ESL Math

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