Exercise Worksheets. Copyright 2002 Susan D. Phillips

Transcription

1 Exercise Worksheets Copyright 00 Susan D. Phillips

2 Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple. Simplifying Fractions 0. Add & Subtract Fractions. Add & Subtract Mixed Numbers. Multiply Fractions. Divide Fractions DECIMALS. Decimals to Fractions. Add & Subtract Decimals. Multiply Decimals. Divide Decimals RATIOS & PERCENTS. Ratios & Rates. Proportions 0. Converting Percents. Percents Problems. Measurements - American. Measurements - Metric STATISTICS. Graphs. Mean, Median & Mode REAL NUMBERS. The Basics. Add & Subtract. Multiply & Divide ALGEBRA. Evaluating Expressions 0. Properties. Simplifying Expressions. Equations: Addition Principle. Equations: Mult. Principle. Multistep Equations. Formulas. Word Problems GEOMETRY. Lines & Angles. Quadrilaterals. Triangles 0. Circles. Composite Figures. Volume ANSWERS

3 Worksheet # Adding Whole Numbers Add , +, + 0 +, +, + +,,00 +,,

4 Worksheet # Subtracting Whole Numbers Subtract ,0 -, - 0 -,, - 0,

5 Worksheet # Multiplying Whole Numbers Multiply. x 0 x x x x 0 0 x x 00 x 0 0 x 00 x x, x

6 Worksheet # Dividing Whole Numbers Divide. Round your answer to the hundredths place ,0

7 Worksheet # Order of Operations & Exponents Write in exponent form. Find the value. x x x x x 0 x x x x 0 Calculate. + - x 0 x ( - ) x - x ( + ) 0 x - ( + ) x

8 Worksheet # Fractions: Mixed Numbers Identify which of the following are improper fractions. a) b) c) d) Change the mixed numbers to improper fractions. Change the improper fractions to mixed numbers. 0 0

9 Worksheet # Prime Factorization Find all of the factors. 0 Identify which of the following numbers are prime: a) b) c) d) e) f) Find the prime factorization. Use exponents when applicable

10 Worksheet # Least Common Multiple Find the LCM. and,, and, and, and and 0, and 0 and 0 0 and 0 and 0 0 and,, and, and

11 Worksheet # Simplifying Fractions Simplify to lowest terms

12 Worksheet #0 Adding & Subtracting Fractions Add or subtract as indicated. Reduce to lowest terms

13 Worksheet # Adding & Subtracting Mixed Numbers Add or subtract as indicated. Reduce to lowest terms

14 Worksheet # Multiplying Fractions Multiply. Reduce to lowest terms. x ( ) ( ) ( ) 0 ( ) ( ) x ( ) ( ) ( ) 0 x

15 Worksheet # Dividing Fractions Divide. Reduce to lowest terms

16 Worksheet # Decimals to Fractions Find the equivalent fraction. Reduce to lowest terms

17 Worksheet # Adding and Subtracting Decimals Add or subtract as indicated

18 Worksheet # Multiplying Decimals Multiply x (.0) (000) x (0.) x 0.. x 0 x x

19 Worksheet # Dividing Decimals Divide. Round your answer to the hundredths place. Write as an equivalent decimal. Round to the thousandths place

20 Worksheet # Ratios & Rates Write each ratio as a fraction in lowest terms. Write each rate as a fraction in lowest terms. 0 feet to 0 feet gallons in mins mph to mph females to males minutes to minutes $.0 for potatoes $00 to $0 correct answers out of questions Find the unit rate. 00 meters in seconds 0 miles per gallons. cars for 0 people $ for lbs of shrimp

21 Worksheet # Proportions Write each proportion. is to as is to. adults is to 0 children as adults is to 0 children. If pens cost $, then pens will cost $. Determine if each proportion is true or false: = acres bags seed = acres bags seed = Solve each proportion to find the value of x. = x x = = 0 x 0 x =. = x. x =

22 Worksheet #0 Converting Percents Write each percent as a fraction or mixed number. Simplify. Write each percent as a decimal. % % %.% % % 0%.0% 0 % % Write each decimal as a percent. Write each fraction as a percent

23 Worksheet # Percents Problems Solve. What is % of 00? % of what amount is? 0 is what percent of 0? Find 0% of 000. What percent of 0 is 0? is 0% of what number? What is 0.% of.?. is what percent of? is what percent of? 0.% of is what number? What percent of. is.? What is.% of 0?

