Download Math 5 Key Concepts

Math 5
Chapter 1 Key Concepts
Write each number in word form.
1.) 45,090,007 _____________________________________________________________________
2.) 399,604,312,000 _________________________________________________________________
__________________________________________________________________________________
Write each number in standard form.
3.) 200,000,000 + 30,000,000 + 4,000,000 + 8,000 _______________________________________
4.) 90,000,000,000+ 1,000,000,000 + 200,000,000 + 3,000,000 + 60,000
__________________________________________________________________________________
Write the number in standard form.
5.) Six billion, two hundred twenty-seven thousand, eighty-nine_________________________
Write the number in expanded form.
6.) 58,021,007,000 __________________________________________________________________
Write the name of the place-value of the underlined digit in each number.
7.) 24,789,153 _____________________________________________________________________
8.). 63,134,072 _____________________________________________________________________
Write the value of the underlined digit in each number.
9.) 45,900 ______________________________________
10. 780,016,000 ______________________________________
Compare each pair of numbers by using >, <, or =.
11.) 4,503,008,000 ______ 4,600,012,000
12.) 9,107,200,143 ______ 9,107,020,143
Rewrite in order from least to greatest. (2 pts.)
13.) 999,009; 900,452,009; 199,000,000 ________________________________________________
Write the word form of each number and tell the value of the underlined digit.
14.) 12.7 __________________________________________________________________________
15.) 76.49 _________________________________________________________________________
Write each number in standard form.
16.) nine and three hundred thousandths _____________________
17.) 35 + 0.6 + 0.08 _____________________
Write two decimals that are equivalent to the given decimal.
18.) 43.6 ___________________________________________________
Compare each pair of numbers by using >, <, or =.
19.) 3.219 ______ 3.314
20.) 15.08 ______ 15.6
Rewrite in order from least to greatest.
21.) 57.604; 57.643; 57.364 _________________________________________________________
Math 5
Chapter 2 Key Concepts
Round each number to the underlined place value. Then name the place value.
Rounded number
Place Value Name
1.) 12,529
____________________
_______________________
2.) 4,176,431
____________________
_______________________
3.) 13.326
____________________
_______________________
4.) 1.847
____________________
_______________________
Find each sum or difference. Then estimate to check your answer! Be sure to show all of
your work including the numbers that you use to estimate.
5.) 258,076 + 207,631
6.) 562,002 – 314,878
7.) 65.32 + 28.98
8.) 37.26 – 28.08
9.) 4.73 + 39.8
10.) 56.3 – 45.27
11.) Michaela earns $11.75 per hour at
her job at a bakery. If she gets a raise of
$2.50 per hour, how much will she
make?
12.) Mrs. Smith’s car gets 3.8 fewer miles
per gallon in the city that it does on the
highway. If the car gets 25.45 miles per
gallon on the highway, how many miles
per gallon does it get in the city?
Write each number in word form and expanded form.
13.) 60,057,004 ___________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
14.) 12.076 ________________________________________________________________________
_________________________________________________________________________________
Write in order from least to greatest.
15.) 3.8; 3.045; 3.12 _________________________________________________________________
Compare each pair of numbers by using <,>, or =.
16.) 56.088 ______ 56.341
17.) 39.2_______ 39.187
Math 5
Chapter 3 Key Concepts
Identify the multiplication property used in each equation.
1.) 324 x 0 = 0
____________________
2.) 7 x (26 x 19) = (7 x 26) x 19
____________________
3.) 129 x 1 = 129
____________________
4.) 61 x 37 = 37 x 61
____________________
Use the multiplication properties to decide what number must be on the line.
5.) 8 x (11 x 38) = (8 x 11) x _____
6.) 71 x ____ = 0
7.) 952 x _____ = 952
8.) 84 x ____ = 23 x 84
Use mental math to find each product.
