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Mathematics Lessons This page is still under construction. Numerals, numbers When we write, we use different symbols to mean certain things. Some of these symbols are called “numerals” because they are symbols that represent numbers. The most common numerals used to represent numerals are: 1 2 3 4 5 6 7 8 9 0 These numerals are arranged in a specific way to represent a certain number. We use the numerals 1 and 2 to represent the number “twelve” if they are arranged as 12 . We use the numerals 1 and 2 to represent the number “twenty-one” if they are arranged as 21 . We use the numerals 1 and 0 to represent the number “ten” if they are arranged as 10 .
Values of individual common numerals We use each of the individual numerals to represent a unique number: We use the numeral 1 by itself to represent the number “one.” We use the numeral 2 by itself to represent the number “two.” We use the numeral 3 by itself to represent the number “three.” We use the numeral 4 by itself to represent the number “four.” We use the numeral 5 by itself to represent the number “five.” We use the numeral 6 by itself to represent the number “six.” We use the numeral 7 by itself to represent the number “seven.” We use the numeral 8 by itself to represent the number “eight.” We use the numeral 9 by itself to represent the number “nine.” We use the numeral 0 by itself to represent the number “zero.” Here is a chart showing each numeral with the number it represents and a visual picture of the number's value:
Organizing numerals Rather than use an individual numeral for each number we want to represent, we use a combination of numerals to represent most numbers. We organize numbers using a “base-ten” system, which means that a numeral represents ten times the value the same numeral to the right would represent. Adding two numbers; addends; sum Three people went into the chapel to pray. Two more went in to pray with them. How any people were in the chapel now? We can also write this faster as 3 people + 2 people
or 3 +2 or 3 + 2 = _____ If we count the people we find there are five of them. We can answer the questions we wrote more quickly as
3 people or
3
5
If we write our question in any of these three ways they will all have the same answer: 5 We call the numbers we add together “addends” (in this case 2 and 3 were the addends) and we call the total of the addends the “sum.” 3 people <--addend +
2 people
<--addend
5
people
<--sum
or 3 <--addend +2 <--addend
5
<--sum
Adding with zero If we have a full pie and an empty pie pan, how many pie do we have? We can also write this as 1 + 0 = ____ Since we know that there is only one pie, we write 1 on the line so it looks like this= 1 + 0 = 1 We can add 0 to any number and the sum (total) will be the same. So if we have 12 eggs and get 0 more we will still have 12 eggs. This is called the Identity Property of Addition. Adding more than two numbers/addends When we need to add more than two groups of numbers at a time, it may be easier to add just two numbers at a time rather than trying to answer a question all at once. If are three clean plates in the cupboard, two clean plates in the dish drainer, and four clean plates on the table, how many dishes do we have that we can use for the meal? We can also write this as 3 plates
2 plates
+4
plates
or 3 +4
If we want to add two of the numbers together before we add the other number or numbers to it, we can use parentheses to enclose what should be added together first. If we wanted to add 2 and 4 together first, we can write it as 3+ (2 + 4)=_______ When we add numbers together that are inside the parentheses, we replace the numbers and signs inside the parentheses with the total of the numbers. So since 2 + 4 = 6, we replace the “2 + 4” with “6” and our question will now look like this: 3 + (6) = ___ We can remove the parentheses from around the 6 because we no longer need them. It will now look like 3 + 6 = ____ We then add the 3 and 6 and write the answer on the line and it looks like this: 3 + 6 = 9 If we write it as 3
2
+4 we can first write it on the scratch paper like this 3
2
+4 then if we want to add the 2 and 4 four together first we can make a line come from each number and join together, then write the sum of the two numbers where they join so that it looks like this: 3
2 \ 6
(show
better picture of this)
+4 / then write a new question adding the 3 and 6 3 +6 and since we know that the sum of 3 and 6 is 9, we write the sum below the line like this: 3 +6 9 so we know there are nine clean dishes we can use for the meal. Subtraction If we had four clean large bowls and used two for a meal, how many are left? We can write this as 4 bowls -
2
bowls
or 4
- 2
or 4 – 2 = _____ If we count the bowls we see there are two clean large bowls left, so we write 2 under the line for the first two ways we wrote the question, and on the line for the third way we wrote the question: 4 bowls -
2
bowls
2
bowls
or 4
- 2
2 or 4 – 2 = 2 So we have two large clean bowls left. We call the original number the minuend and the amount we take away the subtrahend. We call the total the difference. 4 bowls <--minuend -
2 bowls
<--subtrahend
2
bowls
<--difference
or 4 <--minuend -2
<--subtrahend
2
<--difference
Subtracting with zero If we have
a full pie and do
not take any away, how many
pies do we have?
We can also write this as 1 - 0 = ____ Since we know that we still have the one pie, we write 1 on the line so it looks like this= 1 - 0 = 1 We can subtract 0 from any number and the difference (total) will be the same. So if we have 12 eggs and take away 0 eggs we will still have 12 eggs. This is called the Identity Property of Subtraction. Checking subtraction with addition; Checking addition with subtraction If
we add the original difference
and the original subtrahend and it equals the original minuend, we
can see if we subtracted it correctly. So if we have
4 bowls <--original minuend -
2 bowls
<--original subtrahend
2
bowls <--original
difference
we can setup to add the original minuend and the original difference 2 bowls <--original subtrahend + 2
bowls
<--original difference
and add them 2 bowls <--original subtrahend + 2
bowls
<--original difference
4 bowls As we see, our answer (4 bowls) is the same as the original minuend (also 4 bowls). Also, we can check our addition by subtracting one of the original addends from the sum, and it will equal the other original addend. So if we have 3 people <--original addend +
2 people
<--original addend
5
people <--original sum
we can setup to subtract one of the original addends from the sum 5 people <--original sum -
2 people
<--original addend
then subtract
5
people <--original
sum
- 2 people <--original addend 3 people As we see, our answer (3 people) is the same as the other original addend (also three people). As with anything else in life, addition undoes subtraction, and subtraction undoes addition. |
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