Percents & Decimals



Percents & Decimals

Vocabulary

• __________________: Fractions with a denominator of 10 or any power of 10

• __________________: Expression consisting of a whole number and a decimal

• __________________: Represents the ratio of 2 quantities with the denominator being hundredths

• ___________________: The number obtained by finding the percent of another number

• __________________: Numerical expression of the relationship between 2 comparable quantities (i.e., usually the result of dividing the quantity by the second)

What are the seven main areas?

1.

2.

3.

4. Multiplying decimals

5. Rounding off decimals

6. Dividing decimals

7.

Decimals:

1. Reading and writing decimals and mixed decimal numbers

a. __________________ decimals representing tenths or hundredths.

b. _____________________ decimals representing tenths or hundredths

c. Reading and writing ______________; decimals represent tenths or hundredths

d. Reading decimals representing thousandths

e. Writing decimals representing thousandths

f. Reading and writing mixed decimals; decimals represent thousandths

2. Converting decimals to equivalent decimals

• Part A illustrates the rational behind adding zeroes by using equivalent fractions

• Teacher demonstrates that changing a fraction like 3/10 to 30/100 involves multiplying by a fraction equal to 1 (10/10) and therefore does not change the value of the original fraction

• Part B is ________________________________________________________________________________________________________________________

3. Adding and subtracting decimals

2 groups:

1. Problems in which each number in the problem has the_______ number of decimal places.

2. Comprised of those problems in which the addends or the minuend or subtrahend have different numbers of digits after the decimal point

4. Multiplying Decimals

– Teacher introduces the strategy for figuring out where the ___________ goes in the answer

– Teacher distributes worksheets with multiplication problems that have answers and leads students in determining where to place the decimal point

– What do you model next? ____________________________________

5. Rounding Off Decimals

– Students determine how many digits will appear ______ the decimal point when the number is rounded off

– Students count that number of digits and draw a line

– The students look at the numeral after the line. If it is 5 or more, ____________________________. If the number is less than 5, _______________________________.

6. Dividing Decimals

- What is the most difficult decimal operation?

1. Dividing a decimal or mixed decimal by a whole number

2. Dividing by a decimal or mixed decimal

7. Converting Fractions and Decimals

• To convert a fraction to a decimal what rule do you need to follow?

– Fractions that result in repeating decimals require rounding off

– Mixed number fractions are first converted into improper fractions before division occurs

• To convert a decimal to a fraction, students write the decimal as a decimal fraction and then reduce it to its lowest terms

Percents

Elementary Level:

List the two types of percentage problems:

1. Easier type:

• States a _____________________ and asks students to find the ______________________

• Teacher said that 80% was passing. There are 25 problems on the test. How many problems must I get to pass?

2. More difficult type:

• Requires the student to figure the percentage of ________________________ and then either add or subtract that amount from the original quantity

• Bill borrowed $500 from the bank. How must pay 8% interest on the loan. How much must he pay back to the bank?

Converting Percent to Decimal:

• Teacher presents the % sign and teaches student to read percent numbers

• Teacher demonstrates how a percent number can by written as a decimal number by _________________, deleting the ____________, and placing a decimal point so that there are 2 decimal places

Simple Percentage problems:

• Comprised of a quantity multiplied by a given percent and students must determine the percentage. Give an example:_________________________

• Students are taught the rules that will help them determine if their answers to subsequent problems are correct and how to predict the answers to some numerical problems

• The strategy for solving percentage problem is:

Simple Percentage Story Problems:

• State an amount and ask the student to determine a percentage

• Distinguishing characteristic of these problems is the inclusion of the word ___

1. Teachers begin by giving students simple equations where the word ___ is substituted for the times sign

2. Then, teacher introduced story problems, modeling and testing how to solve

3. Teacher then asks if the students multiplied by more or less than 100% and if the answer made sense

Complex Percentage Problems are problems that:

________________________________________________________________________________________________________________________________________________________________________________________________________________________

-Teacher models how to solve by computing the percentage increased or decreased (by converting the percent to a decimal and then multiplying). This amount is then _______ to the original amount to determine the new total.

-Special type of problem involves __________________________ (simple interest ~ elementary and compound interest in junior or senior high) ~ when you borrow money from a bank, you must pay back the bank extra money called interest

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