Transcript fraction - SCHOOLinSITES

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1.01 NEGATIVE NUMBERS
09-02-08
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Understanding Integers
1. What is a positive
number?
1. It’s a number greater than zero. *
2. What is a negative
number?
2. It’s a number less than zero.
3. What are
opposites?
3. The same number with a different sign
4. Show opposites on
a number line:
* Represented with a + or no sign
* Always written with a - sign
* They are the same distance from 0
but are on different sides of 0
Understanding Integers
5. What are
integers?
6. What is
absolute value?
Negatives are
always less than
positives
5. Integers are the set of all whole
numbers and their opposite
6. An integer’s distance from 0
* Represented by I n I
* Never negative
* Always positive
Absolute values
are never
negative
Opposites are the same #
but one is + and one is --
Is it positive or negative? Write the integer:
A. I owe my friend $10.00
B. I live 100 feet above sea level
C. It’s 20 degrees below zero outside
D. I gained 15 yards in my football game
Graphing Opposites. Graph the integer and it’s opposite:
.
-4
-3 -2
-1
0
1
2
3
4
-4
-3 -2
-1
0
1
2
3
4
-4
-3 -2
-1
0
1
2
3
4
-4
-3 -2
-1
0
1
2
3
4
Write the absolute value of:
1. I-2I =
2. I0I =
3. I5I =
4. I-4I =
5. I-1I =
1.03 Ordering integers
09-03-08
Comparing and Ordering Integers
1. How do I compare
integers?
1. Use a number line.
* Numbers to the left are less
than number to the right
-4 -3 -2
2. Compare the
following integers:
3. How do I order
integers?
-1
-4
6
2
-4
3
4
0
1
-14
-9
12
2
3
4
-20
8
14
3. GRAPH them on a number
line, then order them.
-4 -3 -2
-1
0
Order: 2, -4, -1, 5, 0
1
2
3
4
5
Comparing and Ordering Integers
4. Graph then order
4.
the following integers
greatest to least:
-5
-4
-3
-2
-1
5, -2, 1, -4, -1, 3
0
1
2
3
4
5
5. Graph and order
5. 5, -2, 1, -4, -1, 3
the same integers
least to greatest.
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L.L. = LEFT IS
LESS
* Use a # line to
compare or order
integers
ALL objectives
09-04-08
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Solving Word Problems
1. How do I solve word 1. 1. Read the problem until you
problems?
understand what the question is.
2. List the important information
3. Make a plan: how are you going to
solve the problem? Draw pictures,
diagrams, etc. if necessary
4. Solve the problem
5. Check your answer and look back at
the problem. Does your answer
make sense?
1.03 Compare & order decimals
09-04-08
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Ordering and Comparing Decimals:
1. What are the 1. 204.98673
place values
2 = hundreds place
for decimals? 0 = tens place
4 = ones place
9 = tenths place
8 = hundredths place
6 = thousandths place
7 = ten-thousandths place
3 = hundred-thousandths
place
Ordering and Comparing Decimals:
2. How do I say a
decimal number?
2. Always say the decimal as “and”
Say the number the same way you
would if it wasn’t a decimal, then say
the place value of the last digit
Example: 82.34 =
Eight two and thirty four hundredths
3. How do I compare
decimals?
3. Line up all the decimals then
compare each column left to right
Example: 2.014
2.03
3 is greater than 1 so
2.014 < 2.03
Ordering and Comparing Decimals:
4. How do I order
decimals?
4. Line up all the decimals then
compare each column left to right
Example: 2.4, 1.9, 2.19 (L --> G)
5. Compare these
decimals:
5. 1.1
2.354
5.5
6. Order these
decimals L -> G:
1.01
2.6
5.98
5. 1.1, 1.001, 1.01
2.354, 2.55, 2.6
5.5, 5.05, 5.98
Always line up
decimals when
comparing or
ordering
Compare
columns left to
right
1.03 Compare & order fractions
09-04-08
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1. What are the
parts of a fraction?
2. How do I
compare two
fractions?
