition, anaugendand anaddendare added to find asum.In the following equation, 6 is the augend, 3 is the addend, and 9 is the sum:

6 + 3 = 9

NOTE: Sometimes both the augend and addend are calledaddends.Sometimes the sum is called thetotal.Subtraction

In subtraction, asubtrahendis subtracted from aminuendto find adifference.In the following equation, 9 is the minuend, 3 is the subtrahend, and 6 is the difference.

9 3 = 6

Multiplication

In multiplication, amultiplicandand amultiplierare multiplied to find aproduct.In the following equation, 6 is the multiplicand, 3 is the multiplier, and 18 is the product.

6 x 3 = 18

NOTE: Sometimes the multiplicand and the multiplier are both calledfactors.Division

In division, adividendis divided by adivisorto find aquotient.In the following equation, 18 is the dividend, 3 is the divisor, and 6 is the quotient.

18 / 3 = 6

If there is an amount left over, it is called theremainder.The remainder cannot be evenly divided by the divisor. For example, if you divide 18 by 7, you will get a remainder:

18 / 7 = 2, with a remainder of 4

Order of Operations

The information below explains PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction

When you have a math problem that involves more than one operationfor example, additionandsubtraction, or subtractionandmultiplicationwhich do you do first?

Example #1: 6 3 x 2 = ? Do you do the subtraction first (6 3 = 3) and then the multiplication (3 x 2 =6)?

Or do you start with the multiplication (3 x 2 = 6) and then subtract (6 6 =0)?

PEMDAS

In cases like these, we follow theorder of operations.The order in which operations should be done is abbreviated asPEMDAS:

1. Parentheses

2. Exponents

3. Multiplication andDivision(from left to right)4. Addition andSubtraction(from left to right)(One way to memorize this is to think of the phrasePleaseExcuseMyDearAuntSally.)

In the above example, we're dealing with multiplication and subtraction.Multiplication comes a step beforeSubtraction, so first we multiply 3 x 2, and then subtract the sum from 6, leaving 0.

Example #2: 30 5 x 2 + 1 = ? There are noParentheses.

There are noExponents.

We start with theMultiplication andDivision, working from left to right.NOTE:Even though Multiplication comes before Division in PEMDAS, the two are done in the same step, from left to right. Addition and Subtraction are also done in the same step.

30 5 = 6, leaving us with6 x 2 + 1 = ? 6 x 2 = 12, leaving us with12 + 1 = ? We then do theAddition:12 + 1 = 13Note that if we'd done the multiplication before the division, we'd have ended up with the wrong answer:

5 x 2 = 10, leaving30 10 + 1 = ? 30 10 = 3, leaving3 + 1 = ? 3 + 1 = 4(off by 9!)One last example for advanced students, using all six operations:

Example #3: 5 + (4 2)2x 3 6 1 = ? Start with theParentheses:4 2 = 2. (Even though subtraction is usually done in the last step, because it's in parentheses, we do this first.) That leaves5 + 22x 3 6 1 = ? ThenExponents:22= 4. We now have5 + 4 x 3 6 1= ? ThenMultiplication andDivision, starting from the left:4 x 3 = 12, leaving us with5 + 12 6 1 = ? Then moving to the right:12 6 = 2, making the problem5 + 2 1 = ? ThenAddition andSubtraction, starting from the left:5 + 2 = 7, leaving7 1 = ? Finally, moving to the right:7 1 = 6