Math in English…
without calculators!!!
Order of OperationsOrden de operaciones
OperationsHow do we read these?
17+24
45-32 25÷5
6×4plus
minus
times
divided by
OperationsWhat are these?
𝑥𝑦
(6+8)×3 43parentheses exponent
Order of OperationsOperation How to ReadParentheses -------------------
Exponents To the power of
Multiplication × or · Times; multiplied by
Division ÷ or / Divided by
Addition + Plus
Subtraction - Minus
Fractionsfracciónes
Fractions
45
numerator denominator
FractionsCan you say these?
A half
Two quarters
A wholeOrOne
A thirdEight ninths
Four sevenths
Mixed Fractions
• One AND seven eighths
• 4 • Four AND a half
Improper Fractionsnumerator > denominator• 9/4
• 10/3
• 7/6
• 12/5
Mixed ↔ Improper
• Can you write these?• Three halves• One and one half
Mixed ↔ Improper• Multiply the whole
number and the denominator.
• Add the numerator.• The denominator
stays the same.
*Practice on board*
• Divide the numerator by the denominator.
• The quotient(answer) is the new whole number.
• The remainder is the new numerator.
• The denominator stays the same.
Example ⇨
5 132 R 3
-103
2 35
⇨
5×2+3
135
Adding/Subtracting Fractions
1. No whole numbers! Change mixed fractions to improper fractions.
2. Are the denominators the same?1. If YES, read step 5.2. If NO, read step 3.
3. For denominators that are not the same, find the Least Common Denominator (LCD).
4. Don’t forget! If you do anything to the denominator, do the same thing to the numerator.
5. Add numerators. Keep denominators the same.6. Simply. Use the Greatest Common Factor
(GFC).
Example1 12 +
56 ≠
Multiples2 64 126 188 2410 30
96 +56=
146
73 𝑜𝑟 2
13
32 +56
×3
×3
×1
×1
Factors
14
7 2
6
3 2
÷2
÷2
SimplifyGCF
LCD
Multiplying Fractions• This is easy!
• Change mixed fractions to improper fractions.
• Multiply straight across.o Multiply numerators.o Multipy denominators.
Example
97×
45¿3635
Dividing Fractions• This is similar to multiplication.
• Change mixed fractions to improper fractions.
• Invert(switch) the numerator and denominator.
• Multiply straight across.o Multiply numerators.o Multiply denominators.
Example
97׿
3635
45
Place Valuesvalores de lugar
Place Values• Place values tell you how much a digit is worth in
a number. Let’s look at the difference between numbers and digits.
• 256 is a number.o How many digits are there?
• 7,945 is a number.o How many digits are there?
Place Values
43
7
0 00
HundredsTensOnes
Place Values
Millions
--
Hundred
thousands
--
Ten thousands-
-
Thousands
--
Hundreds
--Tens--
Ones--
Decim
al Point--
Tenths
--
Hundredths--
Thousandths--
Ten-
thousandths--
Hundre
d-thousandths--
1 2 3 4 5 6 7 8 9 0 1 2
DecimalsDecimales
Decimals• Decimals are the digits on the right side of the
decimal point.
• 123,456,789 is a whole number.
• .123456789 is a decimal.
• 123,456,789 .123456789 is a combination of a whole number and a decimal.
Fractions ↔ Decimals
• Fractions ARE LIKE decimals!!
Fractions ↔ Decimals• Let’s try with money.• (one fourth) of a dollar is ____?
o $0.25 (twenty five cents, but written as point twenty five dollars)
• What is as a decimal?
o .75
Fractions ↔ DecimalsFrom Fractions to Decimals
• Start with .• Use long division
and divide.• = .75
(three fourths equals point seven five)34
00
-03 0
7
-2 82
0
0
5
00- 2
Fractions ↔ Decimals.5
.3333333333 and keeps going
.6666666666 and keeps going.25.5.75.2.4.6.8
Fractions ↔ Decimals.125
.25
.375
.5
.625
.75
.875
.1
.2
.3
.4
.5
.6
.7
.8
.9
Percentagesporcentajes
Percentages %• Decimals become percentages!!
3 7 9
5 8 2
1
%
%
0 0 %
Thirty-seven point nine percent
Fifty-eight point two percent
One hundred percent
Fractions ↔ Decimals ↔ Percents.5 50%
.3333333333 and keeps going ≈33%
.6666666666 and keeps going ≈67%
.25 25%.5 50%.75 75%.2 20%.4 40%.6 60%.8 80%
Fractions ↔ Decimals ↔ Percents.125 12.5%
.25 25%
.375 37.5%
.5 50%
.625 62.5%
.75 75%
.875 87.5%
.1 10%
.2 20%
.3 30%
.4 40%
.5 50%
.6 60%
.7 70%
.8 80%
.9 90%
Exponentsexponentes
Exponentsexponent
base535×5×5=125
ExponentsMatch the values!
• 1• 49• 32• 81• 9
Exponents• All numbers to the power of zero (0) equals one
(1). , if x≠0
• All numbers to the power of one (1) equals the number.
Equationsecuaciones
Try these. They start easy and become hard.
1) x–19 = 72) 18+y =
133) 6x = 124) 4 = 40x5) X÷5 = 66) 12÷x = 3
A. -5
B. 30C. 2D. 4E. 26
RulesYou see… You do…
+ -- +× ÷÷ ×
opposites
RulesAdd or Subtract?
x + y x + y addx + (-y) x – y subtractx – (-y) x + y add
Negative or Positive?x·yx÷y
two positives! positive
(-x)·y or x·(-y) (–x)÷y or x÷(-y)
one positive…one negative…
negative
(-x)·(-y)(-x)÷(-y)
two negatives! positive