9.) 600 x 800
10.) 60 x 3,000 x 1
11.) 900 x 70
12.) 5,000 x 300
Estimate each product. Be sure to show the rounded or compatible numbers that you use
for your estimation.
13.) 96 x 24
14.) 23 x 81 x 4
15.) 5 x 72 x 19
16.) 396 x 22
19.) 58 x 64
20.) 328 x 42
Multiply. Estimate to check your answer.
17.) 78 x 9
18.) 639 x 7
21.) Write 54 in expanded form.
22.) Write 4 x 4 x 4 in exponential form.
_____________________________________
______________________________________
23.) Write 23 in standard form.
_____________________________________
24.) Cole sold 7 baseball cards for $15 each and 12 baseball cards for $31 each. How much
money did he have from the sale of his baseball cards?
Write each number in word form and expanded form.
25.) 709,005,230 __________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
26.) 8.105 ________________________________________________________________________
_________________________________________________________________________________
Write in order from least to greatest.
27.) 8.3; 8.21; 8.089_________________________________________________________________
Compare each pair of numbers by using <,>, or =.
28.) 12.26 ______ 12.095
29.) 48.35 _______ 48.4
Add or subtract.
30.) 68 – 53.19
31.) 7.328 + 23.64
Math 5
Chapter 4 Key Concepts
Use mental math to find the quotients.
1.) 350 ÷ 5
2.) 32,000 ÷ 8
3.) 300,000 ÷ 6
Use rounding to estimate each quotient.
4.) 358 ÷ 4
5.) 564 ÷ 7
6.) 286 ÷ 3
Use compatible numbers to estimate each quotient.
7.) 236 ÷ 5
8.) 629 ÷ 8
9.) 372 ÷ 9
Find each quotient. You may use graph paper.
10.) 450 ÷ 9
11.) 406 ÷ 4
12.) 79 ÷ 4
13.) 72 ÷ 3
15.) 329 ÷ 7
14.) 108 ÷ 6
List two factor pairs for each number.
16.) 32 _____________ and _____________
17.) 28 _____________ and _____________
Label each number as prime or composite.
18.) 9 _______________________
19.) 16 _______________________
20.) 13 _______________________
21.) 33 _______________________
Find the prime factorization of each number.
22.) 27
23.) 150
24.) Owen has 52 DVDs. He is putting them into cases that hold 9 DVDs. How many cases
can he fill? How many DVDs will be left?
Find each product, sum, or difference.
25.) 84 x 23
26.) 673 x 26
27.) 4.59 + 28.8
28.) 63 – 27.14
Math 5
Chapter 5 Key Concepts
Use mental math to find each quotient.
1.) 480 ÷ 80 ____________________________
2.) 4,000 ÷ 50 ____________________________
3.) 54,000 ÷ 90 _________________________
4.) 2,800,000 ÷ 700 _______________________
Estimate each quotient using compatible numbers.
5.) 476 ÷ 68 ____________________________
6.) 2751 ÷ 42 ____________________________
Find each quotient.
7.) 502 ÷ 20
8.) 628 ÷ 90
9.) 493 ÷ 12
10.) 623 ÷ 15
11.) 6,802 ÷ 11
12.) 5,078 ÷ 22
13.) Anya has just opened a flower shop! She ordered 525 roses for Valentines Day. If the roses are
divided into 60 bouquets, how many roses will each bouquet have, and how many roses will be left over?
14.) Madison is organizing a party for 56 people. Each table in the banquet room seats nine people. How
many tables will she need?
15.) 563 x 76
16.) 71 – 5.21
Round each number to the given place value.
19.) 22.836; tenths ____________________
20.) 8.6289; thousandths ___________________
17.) 2.745 + 31.28
18.) Write the prime
factorization of 64.
Math 5
Chapter 6 Key Concepts
Translate each algebraic expression into words.
1. n + 6 ____________________________________________________________
2. r ÷ 6 ____________________________________________________________
3. 6b
____________________________________________________________
4. c - 7 ____________________________________________________________
Write each word phrase as an algebraic expression.
