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# Basic Math DSPM 0700

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This 17 page Class Notes was uploaded by Sigrid Yost DDS on Tuesday October 20, 2015. The Class Notes belongs to DSPM 0700 at Southwest Tennessee Community College taught by Sheldon Dan in Fall. Since its upload, it has received 71 views. For similar materials see /class/225513/dspm-0700-southwest-tennessee-community-college in Mathematics Education at Southwest Tennessee Community College.

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Date Created: 10/20/15

Name DSPM 0700 CHAPTER 1 REVIEW NOTE Calculations are to be done BY HAND Write the following fractions using decimals The numerator will be the number digits in the decimal The denominator represents the number of decimal places in the decimal 25 1 10 35 1 000 0035 3 Estimate the following sum by rounding to thousands Then find the exact sum and check by adding in reverse order 42387 2954 2768 9735 Make sure that your estimates are to the accuracy desired in this case number of thousands Estimate Actual Check 42 000 42 387 9 735 3000 2954 2768 3000 2768 2954 10000 9735 42387 58000 57844 57844 4 Estimate the following sum by rounding to tenths Then find the exact sum and check by adding in reverse order 31441 297958 164310 Estimate Actual Check 3144 314410 164310 2980 297958 297958 1643 164310 314410 7767 776678 776678 5 Estimate the following difference by rounding to thousands Then find the actual difference and check by addition 48006 7 3215 The check is difference number subtracted number at start Estimate Actual Check 48000 48006 44 791 3000 3215 3215 45000 44791 48006 6 Estimate the following difference by rounding to the nearest whole number Then find the actual difference and check by addition 27401 7 14688 Estimate Actual Check 274 27401 12713 147 14688 14688 127 12713 27401 7 Multiply the following and check by multiplying in reverse order 237 X 702 Actual Check 237 702 x 237 474 4914 M 21060 166374 w 166374 8 Multiply 4124 X 0014 The number of decimal places in the product is the sum of the number of decimal places in the factors 4124 X 0014 16496 41240 057736 9 I am making copies for class One set is 304 copies ofa 4page document a second set is 124 copies ofa 3page document and a third set is 115 copies ofa 3page document How many sheets are used The number of sheets used in each document is the product of the number of copies and the number of pages per copy Then the products are added toge ther 304x 4124gtlt3115 X 3 1216372345 1933 sheets 10 Divide the following If a whole number division results in a remainder show the remainder Then check by multiplication 2342 21 The check is quotient gtlt divisor remainder dividend Actual Check 111 212342 111R11 111 21 X 21 7 111 21 2220 32 2331 21 11 11 2342 11 Divide 3325 25 Eliminate the decimal point in the divisor by moving it to the right Move the decimal point in the dividend the same number of places adding zeros if necessary 25 3325 changes to 25 L 82 E 7 5 E 0 12 Find the average ofthe following salaries 35307 25995 21204 42890 31903 You may use the calculator to nd the sum then show the division Round your answer to the nearest dollar 35307 25995 21 204 42 890 31903 157 299 5 5 3145980 The average salary is about 31460 13 Express 273 as a multiplication then compute the value A power is using a number as a factor a given number of times given by the exponent 273 27gtlt27gtlt27 19683 14 Evaluate l7 4 The square root of a number is the number multiplied by itself to give the original number 4784 28 Multiply or divide using the shortcut procedure To multiply by a power of 10 move the decimal point to the right the number of places represented by the number of zeros in the power of 10 To divide by a power of 10 move the decimal point to the left 15 360 000 1 000 000 360 000 1 000 000 360000 036 16 57 X 1000 57 X 1000 5700 Use order of operations to evaluate the following Make sure you show each step as you evaluate 17 3 25 JE 52 3 25 J1 6 52 81324 25 Powers and roots 81 8 25 Division 89 25 Addition is leftmost 64 Subtractionlast operation 18 40 10212 40 102 1 2 40 103 2 Operation in parentheses 40 30 2 Implied multiplication 40 15 Division 25 