Transcript Document

If you know how to add and subtract whole numbers, then you can
add and subtract decimals!.
To add decimal numbers:
1. Put the numbers in a vertical column, aligning the
decimal points
2. Add each column of digits, starting on the right and
working left. If the sum of a column is more than ten,
"carry" digits to the next column on the left.
3. Place the decimal point in the answer directly below
the decimal points in the terms.
To add these numbers, first arrange the terms vertically,
aligning the decimal points in each term. Don't forget, for
a whole number like the first term, the decimal point
lies just to the right of the ones column. You can add
zeroes to the right of the decimal point to make it easier
to align the columns. Then add the columns working from
the right to the left, positioning the decimal point in the
answer directly under the decimal points in the terms.
To subtract decimal numbers:
1. Put the numbers in a vertical column, aligning the decimal points.
2. Subtract each column, starting on the right and working left. If the digit being
subtracted in a column is larger than the digit above it, "borrow" a digit from the next
column to the left.
3. Place the decimal point in the answer directly below the decimal points in the terms.
4. Check your answer by adding the result to the number subtracted. The sum should
equal the first number.
To subtract these numbers, first arrange the terms vertically, aligning the decimal 27.583
points in each term. You can add zeroes to the right of the decimal point, to make - 0.200
it easier to align the columns. Then subtract the columns working from the right to
27.383
the left, putting the decimal point in the answer directly underneath the decimal
points in the terms. Check your answer by adding it to the second term and making
sure it equals the first.
To multiply decimal numbers:
1. Multiply the numbers just as if they
were whole numbers.
2. Place the decimal point in the
answer by starting at the right and
moving a number of places equal
to the sum of the decimal places in
both numbers multiplied
Multiply 9.683 x6.1
Line up the numbers on the right - do
not align the decimal points.
3.77
x 2.8
2 decimal places
1 decimal place
3016
+754
10556
3 decimal
places means
move the
decimal 3
places to the
left,
To divide decimal numbers:
1. If the divisor is not a whole number, move decimal point to right to make it a
whole number and move decimal point in dividend the same number of places.
2. Divide as usual. Keep dividing until the answer terminates or repeats.
3. Put decimal point directly
above decimal point in the dividend.
4. Check your answer.
Multiply quotient by divisor.
Does it equal the dividend?
Like fractions are fractions with the same
denominator. You can add and subtract like
fractions easily - simply add or subtract the
numerators and write the sum over the
common denominator
Before you can add or subtract
fractions with unlike
denominators, you must first find
equivalent fractions with the
same denominator, like this:
1. Find the smallest multiple
(LCM) of both numbers.
Use your notes from
Number sense I
2. Rewrite the fractions as equivalent
fractions with the LCM as the denominator.
Add
3
2

4
5
The LCM for 4 and 5 is 20
3
4
= 15
20
Convert each fraction to 20ths by using
the backwards Z method.
2
5
8
= 20
Divide the denominator of the original
fraction into the LCD
7
20
5 x 3 = 15
4x2=8


20
4= 5
20
5=4
Multiply by the numerator of the
original fraction to get the new
numerator
Then add or subtract
4
5
Add
+
3
5
7 = 2
15
5
Denominator
remains the
same.
When adding fractions we
sometimes get an improper
fraction as the sum.
To change the improper fraction to a
proper fraction divide the numerator
by the denominator.
1
5 7
5
2
Whole number
numerator
Subtract
5
2 20
2 14
-
2
5
+ 20
20
- 8
20
Convert to like fractions
In this problem 1 whole = 20
20
If we borrow 1 we are going to add 20 to the numerator.
Then subtract
1
25
20
-
8
20
1
17
20
1. Simplify the fractions if not in lowest terms.
2. Multiply the numerators of the fractions to get the new numerator.
3. Multiply the denominators of the fractions to get the new denominator.
Multiplying a mixed number by a whole number
9
5x3
8
Change the whole number
to a fraction
Change mixed number to
improper fraction
Multiply
Simplify
To divide any number by a fraction:
First step: Find the reciprocal of the fraction.
Second step: Multiply the number by the reciprocal of the fraction.
Third step: Simplify the resulting fraction if possible.
Fourth step: Check your answer: Multiply the result you got by
the divisor and be sure it equals the original dividend.
Reciprocal of 1 is 4
4
The Reciprocal of 3 is 4
4 3
Here are the steps for dividing mixed numbers.
1. Change each mixed number to an improper
fraction.
2. Multiply by the reciprocal of the divisor,
simplifying if possible.
3. Put answer in lowest terms.
4. Check to be sure the answer makes
sense.
Solve 30

21
2
1. Write the whole number and the mixed number as improper
fractions.
2. Write the reciprocal of the divisor, 2/5, and multiply.
3. Simplify, if possible.
Notice that we can simplify our problem at this
step, to make our calculations easier. Five goes
evenly into 30, so we can divide both 5 and 30 by
5, to give 1 and 6.
4. Perform the simple multiplication of the numerators
and the denominators.
5. Put the answer in lowest terms, and check the
answer.
Place these numbers in order from least to greatest.
2.1, 0.49, 0.0999, 1, 2.09
There are 3 basic steps.
1. Identify which order is asked for ,
least to greatest, or greatest to least.
( Most people make a mistake here by
not reading the directions)
2. Line up the numbers by the
decimal point vertically.(Annex
zeroes if needed)
2.1000
0.4900
0.0999
1.0000
2.0900
0.0999
0.4900
1.0000
2.0900
2.1000
3. Start at the left and move to
the right. If least to greatest
write the largest number last.
Place these fractions in order from Greatest to Least
1,
2
3,
4
2,
3
0.5, 0.75, 0.66,
54
108
81
108
36
108
5,
9
7,
12
There are several methods to use here.
These are 2 of the easiest when using a
list.
0.55, 0.583
60
108
63
108
1. Change each fraction to a decimal
and then compare.
2. Find the LCM (108) of each
and make equivalent fractions
and then compare.
Place these numbers in order from Greatest to Least
1, 0.32, 3, 1, 0.78
2
5 8
There are 2 basic choices.
1. Change all to fractions. 2. Change all to decimals.
When comparing 2 fractions, cross products works well.
21
3
4
5
7
20
Multiply the denominator of one fraction to the
numerator of the other.
Then compare products
Since 21>20 that means
3 > 5
4
7
In the Language of Algebra, an equation is the basic number
"sentence". An equation is a mathematical expression that contains
an equals sign.
An equation can contain variables
represented by letters
and constants
(numbers).
Key words to look for
“of” means multiplication
“is” means equal to
“times” is multiply
In these examples look for
the key words, plus, more
than, sum.
Other words like product, less
than, decreased, separated
into, quotient all give clues.
Ten dollars is two-thirds of the total
money spent
A number n times 3 is equal to
120.
3n = 120
Another type of sentence used in algebra is called an
inequality.
An inequality is used when we don't know exactly what an expression
is equal to.
Instead of an equals sign, we use one of these symbols:
> greater than
> greater than or equal to
< less than
< less than or equal to
Examples
A number minus 4 is greater than 2.
The sum of x and 5 is less than or equal to -2.
Look for the key words as you did for equations.
n-4>2
x + 5 < -2