Introduction to Fractions and Mixed Numbers

Transcription

1 Name Date Intrductin t Fractins and Mixed Numbers Please read the Learn prtin f this lessn while cmpleting this handut. The parts f a fractin are (shwn belw): 5 8 Fractins are used t indicate f a whle. Use the picture belw t write a fractin representing the shaded prtin f the shape: The fractin 2 7 represents f equal parts. Whle numbers can be thught f as fractins with a denminatr f. Fractin ntatin represents the peratin f. There are tw rules t keep in mind when wrking with the value f zer in a fractin: Fr any nnzer value, b, 0 b = 0. An example f this wuld be 0 4 = 0. Fr any value f a, 0 a = undefined. An example f this wuld be 6 0 = undefined. Steps t multiply fractins: 1. Multiply the. 4.R.1 Intrductin t Fractins and Mixed Numbers Hawkes Learning

2 2. Multiply the. Multiply the fllwing fractin: = = T find an equivalent fractin, yu need t the numeratr and the denminatr by the nnzer whle number. Find an equivalent fractin fr 2 3 = by multiplying bth the numeratr and the denminatr by 5. There are tw steps t reducing fractins t lwest terms: 1. Factr the and int prime factrs. 2. Use the fact that k = 1 and divide ut all f the factrs. k What is the cmmn factr that can be divided ut f the fractin, 4 12? What is 4 12 in lwest terms? A mixed number is the sum f a and a fractin. T change a mixed number t an imprper fractin, yu need t: Change 1. Multiply the whle number by the f the prper fractin. 2. Add the f the prper fractin t this prduct. 3. Write this ver the denminatr f the fractin t an imprper fractin: Multiply the whle number by the denminatr: Add the numeratr t the prduct frm abve: Write this sum ver the denminatr: = + = 24 Hawkes Learning R.1 Intrductin t Fractins and Mixed Numbers

3 Name Date Intrductin t Decimal Numbers Please read the Learn prtin f this lessn while cmpleting this handut. Decimal ntatin uses a system and a pint, with whle numbers written t the and fractins written t the f the decimal pint. T read r write a decimal number: (r write) the whle number. Read (r write) the wrd in place f the decimal pint. Read (r write) the part as a whle number. Then name the fractin with the name f the last n the right. Add th t the end f the fractin place value. Remember that if there is nt a whle number, yu can put a t the left f the decimal pint. Write the fllwing mixed number as a decimal number: =. and it wuld be read as AND When writing seventeen and 5 thusandths in decimal ntatin yu wuld have hlders in the tenths and hundredths place values. It wuld lk like When cmparing decimals: Mving t, cmpare digits with the same value. 4.R.2 Intrductin t Decimals Hawkes Learning

4 When ne cmpared digit is larger, the is larger. Cmpare the fllwing values: Ntice that the numbers are lined up, fr easier cmparisn When mving frm left t right, the digits are the same until the place values. Thse are ging t be used t cmpare. Since the 8 is a larger value than 5, is a larger value. Rules fr runding decimals: Lk at the digit t the f the place f desired accuracy. If this digit is 5 r, make the digit in the desired place f accuracy ne larger and replace all digits t the right with zers. All digits t the left remain unchanged unless a 9 is made ne larger. This effectively changes the 9 t 10 which means the next digit t the left must be increased by 1. If this digit is than 5, leave the digit in the desired place f accuracy as it is and replace all digits t the right with zers. All digits t the left remain unchanged. Zers t the right f the place f accuracy and t the right f the decimal pint must be. In this way the place f accuracy is clearly understd. If a runded number has a 0 in the desired place f accuracy, then that 0 remains. Rund t the nearest hundredth. The digit in the hundredths is. The digit in the place value t the right f the hundredths is. Since that digit is greater than 5, the 6 in the hundredths place value changes t a 7. The runded value is. 26 Hawkes Learning R.2 Intrductin t Decimals

5 Name Date Decimals and Percents Please read the Learn prtin f this lessn while cmpleting this handut. The wrd percent cmes frm the Latin per centum, meaning per. Percent means, r the rati f a number t 100. The symbl is called the percent sign. This sign has the same meaning as the Changing fractins with denminatrs f 100 t percents: 25 Example: 100 = 25% The did nt change. 3.8 Example: 100 = 3.8% The is nt changed, the decimal pint desn t mve if the is 100. T change a decimal t a percent: 1. Mve the decimal pint t places t the. 2. Write the sign. Example: 0.56 = 56% Example: = 34.5% Example: 0.02 = 2% T change percents t a decimal number: 1. Mve the decimal tw places t the. 2. Delete the sign. 4.R.3 Decimals and Percents Hawkes Learning

6 Example: 97% = 0.97 Example: 68.5% = Example: 0.64% = Hawkes Learning R.3 Decimals & Percents

7 Name Date Fractins and Percents Please read the Learn prtin f this lessn while cmpleting this handut. If a fractin has denminatr, it can be changed t a percent by writing the and adding the sign. If the denminatr is a factr f (2, 4, 5, 10, 20, 25, r 50), the fractin can be changed t an equivalent fractin with denminatr f and then changed t a percent. When fractins d NOT have factrs f 100 as denminatrs yu will need t: Change the fractin t decimal frm by, either by lng divisin r with a calculatr (depending n instructins frm instructr). Mve the decimal tw places the and write the symbl. Example: 3 = 43= 0.75 = 75% 4 Helpful calculatin tips: The numeratr ges the divisin symbl and the denminatr ges f the divisin symbl. If yu are using a calculatr, yu will type the numeratr, then the divisin symbl, and then the, fllwed by enter/equal. T change a percent t a fractin r a mixed number: Write the percent as a fractin with 100 as the and drp the symbl. the fractin, if pssible. 4.R.4 Fractins and Percents Hawkes Learning

8 Example: 80% = = = Hawkes Learning R.4 Fractins and Percents

9 Name Date Slving Percent Prblems by Using Prprtins: P/100 = A/B Please read the Learn prtin f this lessn while cmpleting this handut. The prcess f divisin with decimal numbers is similar t divisin with whle numbers. With whle numbers, we are cncerned with the but with decimal numbers, we are cncerned with the in the qutient. T divide decimal numbers: Mve the decimal pint in the divisr t the s that the divisr is a whle number. Mve the decimal pint in the dividend the number f places t the right. Place the decimal pint in the qutient directly the new decimal pint in the dividend. Divide just as with numbers. (0 s may be added as needed t the dividend.) What t d if the remainder is nt 0: Decide first hw many are t be in the qutient. Divide until the is ne digit past the place f desired accuracy. Using this last digit, rund the t the desired place f accuracy. Types f decimals: Is eventually 0, the decimal number is said t be. Example: 3.5 If the remainder is nt eventually 0, the decimal number is said t be. 4.R.5 Slving Percent Prblems by Using Prprtins: P/100 = A/B Hawkes Learning

10 Example: T divide a decimal number by a pwer f 10: Cunt the number f s in the pwer f 10. Mve the decimal pint t the the number f places equal t the number f 0s. Mental Math Quick Tips: Divisin by 10 mves the decimal pint place t the left. Divisin by 100 mves the decimal pint places t the left. Divisin by 1000 mves the decimal pint places t the left. And the pattern keeps ging. In rder t estimate with divisin, bth the divisr and the dividend t the place f the last nnzer digit n the left and then with these runded values. 32 Hawkes Learning R.5 Slving Percent Prblems by Using Prprtins: P/100 = A/B