24 Worksheet # Measurements: American Units Convert. ft = in pt = qt yd = ft oz = lb. gal = qt. tons = lb 0 min = hr. mi = yd days = hours 0 00 ft = mi

25 Worksheet # Measurements: Metric Units Convert. L = ml kl = L 0 g = kg. g = mg 0 m = km 00 mm = m 00 cm = mm. m = cm 0,000 ml = L kg = mg

26 Worksheet # Statistics: Graphs Refer to the circle graph in the tutorial to answer the following questions. What percent of caloric intake should be from fat? What is the ratio of protein to carbohydrates? Write in lowest terms. How many grams of carbohydrates should one have for every grams of protein? Refer to the line graphs in the tutorial to answer the following questions. In the year of highest overall video sales, approximately how many videos were sold? DVD sales exceeded VHS sales for the first time in what year? Write the ratio between VHS sales and DVD sales in. Refer to the bar graphs in the tutorial to answer the following questions. Which month had the greatest number of guests at the Dove Hotel? In which months did the majority of guests choose the mealplan? Approximately how many guests chose the mealplan in June? Refer to the histogram in the tutorial to answer the following questions. 0 Which age range (class interval) has the highest class frequency? Which class interval has the lowest class frequency? How many members of the club are between and 0 years old?

27 Worksheet # Statistics: Mean, Median & Mode Find the mean.,,,,,,,,,,, 0 Find the median.,,,, 0,,, 0,,,,, 0 Find the mode.,,,,,,,,,,,,,,,,, 0,.,.,.,.,.,.

28 Worksheet # Real Numbers: The Basics Fill in the operator (<, > or =) that makes the statement true. Find the number equivalent to the following absolute values Find the opposite of each number. Write TRUE or FALSE for each statement. - > = 0 - < - -. < - ( - ) > - -

29 Worksheet # Real Numbers: Adding & Subtracting Find the sum or difference as indicated. + ( - ) ( - ) - + ( - ) + ( - ) ( - ) + + ( - ) ( - ) ( - ) ( - ) + + ( - ) -. + ( -. ) - ( -. )

30 Worksheet # Real Numbers: Multiplying and Dividing Find the product. Find the quotient. Simplify. ( ) ( - ) - ( - ) ( - ) ( - ) ( - ) 0 ( - ) ( - ) - ( - ) ( ) ( - ) ( - ) ( ) -. ( - ) ( ) ( ) ( ) - 0 ( ) - - ( - ) ( ) ( - ) ( ) ( ) ( - 0. ) -

31 Worksheet # Algebra: Evaluating Expressions Evaluate each expression. Let n = + n Let S = S Let x = - - x + x Let p = - p Let m = 00 m 00 Let q = q 0 Evaluate. Let x = - and y = - x - y x y xy - xy x + y ( xy ) 0 x + y y - x x + y -

32 Worksheet #0 Algebra: Properties Identify the property as commutative, associative or distributive. a + b = b + a ab = ba a + ( b + c ) = ( a + b ) + c a(bc) = (ab)c a ( b + c ) = ab + ac a ( b - c ) = ab - ac a + b c a = + c b c Rewrite using the commutative property. x + y t + 0 pq Rewrite using the associative property. ( x + y ) + z x(yz) (ab)

33 Worksheet #0 Algebra: Properties (continued) Rewrite using the distributive property. 0 e ( g + h ) f ( j - s ) ( a + b ) ( x + ) ( x - ) a ( x + y + ) e + f g x + Rewrite by factoring. ab + ac b + c 0 x + x s - s ax + bx + cx

34 Worksheet # Algebra: Simplifying Expressions Collect like terms to find an equivalent expression. x + x x + y - x - y 0x - x - x + x + t + y - t - y - a - a x - x + + y - y - Remove parentheses to find an equivalent expression. 0 - ( + x ) - ( x + ) - ( - x - y + ) - ( 0x - ) - ( x + ) Remove parentheses and collect like terms to find an equivalent expression. y - ( x - y + ) a + a - ( a + ) y - - ( y - ) 0a - ( a - ) [ ( x + ) + x ] - [ ( y + ) - ( y - ) ]

35 Worksheet # Equations: Addition Principle Solve using the addition principle. x + = - m - = y = z +. =. e + = = q - t - = 0 n + = 0 = - + x 0 = b +

