Math applications lesson 1: how to

solving for portion: 10% of mens paycheck of $1,000 goes for food. what portion is deducted for food?

$100= 1,000 x .10

Fraction Conversion: mixed to improper

(Whole number X denominator + numerator) Over old denominator 4 1/8 = (32+ 1)/ 8 = 33/8

Subtracting Whole Numbers

1. Arrange the whole numbers in rows with like place values in like columns. 2. Subtract in the ones place, regrouping if needed. 3. Subtract in the tens place, regrouping if needed. 4. Subtract in the hundreds place, regrouping if needed. 5. Keep moving through each place, regrouping if needed. "Regrouping" also known as borrowing is necessary to subtract a larger number from a smaller number.

Rounding percents

answer must be in percent to round id specific digit to right. if 5 or higher round up delete digits to right after ID number

Multiplying Decimals

Ignore the decimal point until the answer. Count the number of Decimal places in both factors. Use that number of decimal places to write the answer. 2.48 (2 places) x .018 (3 places 04454 (add 5 decimal places) = .4454

Adding unknown number from both sides of equation

L - 24= 40 L= 24 + 40 L= 64

adding decimals

Line up the decimal points and add normally (ex. 23.62+8.369=31.989)

Subtracting Decimals

Line up the decimal points and subtract normally (ex. 20.02-1.36=18.66)

Raising fractions to higher terms

Multiply numerator and denominator by same number. Does not change the fraction value 15/41 =?/410 = 150/410 410 divided 41 = 10 X 15= 150

multiplying proper fractions

Multiply numerators and denominators Reduce answer to lowest terms or use cancellation method. 4/7 x 7/9 = 4/1 x 1/9= 4/9 7's cancel out to one since they are the same and across each other.

Multiplying unknown number from both sides of equation

R/3= 15 (R/= divide) 3(R/3)= 15 (3's cancel out) R= 15/3 (3 moves to multiply by 15) R= 45

Dividing Fractions

To divide fractions, invert the second one and multiply 1/4 divided by 1/8= 1/4 x 8/1= 1/1 x 2/1= (4 and 8 get reduced since they multiply in to each other) 2/1= 2

Rounding Whole Numbers

To round whole numbers, first find the place value you want to round to (the rounding digit) and look at the digit directly to the right. If the digit is less than five, do not change the rounding digit and replace all #'s after the rounding digits with zeros. If the digit is greater than or equal to five, increase the rounding digit by 1 and replace all numbers after the rounding digit with zeros.

Prime numbers are

Whole numbers larger than 1 that are only divisable by 1 and itself and 1 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

subtracting like fractions

subtract the numerators and write over the denominators

converting percents to fractions

whole percent 1. drop percent symbol 2. multiply number by 1/100 3. reduce to lowest terms mixed decimal 1. drop percent 2. change mixed to improper 3. multiply number by 1/100 4. reduce to lowest terms

dividing mixed fractions

convert any mixed fraction to an improper fraction, and divide as usual (invert the second fraction and multiply) 1 1/2 divided by 1 5/8 3/2 divided by 13/8= 3/2 x 8/13 3/1 x 4/13= ( 2 and 8 get reduced since they multiply in to each other) 12/13

converting mixed number to decimals

convert fraction part of mixed number to decimal add converted fraction part to whole number 6 1/4= 1/4= .25 + 6= 6.25

Multiplying mixed numbers

1. Change the mixed number into an improper fraction by multiplying the denominator by the whole number. Then add the numerator in. Your denominator stays the same. 2. Multiply the numerators. 3. Multiply the denominators. 4. Simplify 1 1/8 x 2 5/8= 9/8 x 21/8= 189/64= 2 61/64

converting fractions to percents

1. divide numerator by denominator 2. move decimal point two places to right; add percent symbol.

solving for base: Assume Mel Spends $100 for food which is 10% of his pay check. What is Mels total pay check?

100/.10= 1,000

solving for rate: assume Mel spends $100 for food from his $1,000 pay check. What percent of his paycheck is spent on food?

100/1000= .10= 10%

Checkbook balancing: Beg, checkbook balance: $300 NSF: $50 Deposit in transit: $100 Outstanding check: $60 ATM service Charge: $ 20

300 +100= 400 400- 50= 350 350- 60= 290 290- 20= 270 balance

calculating percent increases: Stereo. $2,000 original price stereo, $2,500 new price.

500/2000= .25= 25% difference divided by original= percent

using parentheses in solving for unknown

6(A-5)= 12 6A-30= 12 (6 x in to A and 5) 6A= 12+30 6A= 42 A= 42/6 A= 7

Bank Balance: Balance: $632 Deposits in transit: $416 outstanding checks: $292

632+ 416= 1048 1048- 292= 756

combining like unknowns

6A + 2A= 64 6+2= 8 8A= 64 A= 64/8 A= 8

Dividing unknown number from both sides of equation

6B= 24 (number an dletter next to each other = x) B= 24/6 B= 4

Checkbook balancing: Beg. checkbook bal: $800 NSF: $40 Service charge: $4

800- 40= 760 760-4= 756 balance

multiplying whole numbers

Align multiplicand and multiplier at right Start right. And keep multiplying as you move to left. Move left through multiplier and continue multiplying multiplicand.