1. Whole number
2¾
Numerator
Denominator
2. Cross multiply bottom to top and compare
the quotients
Example:
⅔
⅝
⅝
¾
* If the denominators are the same, you can
compare the numerators
Example: ⅜
⅞
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3. How do I order
fractions?
3. Change the fractions into decimals then
compare the decimals
4. How do I change 4. Divide the numerator by the denominator
fractions to
1. The nice numerator goes in the house
decimals?
2. The dorky denominator stays outside
the house
3. Add a decimal and two zeros to the
nice numerator
4. Divide as usual
5. Bring the decimal straight up into your
answer
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5. Change these
fractions to
decimals:
5. ⅞
⅝
⅜
⅛
⅔
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6. Order these
fractions least to
greatest:
6.
⅞, ⅔, ½, ⅝
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7. How else can I
order fractions?
7. Find a common denominator (a number
all of the denominators can go into evenly)
then order the numerators.
1. Find a common denominator
2. Set up each fraction equal to that
denominator
3. Whatever # you x the denominator by,
you MUST x the numerator by
4. Order fractions based on their
numerators
8. Order L using
a common
denominator:
8.
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9. Order GL
using a common
denominator:
9.
The nice numerator
goes in the house,
the dorky
denominator stays
outside the house
Change fractions to
decimals or find a common
denominator to order
fractions or compare more
than 2 fractions
Denominator
Down
Cross multiply to
compare TWO
fractions
1. The run got pushed
backwards 12 yards.
2. Andi jumped 12 feet high.
3. Clinton owes $48.00.
4. The city is 1,895
feet below sea level.
5. The diver dove 60 feet
under the surface.
6. The temperature was 5
degrees F but then it
dropped 7 degrees. What’s
the temperature now?
7. In the game of golf, the
lowest score wins. Who won
the game?
Amy = -7
Clinton = -4
Kira = 2
Andi = -9
1. -12
-14
1. What is the opposite of -12?
2. -2
2
2. Graph 4 and its opposite:
3. -43
-31
3. Graph -3 and its opposite:
Clinton dove 45 feet under water.
Amy dove 60 feet under water.
Kira dove 12 feet under water.
Who dove the deepest?
1. Clinton has 2.3 gallons of
gas. He needs 2.76 gallons.
Does he have enough?
2. Write in words: 2.16
3. Clinton dove 23.89 feet.
Amy dove 23.66 feet. Andi
dove 23.9 feet. Kira dove 23
feet. Put their names in order
from the deepest to shallowest
dives.
4. What place is the 6 in?
45.688
5. Andre has three sticks. Their
lengths are 2.21 inches, 2.20
inches and 2.222 inches. What
is the length of the shortest
stick?
1. Our gas tank has 4/9 of
a gallon in it. We need
7/13 of a gallon for the
lawn mower. Do we have
enough?
2. Order least to greatest:
3/6, 2/7, 4/5
4. Turn this fraction
into a decimal:
5/9
5. The recipe calls for
1/3 cups of sugar. I
have 3/9 cups of
sugar. Is that enough?
3. The store has 3 nails left. One is
3/5 inches, one is 8/11 inches, and
one is 6/9 inches. Which one is
shortest?
1. Put all cards face down on your desk
2. Mix them all up (please)! be gentle so the cards don’t
bend or rip
3. Distribute them evenly between you and your partner
4. Flip them over one at a time
5. The LOWEST number wins
6. The first player with all of the cards wins
1.03 Fractions
09-13-09
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1. What are like
fractions?
1. They’re fractions with the same denominator (de
nomber on de bottom)
EX: ⅝ ⅞ ⅛
2. What are unlike
fractions?
2. They’re fractions with different denominators
EX: ⅛, , ½
3. What are proper
fractions?
3. Fractions in which the numerator is less than the
denominator
EX: ½ ⅞ ⅛
4. What are
improper fractions?
4. Fractions in which the numerator is greater than the
denominator
EX:
, ,
5. What are
equivalent fractions?