5. 8 less than a number _____________________________________________
6. 4 times a number
_____________________________________________
7. 5 more than another number ________________________________________
8. 6 divided by a number ____________________________________________
Evaluate for x = 3 and x = 5.
9. 3x
_____
10. 4 + x
_____
_____
11. 7 - x
_____
_____
12. x /15
_____
_____
_____
Complete each table.
Find the value of each expression using the order of operations.
16. (12 - 4) + 2 x 3
17. 10 + 21 ÷ 7 - 2
Math 5
Chapter 7 Key Concepts
Use mental math to find each product of quotient.
1.) 10 x 0.28
2.) 1.98 x 1,000
3.) 228.9 ÷ 100
4.) 0.27 ÷ 10
___________________
___________________
___________________
___________________
Find each product.
5.) 63 x 0.4
6.) 15 x 0.39
7.) 420 x 0.8
8.) 0.56 x 0.07
9.) 5.4 x 0.32
10.) 71.4 x 0.36
Find each quotient.
11.) 4.2 ÷ 7
12.) 0.072 ÷ 9
13.) 2.24 ÷ 14
14.) 2.08 ÷ 0.8
15.) 3.09 ÷ 0.06
16.) 0.156 ÷ 0.12
17.) Hannah has a spool of ribbon at her hair accessories store that is 8.4 feet long. She wants
to divide it into 0.7 foot pieces. How many complete 0.7 foot long pieces can she cut?
18.) Phoenix, Arizona is one of the driest cities in the U.S. It receives just 7.56 inches of rain
each year. If Phoenix receives the same amount of rain each year, how much rain will it get
in 2.5 years?
Write each number in word form and expanded form
19.) 40,058,020 _____________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
20.) 46.709 ________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
Round each number to given place value.
21.) 71.356; tenths _______________________
22.) 329,604,023; millions _______________________
Math 5
Chapter 8 Key Concepts
Describe the relationship between the two lines.
1.
2.
Name, classify, and measure each angle.
3.
4.
Name: ___________________
Name: ___________________
Classify: _________________
Classify: _________________
Measurement: ____________
Measurement: ____________
Classify each triangle by its angles and sides.
5.
6.
Classify by angles: ___________________
Classify by angles: ___________________
Classify by sides: ___________________
Classify by sides: ___________________
Find the missing angle measure in each triangle.
7. m∠X = 61°, m∠Y = 97°, m∠Z = x°
8. m∠A = 22°, m∠B = 109°, m∠C = y°
9. Name the polygon. Then tell whether it is
regular or irregular.
10. Classify this quadrilateral in as many
ways as you can.
Find the missing angle measure in each quadrilateral.
11. In quadrilateral QRST: m∠Q = 78°,
12. In quadrilateral ABCD: m∠A = 99°,
m∠R = 140°, m∠S = 27°, m∠T = x°.
m∠B= 52°, m∠C = 112°, m∠D = y°.
Find each product, sum, or difference. Write your answer in simplest form!
2
1
1
5
2
1
13. 4 · 1
14. 13 + 8
15. 3 - 1
5
4
9
6
3
6
Math 5
Chapter 8 Vocabulary Review
Match the definition to the corresponding term. Write the letter on the line.
One letter will NOT be used.
1. ______ equilateral triangle
A. intersecting lines that form right angles
2. ______ ray
B. a triangle with no sides of the same length
3. ______ right angle
C. a triangle with 2 sides of the same length
4. ______ hexagon
D. an angle measuring 180°
5. ______ regular polygon
E. a polygon with 6 six sides
6. ______ perpendicular lines
F. all sides have equal length and angle measure
7. ______ quadrilateral
G. formed by two rays with a common vertex
8. ______ straight angle
H. a polygon with 4 sides
9. ______ scalene triangle
I. an angle measuring 90°
10. ______ angle
J. a triangle with all equal sides
K. has one endpoint and extends forever in the
other direction
Math 5
Chapter 9 Key Concepts
1.) Use division and multiplication to find
numerator and two fractions equivalent to
2.) For the fraction
6
.