Subtraction Use the following formulas for problems 1920 Show the formula you used and include the correct units in the answer Perimeter is the distance around a gure Area is the amount of space within the borders of a figure Volume is the amount of space within a threedimensional figure Square P 4s A sz Rectangle P 21 2w 2l w A W Parallelogram P 2b 2s 2b s A bh Name DSPM 0700 CHAPTER 2 REVIEW 1 Find the least common multiple and the greatest common factor of 25 30 and 40 The least common multiple LCM is the smallest number that is a multiple of all the numbers The greatest common factor GCF is the largest number that is a factor of all the numbers You can find the prime factorization of all of the numbers The LCM will have the primes that appear in at least one line raised to the highest power in any one line The GCF will have the primes that appear in all the lines raised to the lowest power in any one line or 1 if there are no common primes 2552 302gtlt3gtlt5 4023gtlt5 The LCM must have some 2 s 3 s and 5 s It needs three 2 s from 40 one 3 from 30 and two 5 s from 25 The GCF will have only 5 s since no 2 s and 3 s appear in 25 and there is only one 5 in 30 and 40 LCM23gtlt3gtlt52 600 GCF5 3 2 Find the equ1valent fraction With the given denom1nator Z E To find an equivalent fraction with a larger denominator find the factor the given denominator is multiplied by to get the desired denominator Multiply the numerator by that factor 3gtlt5l5 4gtlt5 20 2 4 48 3 Reduce to lowest terms To find an equivalent fraction with a smaller denominator find the factor the given denominator is divided by to get the desired denominator and divide the numerator A fraction is in lowest terms if there is no common factor other than 1 Therefore use the GCF to reduce to lowest terms 48481 96 96482 Change the following to a mixed number equivalent in lowest terms To change an improper fraction to a mixed number divide numerator by denominator The whole number part is the quotient the remainder is the numerator and the original denominator is the denominator 4 e 16 a 3 l6 l6 5 E 25 n i 25 25 z 31 5 7 6 Change 3g to an improper fractlon To change a mixed number to an improper fraction multiply the whole number by the denominator add the numerator and place the result over the denominator 3123x87 8 8 31 7 Change 25 to an improper fraction with a denominator of 14 Simply multiply the whole number by the desired denominator and place the result over the denominator 2525gtltl4 14 E 14 8 Change 4275 to a fraction in lowest terms Change the decimal part to a fraction with a powerof 10 denominator 4275 4 275 1000 42 40 Change the following fractions to decimals If a decimal is a repeating decimal use the bar or ellipsis notation to describe it DiVide the numerator by the denominator Add zeros until the decimal terminates or there is a repeating block 7 39 12 058333 7 12W 5 0583 g 1 00 058333 i 40 J 40 10 13 16 You can change i to a decimal if there is a mixed number 03125 16 50000 1113125 16 E 11 Determine the larger of g and Show the change to common denominators iz ilti 9 99 9 11 5 45 12 Place these fractions and decimals in order from smallest to largest by changing fractions to decimals 12 167 12 1666 121666 12166612167 3 5 3 167167 1216 5 16661666 13 Add 31i 2 5 Find common denominators if necessary and if mixed numbers add whole number parts and fractions separately Regroup if fractions add to an improper fraction 33 10 i 10 E 41 10 10 3 VIIl NID I 14 The studs of an outside wall are 5 in thick The inside wallboard is g in thick and the outside covering is 2 in thick What is the total thickness of the wall 51 i 2 16 L n 8 16 2E 2E l6 l6 29i1n l6 16 15 Subtract 3 1 12 30 Find a common denominator If mixed numbers subtract whole number parts and fractions separately If fractions cannot subtract regroup one unit from whole number part and include that in fraction part so that you can subtract 525 5 5 714 5 5 11 5 16 A fence board is 96 in long 2 in is cut off The saw blade takes off an additional in How long is the nished board 232E 96 95 4 8 8 l l 21 21 8 8 8 8 21 931 in 8 8 Multiply the following fractions If necessary change improper fractions to mixed numbers in lowest terms Generally fractions are multiplied by multiplying