Adding whole numbers

Align numbers at the right Add units in column, if sim is more than 9, carry the tens digit. Live left, repeat step 2 until all are complete

Equation that uses subtraction and multiplication to solve unknown

B/3 + 6= B/3= 13- 6 3(B/3)= 7 B= 7x3 B= 21

Subtracting unknown number from both sides of equation:

D + 10= 12 D= 12- 10 D= 2

Fraction Conversion: improper to mixed

Divide numerator by denominator; place remainder over old denominator 17/4= 4 1/4

Step approach for finding greatest common denominator.

Divide small number of fraction into larger number Divide remainder into divisor of step 1. Continue until there is no remainder. The last divisor used is the greatest common divisor. 15/65 15 divided by 65= 4 R5 5 divided by 15= 3 R0 Greatest common divisor is 5

convert fraction to percent

Divide the numerator by the denominator, multiply by 100 and add a percent sign.

convert percent to fraction

Drop the percent sign and write the value of the number as the numerator. Place it over a denominator of 100 and reduce.

Adding unlike fractions

Find LCD and add

Subtracting Unlike Fractions

Find LCD and subtract

Subtracting Mixed Numbers

You may have to borrow from the whole number, just like you sometimes borrow from the next column when subtracting ordinary numbers. Example: 4 1/6 - 2 5/6 = ? 4 1/6 - 2 5/6 = 3 7/6 - 2 5/6 = 1 2/6 = 1 1/3 To subtract a mixed number from a whole number, you have to borrow from the whole number. Example: 6 - 3 1/5 = ? 6 - 3 1/5 = 5 5/5 - 3 1/5 = 2 4/5

improper fraction

a fraction whose numerator is larger than the denominator

Proper fractions

a fraction whose numerator is smaller than the denominater

Rounding all the way

a process of rounding the number to the first digit

mixed fraction

a whole number and a fraction

adding like fractions

add numerators and write over the denominators

rounding percents

answer must be in percent before rounding. ID specific digit. if digit to right is 5 or greater round up delete digits to right of ID digit.

LCD by prime numbers

copy denominators and arrange in a separate row Divide denominators by smallest prime that will divide evenly into at least two numbers. Continue until no prime number divides evenly into at least two numbers Multiply all the numbers in the divisors last row to find LCD Raise fractions so each has a common denominator and complete computation.

converting decimal fractions to fractions

decimal fraction has a denominator with multiples of 10. count number of 0's in denominator zeros show how many places are in the decimal. 8/1,000 = .008 6/10,000= .0006

reducing fractions to the lowest terms

divide both the numerator and the denominator by the largest whole number that will go evenly into them both 18/46= (18/2)/(46/2)= 9/23

converting proper fractions to decimals

divide numerator of fraction by denominator round as necessary 1/3 (nearest tenth)= .3

converting percents to decimals

drop the % sign and put the number over 100 & simplify or drop the sign and move the decimal two places to the left .89%= .0089 95%= .95 for fractional percents: convert decimal by dividing numerator by denominator. round if necessary mixed fraction percent, convert fractional percent first. combine whole number and fractional percent drop percent symbol, move decimal point two places to left. 8 3/4%

adding mixed fractions

first add the whole numbers, then add the fractions (apply common denominators if needed) 1 4/7 + 1 3/7 4/7 + 3/7= 7/7 1+1=2 2 7/7= 3

Rounding Decimals

identify place value of digit you want to round if digit to right of chosen digit is 5 or more increase identified digit by 1. if less than 5 leave chosen digit drop all digits to right of chosen digit

dividing if the divisor is a decimal

make divisor a whole number by moving decimal point to right move decimal point in dividend to right same number of places as in the first step place decimal point in quotient above decimal point in dividend. dived as normal 41.39 divided by 2.9 2.9 (move decimal to end ) & 413.9 (move decimal 1 place as in first number) 413.9 divided by 29 = 14.3

dividing decimals by whole numbers

move decimal straight up to put in the quotient-then divide

converting decimals to percents

moving the decimal two places to the right and adding % sign.

Converting decimals to percents

moving the decimal two places to the right and adding % sign. .81= 81% .008= 00.8= .8% 4.15= 415.00= 415%

Dividing whole numbers

partitioning the dividend into an equal number of groups or into groups of equal size that are equivalent to the divisor.

converting pure and mixed decimals to decimal fractions.

place digits to right of decimal point in numerator of fraction (.984) move decimal 3 places (984) put 1 in denominator (984/1) add zeros to denominator, depending on decimal places of original number. (984/1000)