9
2
, identify the
7
the denominator.
Show your work!!
numerator: _______
denominator: ______
Write each mixed number as an improper fraction and each improper fraction as a mixed
number.
2
17
4.)
3.) 7
3
5
Compare using >, <, or =. Show your work!!
5.)
6
3
_____
11
5
6.)
5
9
_____
12
24
Order from least to greatest.
7.) 2
1
4
3 3
,
, 1 ,
2 9
4 5
Find the Greatest Common Factor (GCF) of each pair of numbers.
8.) 16, 60
9.) 36, 160
Write each fraction in simplest form. Show your work!!
65
18
10.)
11.)
100
24
Write a decimal and a fraction for the shaded portion of each model.
12.) Fraction: _________
14.) Fraction: _________
13.) Decimal: _________
15.) Decimal: _________
Write each fraction as a decimal. Show your work!!
1
3
16.)
17.) 4
5
10
Write each decimal as a fraction. Make sure that your answer is in simplest form. Show
your work!!
18.) 0.24
19.) 0.05
20.) 9.6
21.) Tyrell’s Tasty Tacos just received a shipment of 42 gallons of orange juice and 18 gallons
of cranberry juice. The juice needs to be poured into equal-sized containers. What is the
largest amount of juice that each container can hold of each kind of juice?
22.) At a day camp, there are 56 girls and 42 boys. The campers need to be split into equal
groups. Each has either all girls or all boys. What is the greatest number of campers each
group can have?
Math 5
Chapter 10 Key Concepts
Use a list to find the Least Common Multiple (LCM) of each pair of numbers.
2. 10 and 15
1. 4 and 18
Add or subtract. Give answers in simplest form and/or as mixed numbers.
17 11
8
4
8
5
4
1
–
–
3.
+
4.
5.
+
6.
9
9
30 30
8
5
11 3
Add or subtract. Write each answer as a whole number or a mixed number in simplest form.
Estimate to check your answers.
3
2
7
5
2
7. 18
+ 15
8. 20
+ 9
9. 9 + 6
8
8
12
6
3
10. 50
13
9
– 19
14
14
11. 9
2
3
– 3
7
4
12. 22 – 11
5
16
3
8
pounds of tomatoes. Today, she canned pounds of tomatoes.
7
9
How much more did she can today than yesterday?
13. Yesterday, Mrs. Smith canned
14. During a rainstorm, the water level of Big Muddy Creek rose
1
7
feet. Then it rose another
feet.
6
9
How much did it rise in all?
Find each product or quotient.
15. 16.8 x 0.07
16. 1.68 ÷ 0.3
17. Write 0.44 as a fraction in simplest form.
18. Write
3
as a decimal number.
5
Math 5
Chapter 11 Key Concepts
Find each product. Write your answer as a mixed number and/or in simplest form.
1. 18 x
2
3
2.
2 3
x
5 8
4. 35 x
3
20
5. 4
2
3
x 1
5
7
3.
5
8
x
16 15
6. 3
1
1
x 3
6
3
Math 5
Chapter 12 Key Concepts
Find the perimeter of each figure. Be sure to use the correct label!
1.
2.
Find the area of each figure. Be sure to use the correct label!
3.
4.
6. Find the circumference of a circle whose
radius is 6 in. Use 3.14 for π.
5.
7. Find the circumference of a circle
whose diameter is 40 mm. Use 3.14 for π.
Use the circle at right to answer the following questions. Don’t forget your labels!
8. List the center. ___________________
9. List two radii. __________________
10. List two chords. __________________
11. List a diameter. ___________________
12. List two central angles ________________________________
Name each solid. Be sure to give a complete answer!
13.
14.
Name the solid that each net will form when folded up.