5. Fractions that have the same value
EX:
6. How do I make an
equivalent fraction?
=
= =
=
6. * Multiply the numerator and denominator by
the same number
EX:
x
=
x
=
OR
* Divide by a number that goes into the numerator
AND denominator evenly
EX:
÷
=
÷
=
7. What does
simplest form mean?
7. The fraction cannot be reduced
* No numbers other than 1 can go into the numerator
and denominator evenly
EX: ⅝ , ⅔ , ⅞
8. How do I change
a whole number into
fraction?
8. Put the whole number over 1
EX: 7=
10=
5=
9. The numerator must be the same as the denominator
9. How do I make a
fraction equal to 1?
EX:
=1
=1
=1
10. What is a mixed
number?
10. A whole number with a fraction
EX: 4⅝ , 7⅔ , 3⅞
11. How do I change
a mixed number into
an improper
fraction?
11. 1. Multiply the whole number and denominator
2. Add the numerator to your answer
3. The sum becomes the numerator
Then add.
4. The denominator stays the same
EX:
4⅝
7⅔
3⅞
2
33
Multiply.
11. How do I change
an improper fraction
into a mixed number?
12. Change the
improper fractions to
mixed numbers:
11.
1
__
24
=
12. 1.
2.
3.
4 9
-8
1
1. Divide the numerator by
the denominator.
2. The remainder becomes the
numerator, the denominator stays
the same.
1.03 Multiply fractions
1. How do I multiply
fractions?
1. A. Multiply the numerators
B. Multiply the denominators
C. Write the answer in simplest form
Example: 1/3 * 3/5
2. How do I multiply a 2.
fraction by a whole
number?
A. Change the whole number into a fraction
** put it over 1
B. Multiply the numerators
C. Multiply the denominators
D. Write your answer in simplest form
Example: 4 * 7/8
1.03 Multiply fractions
3. How do I multiply
mixed numbers?
3. A. Change the mixed numbers to improper fractions
B. Multiply the numerators
C. Multiply the denominators
D. Write the answer in simplest form or as a mixed
number
Example 1: 1/3 * 1 1/2
Example 2: 2 1/2 * 1 1/3
4. How do I
evaluate fraction
expressions?
4. A. Replace x with the given number
B. Multiply
C. Write your answer in simplest form
Example: x = 5/8
1/3 * x
1.03 Multiply fractions
6. How do I multiply a 6.
whole number by a
A. Write both numbers as improper fractions
mixed number?
B. Multiply the numerators and denominators
C. Change your answer to a mixed number
1.03 Divide fractions
1. What is a
reciprocal?
1. It’s when you flip a fraction upside down
2. How do I find the
reciprocal of a
fraction?
2. Switch the numerator and denominator
* Two fractions are reciprocals if their product is 1
Example: 2/5 =
8/9 =
1.03 Divide fractions
3. How do I divide
fractions?
3. 1. Copy the first fraction
2. Change the division sign to multiplication
3. Flop (flip) the second fraction
4. Multiply
5. Write your answer in simplest form
Example: 4/5 - 5
Example 2: 1/2 - 1/4
1.03 Add & subtract fractions
1. How do I add like
fractions?
1. A. Add the numerators
B. Keep the same denominator
C. Write your answer in simplest form
Example: 2/7 + 3/7
2.How do I subtract
like fractions?
2. A. Subtract the numerators
B. Keep the same denominator
C. Write your answer in simplest form
Example 1: 4/5 - 1/5 =
Example 2: 1- 4/5=
3. How do I subtract
like mixed
numbers?
3. A. Subtract the fractions
B. Subtract the whole numbers
C. Write your answer in simplest form
Example: 2 3/4 - 1 1/4 =
1.03 Add & subtract fractions
4. How do I evaluate
expressions with
fractions?
4. A. Write the expression
B. Replace x with the given number
C. Subtract/Add the numerators
D. Keep the same denominator
E. Write your answer in simplest form
Example 1 : x = 5/8
x - 2/8
Example 2: x = 3/8
x + 1 1/8