UNIT 4 PRACTICE PROBLEMS

Transcription

1 UNIT 4 PRACTICE PROBLEMS 1 Determine the fraction represented by the area shaded pink using the given unit Unit Fraction 2 Determine the fraction represented by the shaded area using the given unit Unit Fraction 1

2 Represent the unit fraction 1 8 using each of the representations below a) Number line b) Area models Use the unit labeled in the second row of the table c) Discrete objects 2

3 4 Represent the unit fraction 1 using each of the representations below a) Number line b) Area models Use the unit labeled in the second row of the table c) Discrete objects

4 Represent the unit fraction 8 using each of the representations below a) Number line b) Area models Use the unit labeled in the second row of the table c) Discrete objects 4

5 6 Represent the unit fraction a) Number line 6 using each of the representations below b) Area models Use the unit labeled in the second row of the table c) Discrete objects 7 Plot the following fractions on the number line 1,, 1, Label your points Plot the following improper fractions on the number line,,,, Label your points

6 9 Represent the composite fractions using an area model A single rectangle is the unit An additional rectangle is given in each problem for the fractions which may require it a) Represent 8 with a rectangle as the unit copies of (unit fraction) b) Represent 8 with a rectangle as the unit copies of (unit fraction) 10 Represent the composite fractions using the discrete objects The unit is all of the stars in the rectangle a) Represent 6 of the stars copies of (unit fraction) b) Represent 4 of the stars copies of (unit fraction) 6

7 11 Represent unit) Unit 4 Practice Problems with a rectangle as the unit Then rewrite it as a mixed number (A single rectangle is the Mixed Number: 12 Represent on the number line Then rewrite it as a mixed number Mixed Number: 1 Represent 7 4 on the number line Then rewrite it as a mixed number Mixed Number: 14 Represent of the stars Then rewrite it as a mixed number Mixed Number: 7

8 1 Represent 1 with a rectangle as the unit Then rewrite it as an improper fraction (A single rectangle 8 is the unit) Improper fraction: 16 Represent 2 4 on the number line Then rewrite it as an improper fraction Improper fraction: 17 Represent 1 1 on the number line Then rewrite it as an improper fraction Improper fraction: 18 Represent of the stars Then rewrite it as an improper fraction Improper fraction: 8

9 19 Use the image below to answer the following questions The unit is one circle a) Determine the improper fraction that represents the shaded portion of the circles b) Determine the mixed number that represents the shaded portion of the circles 20 Use the image below to answer the following questions The unit is one rectangle a) Determine the improper fraction that represents the shaded portion b) Determine the mixed number that represents the shaded portion 9

10 21 Complete the table below Improper Fraction Mixed Number Identify the fractions labeled with the letters A and B on the scale below If appropriate, write your answers as both an improper fraction and a mixed number a) Letter A represents the fraction: b) Letter B represents the fraction: 10

11 2 Rewrite the given fractions as equivalent fractions given the indicated numerator or denominator a Rewrite 2 with a denominator of 21 b Rewrite 6 1 with a numerator of 0 c Rewrite 8 with a numerator of 20 d Rewrite 60 6 with a denominator of 2 e Rewrite 6 48 with a numerator of 9 f Rewrite 2 with a denominator of g Rewrite with a denominator of 4 h Rewrite 1 with a numerator of 7 11

12 24 For each problem below, write the fraction that best describes the situation Be sure to reduce your final result a John had 12 marbles in his collection Three of the marbles were Comet marbles What fraction of the marbles were Comet marbles? What fraction were NOT Comet marbles? b Jorge s family has visited 8 of the 0 states in America What fraction of the states have they visited? c In a given bag of M & M s, 14 were yellow, 12 were green, and 20 were brown What fraction were yellow? Green? Brown? d Donna is going to swim 28 laps She has completed 8 laps What fraction of laps has she completed? What fraction of her swim remains? e Last night you ordered a pizza to eat while watching the football game The pizza had 12 pieces of which you ate 6 Today, two of your friends come over to help you finish the pizza and watch another game What is the fraction of the LEFTOVER pizza that each of you gets to eat (assuming equally divided) What is the fraction of the ORIGINAL pizza that each of you gets to eat (also assuming equally divided) 12

13 2 Which of the following CANNOT be written as a mixed number and why? a 8 b 1 8 c 21 2 d 4 27 e Write two equivalent fractions for each of the fractions below a 7 b 4 c 2 9 d 8 e Write each fraction in simplest form a 6 b 1 c 12 6 d e f Using equally spaced tick marks, plot the following numbers on the number line ,,,, Simplify each of the following fractions if possible a) 1 b) 6 6 c) 0 4 d) 1 6 e) 1 1 f) 1 0 1

14 0 Order the fractions from least to greatest and justify your answer a) ,,,, Ordering: b) ,,,, Ordering: c) 8 8 8,,,, Ordering: d) 7 2 8,,,, Ordering: 14

15 1 Simplify the given fractions completely using both the repeated division and prime factorization methods In each case, state which you think is easier and why Fraction Repeated Division Method Prime Factorization Method a) b) c)