15.
16.
Math 5
Chapter 14 Key Concepts
What is the best unit to weigh each item? Write ounce, pound, or ton.
1. a bag filled with oranges __________________
2. airplane ____________________
3. a math textbook ____________________
What is the best unit to measure the capacity of each item? Write milliliters or liters.
4. jug of milk __________________
5. medicine dropper __________________
6. bath tub __________________
6.) Measure the line segment to the nearest centimeter and millimeter.
cm: ____________
mm: ____________
7.) Measure the line segment to the nearest inch and ¼ inch.
Inch: ____________ ¼ inch: ____________
Convert each measurement.
8.) 64 oz = ____ lb
9.) 34 ft = ____ yd, ____ ft
10.) 36 qt = _____ gal
Convert each measurement.
11.) 71 mm = ____ cm
12.) 0.09 kg = _____ g
13.) 9,023 mL = ____ L
Find the elapsed time. Remember to include labels!
14.) Start 4:46 P.M.
End 7:00 P.M.
15.) Start 5:37 P.M.
End 4:00 A.M.
16.) Start 8:00 A.M.
End 3:25 P.M.
17.) Mrs. Smith plans to arrive at the airport 18.) If it is 72° F inside and 29° F outside, how
at 10A.M. It is a 1 hour and 20 minute ride by many degrees lower is the temperature
car. At what time should she leave home?
outside than inside?
19.) Find the change in temperature.
Morning: - 11 ° C Afternoon: 15 ° C
21.) Find the product of 3
3
4
and 2 .
4
5
20.) Find the temperature after the change.
Start: 28° F Change: decrease 30° F
22.) Find the difference of 33 and 17.9
Math 5
Chapter 16 Key Concepts
SHOW YOUR WORK!
Write the ratio three different ways. Be sure to write in lowest terms.
1. Six out of 54 teachers
2. 12 computers for 72 students.
Give two ratios equal to the given ratio using multiplication and division.
3. 3 to 9
4. 16: 32
State if the ratios are equal. Show why they are or are not equal.
6
5.
; 18 to 24
6. 7:9; 21 to 36
8
For each figure, write a ratio, decimal, and a percent to represent the shaded portion.
7.
8.
Ratio: __________
Ratio: __________
Decimal: __________
Decimal: __________
Percent: __________
Percent: __________
Write the percent as a fraction in lowest terms.
9. 48%
10. 6%
11. 240%
Convert each number to a percent. Remember to include labels!
12. 0.39__________________
13. 3.04__________________
14. 0.05__________________
Convert each percent to a decimal number.
15. 52% __________________
16. 123% __________________ 17. 3%__________________
Math 5
Chapter 18 Key Concepts
In 1-2, use the line graph at right.
1. What was the Museum Admission price
in 1991?_________ in 1994?_________
2. How much did the Museum Admission price increase
between 1991 and 1994? Show your work below!
In 3-6 use the following set of data:
6, 5, 10, 5, 7, 8, 10, 11, 6, 6, 9, 5, 10, 5, 5
3. Record the data in a tally chart
4. Record the data in a frequency chart
5. Make a line plot of the data
6. Make a stem-and-leaf diagram of the data
In 7-10, use the stem-and-leaf diagram of Spring Temperatures.
7. On how many days was the temperature in the forties?
____________
Spring Temperatures (°F)
8. What is the mode? ____________
9. What is the median? ____________
10. What is the range of the data?
For 11-14, find the mean, median, mode, and range for this set of data: 38, 5, 39, 14, 9
11. mean:
12. median:
13. mode:
14. range:
____________
____________
____________
____________
Math 5
Chapter 18 Key Concepts
Directions: In the space to the right, determine the mean, median, and mode for each data
set.
