Whole Number Arithmetic Online Documentation

Use the Language of the Operations


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Learning to recognize the language associated with the operations helps learners recognize when to use each operation. Use the following vocabulary lists as guides for discussing arithmetic problems. Use the lists of question phrases, and other phrases, for making up arithmetic problems in everyday activities. These recommendations for language are not exhaustive. There are many more words and language forms possible. The lists are also not completely reliable. In many instances the learner cannot rely on the clues of language to determine the correct operation to use.

Addition

Vocabulary to Use When Describing Addition Problems

    addition The process of combining two or more numbers to find their sum. Addition is used to find the result of putting together items in a group, or parts in a whole. Addition is indicated by the plus sign (+). The sum of positive whole numbers added together is larger than any of the original numbers. Addition is the opposite of subtraction.

    addend A number that is added in an addition problem.

    sum The result of numbers being added in an addition problem.

             2      addend
            +2	addend
             4	sum
    

Question Phrases to Use When Forming Addition Problems

    What does that add up to?
    How many are there altogether?
    How many are there in all?
    If we put this together with that, how many will there be?
    What is the total?
    How much is there altogether?

Phrases Representing Ways of Saying Addition Problems

    2 plus 2 equals 4
    3 and then 5 more is
    increase 8 by 1
    9 and 3
    1 in addition to 2
    have 7, also have 6
    add 3 to 0
    7 grew by 4
    expand 2 by 8 more
    lengthen this length by 5
    the sum of 9 and 7 is

Subtraction

Vocabulary to Use When Describing Subtraction Problems

    subtraction The operation used to find the result of taking away something from a group, or finding parts of a whole. Subtraction is indicated by the minus sign (Ð). Subtraction is the opposite of addition. When a number is subtracted from another number, the resulting number is smaller than the minuend.

    minuend The quantity from which the subtrahend is deducted in subtraction.

    subtrahend The quantity that is deducted from the minuend in subtraction.

    difference The number that results from subtraction.

             3 	minuend
          -  2 	subtrahend
          	 1 	difference
    

Question Phrases to Use When Forming Subtraction Problems

    How many are left?
    How many are left over?
    How many more than...?
    How many less than...?
    How many more are needed?
    How many do you have to take away to get....?
    How many fewer?
    How much less?

Phrases Representing Ways of Saying Subtraction Problems

    4 minus 3 equals...
    7 less 2 equals...
    8 take away 6 equals...
    9 decreased by 1
    Reduce 4 by...
    Subtract 7 from 9
    Deduct 2 from 3
    Remove 2 from 5

Multiplication

Vocabulary to Use When Describing Multiplication Problems

    multiplication The operation used to put together a number of sets of the same size. Multiplication is indicated by the times sign (X), which may also be represented by a dot (·) or an asterisk (*). The operation of multiplication is the same as repeating addition (e.g., the answer to 2 X 3 is the same as adding 2 to itself 3 times or 2+2+2). Multiplication is the opposite of division.

    factor One of the numbers to be multiplied in a multiplication problem.

    multiplicand The number that is multiplied by the multiplier.

    multiplier The number by which the multiplicand is multiplied.

    product The number resulting from two numbers being multiplied.

    	3 	 multiplicand or factor
         X  2 	 multiplier or factor
            6  	 product
    

multiple A number that is a product of a number and another number.

    6 X 2 = 12 12 is a multiple of 2
    12 is a multiple of 6
    4 X 2 = 8 8 is a multiple of 2
    8 is a multiple of 4

Question Phrases to Use When Forming Multiplication Problems:

    How many altogether?
    How many in all?
    If we multiply this number times that number, how many will there be?
    What is the total?
    How much altogether?

Phrases Representing Ways of Saying Multiplication Problems:

    2 times 3 equals
    4 multiplied by 7 equals
    the product of 8 and 1 is
    repeat this set of 5, three times
    duplicate these 4 items, three times
    this set of 9, reproduced 6 times
    6 occurrences of those 2 events, yields...

Division

Vocabulary to Use When Describing Division Problems

    division The operation used to determine how many times a given number, or quantity, is contained in another number. Division is used to divide or partition a whole into parts. Division is the opposite of multiplication.

    divisible A number is divisible by another number if it goes into the number evenly with no remainder.

    dividend The number or quantity being divided.

    divisor The number by which the dividend is divided in a division problem.

    quotient The number that results when numbers are divided.

    remainder The number that is left over in a division problem if the dividend was not evenly divisible by the divisor.

Question Phrases to Use When Forming Division Problems

    When used to put a number into a number of sets, the question is:
    How many in each set?
    When used to put into sets of the same size, the question is:
    How many sets?
    How to distribute this group evenly?
    What part of the whole goes to each?
    How many pieces of the set go to each?
    How many times does this number go into this number?

Phrases Representing Ways of Saying Division Problems

    9 divided by 3
    divide 8 by 4
    4 goes into 8
    separate into parts
    distribute this set of items
    give out an equal number to each
    break this apart into sections
    what part of the group
    partition this area into even sizes
    deal out these items

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Last Updated on October 6, 2000 by Chuck at SSSoftware.com