16 2 Shade the indicated quantity and rewrite in the indicated forms a) 8 hundredths b) Decimal: Expanded Form: Fraction Form: Decimal: Expanded Form: Word Name: c) 2 tenths and 2 hundredths d) Decimal: Decimal: Expanded Form: Expanded Form: Fraction Form: Word Name: 16

17 Shade the indicated quantity and rewrite in the indicated forms a) 04 b) 080 Fraction Name: Word Name: Expanded Form: Fraction Name: Word Name: Expanded Form: c) 091 d) 00 Fraction Name: Word Name: Expanded Form: Fraction Name: Word Name: Expanded Form: 17

18 4 Shade the indicated quantity and write the corresponding decimal number a) 6 tenths and hundredths and thousandths Decimal Number: Expanded Form: b) hundredths and 2 thousandths Decimal Number: Expanded Form: c) 42 thousandths Decimal Number: Expanded Form: 18

19 Shade the indicated quantity Then write the number in words and expanded form a) 012 Expanded Form: In words: b) 0016 Expanded Form: In words: c) 002 Expanded Form: In words: 19

20 Thousandth Hundredth Tenth One Ten Hundred 6 Use the give number lines to plot the following decimals Unit 4 Practice Problems a) Plot 0, 08, 0, and 09 on the number line below Label the points underneath the number line b) Plot 18, 02, 11, and 27 on the number line below Label the points underneath the number line 7 Use the place value chart to order the numbers from least to greatest 28, 208, 288, 2088, 2008, 2808, 028 Ones Decimals 8 Use your knowledge of negative numbers to order the numbers below 28, 208, 288, 2088, 2008, 2808, Place the following numbers in order from smallest to largest 02, 02, 074, 07, 040,

21 40 Order the signed decimals below using the symbols <, =, or > Unit 4 Practice Problems a) b) c) d) 00 0 e) 0 0 f) g) 09 1 h) i) j) k) 96 6 l) Round the number represented below (Note: The big square is the unit Gray shading represents a whole) Given number: Rounded to the one s place: Rounded to the tenth s place: Rounded to the nearest whole number: Rounded to one decimal place: 42 Round the number represented below Rounded to the nearest whole number: Rounded to one decimal place: Rounded to the nearest tenth: 21

22 Thousandth Hundredth Tenth One Ten Hundred 4 Round the number represented below Unit 4 Practice Problems Rounded to the nearest whole number: Rounded to one decimal place: Rounded to the nearest hundredth: 44 Put the numbers in the place value chart Use the place value chart as an aid to round the number to the indicated place value a) Round 8 to the nearest tenth Ones Decimals b) Round to the nearest whole number c) Round 28 to the nearest hundredth d) Round to the nearest tenth e) Round 7816 to two decimal places f) Round 8 to the ones place g) Round to the nearest tenth h) Round 28 to one decimal place i) Round to the nearest ten 22

23 4 Round the results of the application problems so that it makes sense in the context of the problem a) Amy is buying ribbon for an art project She estimates that she will need 4 meters of ribbon The store only sells ribbon by the tenth of a meter How many meters should she buy? b) John is catering a luncheon and needs 127 pounds of sugar If sugar is only sold in one pound bags, how many bags should John buy? c) Shelly is buying shoes online and computes that she has enough money to buy 278 pairs of shoes How many pairs of shoes can she buy? d) Tia is making a work bench for her art studio She measures the space and needs 824 meters of plywood The store only sells plywood by the tenth of a meter How many meters should Tia buy? e) Jamie is running a booth at the local fair She computes that she needs to sell 862 snow cones that day to make a profit Since she can only sell a whole number of snow cones, how many does she need to sell to make a profit? f) Crystal is buying Halloween candy at the store She has $20 and wants to buy as many bags of candy as possible She computes that she has enough to buy 691 bags of candy How many bags of candy can she buy? 2

24 46 Write the decimal approximations for the given numbers as place value numbers a) In 201, the population of Tallyville was approximately 882 million people b) The tallest building in Tallyville is approximately 224 thousand feet c) The smallest bug in Tallyville has a radius of approximately 6 hundredths of an inch d) The width of a piece of paper in Tallyville is approximately 181 tenths of an inch 47 Write each fraction in decimal form a) 100 b) Decimal: Decimal: c) d) 100 Decimal: Decimal: e) f) 1000 Decimal: Decimal: 24

25 48 Write the following fractions in decimal form Round to the nearest thousandth as needed Unit 4 Practice Problems a) 1 9 b) 2 c) Approximate the following fraction with a decimal by dividing on your calculator Round to the indicated place value a) 9 Tenth: Whole Number: Hundredth: One decimal place: b) 11 1 Two decimal places: Thousandth: Four decimal places: Integer: c) Four decimals: Whole Number: Tenth: Hundredth: d) 4 11 Tenth: Integer: Hundredth: Thousandth: e) Tenth: Whole Number: Hundredth: Ten: f) 8 Two decimal places: Thousandth: Four decimal places: Integer: g) Ten: 48 7 Hundred: Tenth: Hundredth: 2

26 0 Complete the table below Show all of your work for simplifying the fraction a) 0 Decimal Fraction Simplified Fraction b) 046 c) 042 d) 0008 e) 02 f) 70 g) h)