36 Worksheet # Equations: Multiplication Principle Solve using the multiplication principle. x = 0 y = - y = s = - v = x = n =.w =. = x 0 a 0 =

37 Worksheet # Algebra: Multistep Equations Solve for x. x - = x + = x - = + x ( x + ) = x + x = - ( x + ) = + x - x - 0 = - x + x - ( 0x + ) = + x x + = 0 + ( x - ) = 0

38 Worksheet # Algebra: Formulas Evaluate the following formulas. Use the given values to find the values of the remaining variables. P = s P = Find s. A = x + y + z x = y = z = Find A. A = x + y + z A = x = y = Find z. C F = + C = - 0 Find F. P = L + W L = W = Find P. P = L + W P = L = Find W. d = r t Find t. P = a + b + c Find b.

39 Worksheet # Algebra: Word Problems Jennifer has $ less than triple the savings of Matthew. Matthew has saved $. How much has Jennifer saved? Mark has consumed of a box of cookies, and Patricia has gobbled up another. If the box origonally had 0 cookies, how many are now left? Harold has typed more pages than Rebecca. Together they have typed a total of pages. How many pages have each of them typed? The sum of consecutive whole numbers is. What are the numbers? Jerome ate of the pizza. How much did that leave for Zachary?

40 Worksheet # Geometry: Lines & Angles Identify each of the following angles as right, straight, acute or obtuse. 0 0 A and B are congruent. If A is 0, what is the measurement of B? E and F are complimentary. If E is, what is the measurement of F? S and T are supplementary. If S is, what is the measurement of T?

41 Worksheet # Geometry: Quadrilaterals m m Find the perimeter of the rectangle. Find the area of the rectangle. ft Find the perimeter of the square. Find the area of the square. km km km Find the perimeter of the parallelogram. Find the area of the parallelogram. mm mm 0 mm mm mm Find the perimeter of the trapezoid. Find the area of the trapezoid. What is the sum of the angles of a quadrilateral?

42 Worksheet # Geometry: Triangles in in in in Find the perimeter of the triangle. Find the area of the triangle. m? m m m m Find the missing side to the similar triangles. What is the sum of the angles of a triangle? Identify the type of each triangle according to its description. equal sides, equal angles acute angles right angle equal sides, equal angles no equal sides, no equal angles 0 obtuse angle

43 Worksheet #0 Circles A circle has a diameter of km. What is the radius? Find the diameter of a circle whose radius is 0 miles. What is the value of π, rounded to the hundredths place? Find the circumference of a circle whose diameter is m. Find the circumference of a circle whose radius is. ft. Find the area of a circle whose radius is mm. Find the area of a circle whose diameter is yd. Find the area of a semicircle whose radius is cm.

44 Worksheet # Geometry: Composite Figures 0 m m m m Find the perimeter of the above figure. Find the area of the above figure. in in Find the perimeter of the above figure. Find the area of the above figure. m m 0 m Find the shaded area of the above figure.

45 Worksheet # Geometry: Volume Find the volume of the following figures. A rectangular solid that is mm long, mm wide and mm high. A pyramid whose length = ft, width = ft, and height = 0 ft. A cone whose radius = m, and height = m. A sphere with a radius of km. A hemisphere with a radius of in. A cylinder whose radius = yd and height = yd.

46 ANSWERS Adding Whole Numbers ) ) ) ) )0 ) ) ) ) 0) 0,0 ),, ) 0,0, Subtracting Whole Numbers ) ) ) ) ) ) 0 ) ) ) 0) ) 0 ), Multiplying Whole Numbers ) ) ) ) ) 0 ) ),000 ),0 ),0 0),0 ),0,000 ),,0 Dividing Whole Numbers ) ) ). ). ). ). ) ) ). 0) 0.0 ). ).0 Order of Operations, Exponents ) ) ) ) ) ) 000 ) ) ) 0) 0 ) ) ) - Mixed Numbers 0 ) a, d ) ) ) ) ) ) ) ) 0) ) Prime Factorization ),,, ), ),,,,, ),,,,0,0 ) c,e,f ) ) ) ) 0) ) ) Least Common Multiple ) 0 ) ) 0 ) ) 0 ) 0 ) ) 0 ) 0 0) 0 ) )

