Math Chapter 5 & 6

Rates Key Words

"for every" or "per" means 1 unit Write both units in the answer Ex: 60oz/3000 sq feet

Write ratios as fractions

1st number goes on top 2nd number goes on bottom Ex: 1 to 7 = 1/7 Note: you can have fractions or decimals as either the numberator or the denominator

. 66666666666 (repeating) to a fraction

Memorize: (because the calculator will give you a syntax error) .6666666666 ect = 2/3

Percents to Decimals

Move the decimal two places to the left and drop the % symbol.

Decimals to Percents

Move the decimal two places to the right and add the % symbol

Changing to Percents and Fractions When the Decimal Repeats

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Find Fraction Notation When Decimal Repeats

1) Change to an improper fraction (65 2/1% = 65 + 2/11 The 2/11 = 181818 etc.) 2) Change to an improper fraction (multiply denominator by the whole number, add the numberator, and put it over the original denominator (65 2/11 = 717 / 11) 3) Remove the % by multiplying byt 1/100 (171/11% = 171/11 x 1/100 = 717 / 1100) 4) Simplify if possible - use the calculator

Fraction to Percent Method 1 (change to a decimal first)

1) Multiply the fraction by 100 (don't enter the % symbol) to get a fraction 2) Hit 2nd, PRB, = to change it to a decimal 3) Write the % symbol

Fraction to Percent Method 2 (change to a decimal first)

1) Turn the fraction into a decimal number by dividing the numerator by the denominator 2) Move the decimal point two places to the right 3) Add the % symbol

Percent to Fraction

1) Write the percent over 100 (75%=75/100) Drop the %. 2) Reduce as needed OR use the calculator: type in the percent using the 2nd, (/%, = keys to get a decimal. Use 2nd, PRB, = to get a fraction.

Ratio Rules

1) no decimals allowed in a ratio 2) no mixed numbers allowed in a ratio 3) all proper fractions must be in reduced form 4) no units in ratios So even though 3/2 = 1 1/2 we still use 3/2

Finding Missing Numbers in Proportions

1) write the equasion (x/30 = 2/3) 2) Simplify by cross multiplying 3) Divide that product by the remaining number (the one with the variable letter) 4) Write the answer Note: When the answer is a repeating deciamal, always express it as a fraction by hitting 2nd PBR

Proportion

A proportion is two equal ratios (which is the same as two equal fractions) Ex: 5/6=10/12 means five is to six as ten is to twenty)

Similar Shapes

Choose a side from the first shape (ex: A) and put it over the corresponding side from the second triangle (ex: D) Repeat with another side. Cross multiply to solve. If you must find two variables, solve for one at a time.

Determine If You Have a Proportion

Cross multiply. If the numbers are the same you have a proportion.

Ratios in Simplest Form (Decimals)

Decimals in ratios: divide the numerator by the denominator to get a decimal. Hit 2nd PRB to change it to a fraction. If you get a mixed numeral, hit 2nd Ab/c to change it to an improper fraction (because there should be no mixed numbers in ratios)

Fractions to Decimals

Enter the numerator divided by the denominator (use the division key). Use 2nd, PRB, = to

To find percent notation from a fraction

First turn it into a decimal. Divide the top number by the bottom one. Move the decimal point two places to the right. Add the % symbol. Does the answer look reasonable?

Proportion Word Problems

In proportion word problems the proportion is always given to you. Key words are "corresponds to" and "for every" Identify the two things being compared. 1) Write a ratio (fraction) with words taht describe the things being compared. 2) Set up the ratio that is given 3) Make a proportion using a variable and the other "given" piece of information 4) Solve for the variable 5) Write the answer, including units!

.333333333333 (repeating) to a fraction

Memorize (because the calculator will give you a syntax error) .3333333333 etc = 1/3

Percent

Percent = Per (for every) Cent (100)

Writing Proportions

Proportions must include units for the numerator and the denominator - abbreviations are okay Ex: 12 rubies / 6 diamonds

Ratio vs Rate

Ratio compares like quantitites Rate compares different quantities.

Solving Percent Problems with Proportions

Set up like this: part / whole = % / 100 To translate problems, circle the %. Find the number that goes with the word "is" and put this on top (this is the part). Find the word that goes with "of" and put that on the bottom (this is the whole) If the question has the % symbol in it, you do not have to write it in your answer, however, if it does not have a % symbol in it, you do have to write it in the answer.

Unit Pricing

To determine the unit price divide the cost/item using the divide key. (Do not enter as a fraction) Include the units in the answer and round to the thousandths place (3 places to the right of the decimal)

To find a fraction notation from a percent

Use Calculator. Enter number, 2nd, PRB, = to get a deciaml. Then enter 2nd, PRB, = again to get the fraction.

Ratios in Simplest Form (Fractions)

Use the Ab/c key to enter the first fraction (numerator), use the divide key (in between) then use the Ab/c key to enter teh second fraction (denominator). If you get a mixed numeral, hit 2nd Ab/c to change it to an improper fraction (because there should be no mixed numbers in ratios)

Ratios in Simplest Form (Whole Numbers)

Whole numbers: enter as a fraction, then hit = If you get a whole number, change it to a fraction by putting it over 1 (Ex: 4 = 4/1)