numerators multiplying denominators and simplifying If mixed numbers change to improper fractions 172gtlt43 7 3 2 22X422X 7 3 j 3 1 3 2123 3 18in 8 14 Name DSPM 0700 CHAPTER 2 REVIEW 1 Find the least common multiple and the greatest common factor of 25 30 and 40 The least common multiple LCM is the smallest number that is a multiple of all the numbers The greatest common factor GCF is the largest number that is a factor of all the numbers You can find the prime factorization of all of the numbers The LCM will have the primes that appear in at least one line raised to the highest power in any one line The GCF will have the primes that appear in all the lines raised to the lowest power in any one line or 1 if there are no common primes 2552 302gtlt3gtlt5 4023gtlt5 The LCM must have some 2 s 3 s and 5 s It needs three 2 s from 40 one 3 from 30 and two 5 s from 25 The GCF will have only 5 s since no 2 s and 3 s appear in 25 and there is only one 5 in 30 and 40 LCM23gtlt3gtlt52 600 GCF5 3 2 Find the equ1valent fraction With the given denom1nator Z E To find an equivalent fraction with a larger denominator find the factor the given denominator is multiplied by to get the desired denominator Multiply the numerator by that factor 3gtlt5l5 4gtlt5 20 2 4 48 3 Reduce to lowest terms To find an equivalent fraction with a smaller denominator find the factor the given denominator is divided by to get the desired denominator and divide the numerator A fraction is in lowest terms if there is no common factor other than 1 Therefore use the GCF to reduce to lowest terms 48481 96 96482 Change the following to a mixed number equivalent in lowest terms To change an improper fraction to a mixed number divide numerator by denominator The whole number part is the quotient the remainder is the numerator and the original denominator is the denominator 4 e 16 a 3 l6 l6 5 E 25 n i 25 25 z 31 5 7 6 Change 3g to an improper fractlon To change a mixed number to an improper fraction multiply the whole number by the denominator add the numerator and place the result over the denominator 3123x87 8 8 31 7 Change 25 to an improper fraction with a denominator of 14 Simply multiply the whole number by the desired denominator and place the result over the denominator 2525gtltl4 14 E 14 8 Change 4275 to a fraction in lowest terms Change the decimal part to a fraction with a powerof 10 denominator 4275 4 275 1000 42 40 Change the following fractions to decimals If a decimal is a repeating decimal use the bar or ellipsis notation to describe it DiVide the numerator by the denominator Add zeros until the decimal terminates or there is a repeating block 7 39 12 058333 7 12W 5 0583 g 1 00 058333 i 40 J 40 10 13 16 You can change i to a decimal if there is a mixed number 03125 16 50000 1113125 16 E 11 Determine the larger of g and Show the change to common denominators iz ilti 9 99 9 11 5 45 12 Place these fractions and decimals in order from smallest to largest by changing fractions to decimals 12 167 12 1666 121666 12166612167 3 5 3 167167 1216 5 16661666 13 Add 31i 2 5 Find common denominators if necessary and if mixed numbers add whole number parts and fractions separately Regroup if fractions add to an improper fraction 33 10 i 10 E 41 10 10 3 VIIl NID I 14 The studs of an outside wall are 5 in thick The inside wallboard is g in thick and the outside covering is 2 in thick What is the total thickness of the wall 51 i 2 16 L n 8 16 2E 2E l6 l6 29i1n l6 16 15 Subtract 3 1 12 30 Find a common denominator If mixed numbers subtract whole number parts and fractions separately If fractions cannot subtract regroup one unit from whole number part and include that in fraction part so that you can subtract 525 5 5 714 5 5 11 5 16 A fence board is 96 in long 2 in is cut off The saw blade takes off an additional in How long is the nished board 232E 96 95 4 8 8 l l 21 21 8 8 8 8 21 931 in 8 8 Multiply the following fractions If necessary change improper fractions to mixed numbers in lowest terms Generally fractions are multiplied by multiplying numerators multiplying denominators and simplifying If mixed numbers change to improper fractions 172gtlt43 7 3 2 22X422X 7 3 j 3 1 3 2123 3 18in 8 14

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