47 ANSWERS Simplifying Fractions ) ) ) ) ) ) ) ) ) 0) ) ) 0 0 Adding & Subtracting Fractions ) ) ) ) ) ) ) 0 ) ) 0) ) ) 0 Adding & Subtracting Mixed Numbers ) ) ) ) 00 ) ) ) ) ) 0) ) ) 0 Multiplying Fractions ) ) ) ) ) ) ) ) ) 0) Dividing Fractions ) ) ) ) 0 ) ) ) ) ) 0) Decimals to Fractions ) 0 ) ) ) ) 00 ) ) 0 ) 000 ) 00 0) 000 Adding & Subtracting Decimals ). ). ) 0. ). ) 0.0 ) 0. ). ). ).0 0). Multiplying Decimals ) 0. ).0 ).0 ) ).000 ). ) 0 ) 0. ) 0).0

48 ANSWERS Dividing Decimals ). ). ). ) 0. ) 0.0 ) 0. ) 0. ) 0. ) 0. 0).0 Ratios & Rates gallons females ) ) ) ) ) ) minutes males ) $. ) correct ) 0 meters/second 0) miles/gallon potatoes questions ) people/car ) $/lb shrimp Proportions adults adults pens pens ) = ) 0 children = 0 children ) $ = $ ) false ) true ) true ) ) ) 0) 0 ). ) 0 Converting Percents ) ) ) ) ) ) 0. ) ). ).000 0) 0.0 ) % ) % ) % ) 0% ) 00% ) % ) 0% ) 0% ).% 0) 0% Percents Problems ) 0 ) 0 ) 0% ) 00 ) % ) 0 ) 0.0 ).% ) % 0) ) 00% ). Measurements - American Units ) ) ) ) ) ) 0 ) ) 0 ) 0) Measurements - Metric Units ) 000 ),000 ) 0. ) 00 ) 0.0 ). ) 000 ) 0 ) 0 0) 000

49 ANSWERS Graphs VHS ) 0% ) ) ) 00 ) 00 ) ) JUL DVD ) JUL, AUG & SEP ) 00 0) - 0 ) - ) Mean, Median & Mode ) ) ).0 ) ) 0 ) ) ) ). Real Numbers: The Basics ) > ) < ) > ) = ) > ) ) ) 0 ) - 0) - ) - ) ) 0 ). ) - ) True ) True ) False ) True 0) True Adding & Subtracting Real Numbers ) ) ) - ) - ) 0 ) - 00 ) 0. ) - ) 0) - 0 ) - ) - ) 0 ) -. Multiplying & Dividing Real Numbers ) - ) ) - ) - ) ) ) - ) 0 ) 0) - ) - ) - ) ) - ) - 0 ) - ) ) - 0. ) 0) - ) - ) - ) - ) Evaluating Expressions ) ) ) 0 ) - ) ) undefined ) ) ) - 0) ) - ) - ) ) - 0 Properties ) commutative ) associative ) distributive ) y + x ) 0 + t ) qp ) x + (y + z) ) (xy)z ) (a)b 0) eg + eh ) fj - fs ) a + b

50 ANSWERS 0 Properties (continued) e f x ) x + ) 0x - ) ax + ay + a ) + ) + g g ) a(b + c) ) (b + c) 0) x( + ) = x ) s( - ) = s ) x(a + b + c) Simplifying ) x ) x - y ) x ) - x ) + t + y ) - a ) x + y + ) - - x ) - x - 0) x + y - ) - 0x + ) -x - ) y - x - ) - ) y + ) a + ) x - y - Equations: Addition Principle ) - ) ) ). ) ) ) ) - ) 0) Equations: Multiplication Principle ) ) ) - ) - ) 0 ) ) ) ) 0) 0 Multistep Equations ) ) ) ) - ) or ) - ) - ) - ) 0 0) Formulas ) ) ) ) - ) 0 ) ) ) P - a - c d r Word Problems ) $ ) ) Harold:, Rebecca: ),, ) Geometry: Lines & Angles ) acute ) straight ) obtuse ) right ) obtuse ) acute ) 0 ) )

51 ANSWERS Quadrilaterals ) m ) m ) ft ) ft ) km ) km ) 0 mm ) mm ) 0 Triangles ) in ) 0. in ) m ) 0 ) Isosceles ) Acute ) Right ) Equilateral ) Scalene 0) Obtuse 0 Circles ) km ) 0 miles ). ). m ). ft ). mm ). yd ). cm Composite Figures ) m ) m ) 0. in ). in ) 0.0 m Volume ) mm ) 0 ft ) 0. m ) 0. km ). in ) 0. yd