mean =
1) 18, 18, 15, 18, 18, 24, 21, 21, 24, 14
median =
mode =
mean =
2) 94, 69, 84, 69, 90, 75, 94, 90, 90, 9, 5
median =
mode =
mean =
3) 4, 18, 18, 23, 23, 19, 8, 8, 8, 8, 28
median =
mode =
mean =
4) 12, 15, 16, 17, 15, 17, 17, 17, 18, 17
median =
mode =
mean =
5) 16, 3, 3, 3, 8, 24, 16, 9, 11, 11
median =
mode =
mean =
6) 22, 5, 22, 13, 12, 24, 24, 9, 24, 19
median =
mode =
mean =
7) 23, 1, 1, 18, 1, 3, 18, 10, 7, 3
median =
mode =
mean =
8) 23, 10, 2, 6, 10, 14, 1, 19, 8, 19
median =
mode =
mean =
9) 8, 21, 13, 8, 18, 15, 8, 8, 11, 15
median =
mode =
mean =
10) 7, 9, 24, 19, 24, 9 , 18, 3, 3, 3
median =
mode =
Math 5
Chapter 19 Key Concepts
Tell if the second figure is a translation, reflection, or rotation of the first. If
it is a rotation, state the amount of the rotation (degrees or fraction).
1.
2.
4. Translate the triangle right 3 units
and up 1 unit.
3.
5. Rotate the figure 90°°.
6. Write the coordinates of the original figure in problem #4:
Point A: ________________
Point B: ________________
Point C: ________________
7. Reflect the triangle over the x-axis.
8. Reflect the triangle over the y-axis.
Write congruent or not congruent for each pair of figures.
9.
10.
Draw the lines of symmetry then write how many each figure has.
11.
12.
Math 5
Chapter 20 Key Concepts
Determine the number of possible outcomes.
1) At Paula’s Pizza Place, you can order a small, medium or large pizza. Each pizza has 1, 2
or 3 toppings. Create a tree diagram & write the outcomes for ordering 1 pizza and write
the outcomes.
___________________________
2) Barrel racers at a rodeo often have a variety of saddles and bridles. If a rider has 3 saddles
and 6 bridles, how many combinations of a saddle and bridle can the rider have? Use the
counting principle & show your work!
___________________________
3) Find the possible outcomes of tossing a number cube and spinning a spinner with 4
different colors. Use the counting principle & show your work!
___________________________
Find the probability of the following. State the probability as a fraction. *Write answer as
Probability equation!
4) A jar contains 24 navy, 5 white, 8 orange, and 16 red marbles. You pick a marble without
looking. Find the probability of drawing a navy marble.
_________________________________________
5) A standard number cube with the number 1 through 6 is rolled. Find the probability of
rolling a number greater than 3.
_________________________________________
6) One letter is chosen at random from the word BULLDOGS. What is the probability that
the letter chosen is the letter L?
_________________________________________
7) A jar contains 11 red, 16 violet, 6 green, and 25 white marbles. A marble is drawn at
random. Find P(green).
_________________________________________
A number cube is rolled once. Find the probability of each event. Write your answer as a
fraction.
8) P(6) = ___________
9) P(an even number) = ____________
10) P(7) = ____________
11) P(a number less than 5) = _______________
A piggy bank contains three quarters, two dimes, two nickels, and one penny. You pick a
coin at random. Find each probability. *Simplify probabilities if necessary!
12) P(quarter) _____________
13) P(not dime or nickel) _____________
Find the experimental probability. *Write answer as an Experimental Probability
equation!
14) You toss a coin 20 times and record 8 tails. Find the experimental probability of the
outcome of tails. *Simplify probability if necessary.
_________________________________________
15) Naomi won 168 out of 196 games. Find the experimental probability.
_________________________________________
Write and solve a proportion to make a prediction.
16) A teacher asks 70 random students, “Did you see the Reptiles exhibit?” Fourteen answer
yes. If 1,000 students went on the zoo trip, how many likely saw the exhibit?
17) Out of 300 computers, 22 are defective. How many defective computers would you expect
in a group of 30,000?