Transcript askrks - MathRulz.com

Order Of Operations
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Parentheses
Multiply or Divide
Addition or Subtraction
Start out using parentheses, then move on to
multiplication or division, then add or
subtract, and perform these actions in order.
Order of Operations (continued)
• 2(2+4)-10+5x2= 2(6)-10+5x2= 12-10+5x2=
12-10+10= 2+10= 12
• 3(5+2)+15= 3(7)+15= 21+15= 36
• 2(2+4)x6= 2(6)x6= 12x6= 72
Change Mixed Number to Improper
Fractions
• To change a mixed number to an improper
fraction you multiply the whole number times
the denominator plus the numerator. The
new number become the numerator, and
placed over the denominator.
• 5 2/3=17/3
• 3 2/3=11/3
• 2 25/2=29/2
Add Fractions and Mixed Numbers
• Convert the mixed numbers to improper
fractions then add them together.
• 2 2/3 + 3 3/5= 8/3+18/5= 26/8= 3 2/8
• ¾+ 2 6/7= 3/4+ 20/7= 23/11= 2 1/11
• 5 5/8+ 5 3/4= 45/8+ 23/4= 68/12= 5 8/12 11 3/8
Subtracting Fractions and Mixed
Numbers
• In order to subtract fractions, as in adding
fractions, the denominators must be the
same.
• ¼ + ¼ = 2/4 or simplified, ½
• However, when denominators are not the
same, they must be multiplied to the lowest
common denominator, or LCD
Subtracting Fractions and Mixed
Numbers
• ¼ - 1/5 = ?
• ¼ and 1/5 do not have the same denominator,
so you multiply to the lowest number they
both have in common. In this case, that
number is 20.
• 5/5 X ¼ = 5/20
• 4/4 X 1/5 = 4/20
Subtracting Fractions and Mixed
Numbers
• With our new numbers now having the same
denominator we can subtract them
• 5/20 – 4/20 = 1/20
• Also, if needed, you can reduce
Multiplying Fractions and Mixed
Numbers
• To multiply fractions, the simplest way is to
“cross simplify.” this means simplifying by the
opposite diagonal number. Then, you simply
multiply straight across. (numerator times
numerator, denominator times denominator
• Lets say or problem is 15/21 X 2 1/3 or 7/3
Multiplying Fractions and Mixed
Numbers
• 15/21 X 7/3 simplifies to 3/3 X 1/1
• Then you simply multiply across
• 3X1 = 3 and 3X1 = 3
• Turns out to 3/3 or 1
Dividing Fractions and Mixed Numbers
• To divide fractions and mixed numbers, you
follow the same steps as multiplying fractions
and mixed numbers, except that when you
multiply, you multiply one fraction by the
other’s reciprocal.
Dividing Fractions and Mixed Numbers
• You set it up the same as multiplying, except
that you take one of the fractions, and switch
the numerator and denominator.
• Then, you simplify, and multiply across
• Say our problem is 4 4/7 or 32/7
divided by 20/21
Dividing Fractions and Mixed Numbers
• First, you switch one of the fractions to it’s
reciprocal.
• For this problem lets switch 20/21
• 32/7 X 21/20
• This simplifies to 8/1 X 3/5
• Turns out to 24/5 or 4 4/5
Adding, Subtracting, Multiplying, and
Dividing fractions to solve problems
• A pitcher of lemonade contains 64 ounces of
lemonade. If you have 2½ pitchers left after a cookout,
how many ounces of lemonade do you have left?
2½ pitchers= 75 ounces
64 ounces=2 quarts
75 – 64
Answer: 11 ounces
Solving Problems using percents
• 12kg is what percentage of 32 kg?
– Divide the first number by the second (12  32)
– Multiply the answer by 100 (0.375  100)
– Round to the nearest unit (37.5)
– Add the percent sign to the end
Answer: 38 %
Examples
1) 75 is what percent of 300?
Answer:25%
2) 6 is what percent of 50?
Answer:12%
3) 7 is what percent of 280?
Answer:2.5%
Adding and Subtracting Signed
Numbers
1) EX: -24-(-13)
When two negatives are next to each other, you can
change them into one positive.
2) -24+13
3) Take 13 out of 24 then put on the negative to the
answer.
Answer:11
Examples
1) -53-(-17)
Answer:-36
2) 14-(-45)
Answer:59
3) -8+(-3)
Answer:-11
Multiplying and Dividing Signed
Numbers
Ex : 18  2
• Same signs: positive
• Different signs: negative
 2  18
Answer : 9
Examples
1)-9 14
Answer: -126
2) -32/(-8)
Answer: 4
3) -88  (-4)
Answer: 352