Rounding Mixed Numbers

Transcription

1 Rounding Mixed Numbers Lesson 0 0 To round a mixed number, compare the fraction to 2. If the fraction is greater than or equal to, round up to the nearest 2 whole number. If the fraction is less than, round down to the nearest whole number. 2 These numbers are nearer 7. These numbers are nearer Halfway Examples: 2 runs u be ause 2 > 2. 7 r un s wn 7 be ause < 2. un ea h m e number he near es wh le number. m ar e ea h fra n. se fra n man ula es f r hel s ma e he r u f 8 7 an. 8. s ma e he sum f 2 an. 9. s ma e he er me er f h s r e an le. emember wr e he un s. n. 8 n. Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved.

2 Subtracting Decimal Numbers Using Zeros Line up the decimal points. Use zeros as holders. Put a decimal point to the right of any whole number. Subtract after borrowing across s. Lesson Examples: Subtract Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5

3 Volume Lesson The volume of a shape is the amount of space the shape occupies. Volume is measured in cubic units. V = l w h height (h) length (l) width (w) Example: Find the volume of this rectangular solid. V = l w h V = V = 2 cubic centimeters To estimate volume, round the measures before multiplying. 3 cm 2 cm 2 cm Find the volume of each rectangular solid. Remember to write the units in. 2 in. 5 in. 5 in. 5 in. 4 in ft 3 ft 6 ft 2 cm 2 cm 6 cm 5. Narissa s toy chest is 4 feet wide, 2 feet deep, and 3 feet high. How many boxes that are -foot cubes could Narissa fit into her toy chest? 3 ft 4 ft 2 ft Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 3

4 Lesson 04 Rounding Decimal Numbers to the Nearest Whole Number 04 Compare the number after the decimal point to 5. These numbers are nearer 7. These numbers are nearer Halfway Examples: (because 4 < 5) (because 6 > 5) Round money amounts to the nearest dollar. Examples: $2.92 rounds up to $3.00 because 9 > 5. $2.35 rounds down to $2.00 because 3 < 5. Round each money amount to the nearest dollar. Remember to write the dollar sign.. $ $ $ Estimate the sum of $4.56 and $ = Round each decimal number to the nearest whole number Estimate the sum of 5.83 and = 9. Annalucia rode her bike 2 blocks in seconds. Round her time to the nearest second. Remember to write the units. 4 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5

5 Symmetry and Transformations Lesson A line of symmetry divides a figure into mirror images (reflective symmetry). Figures often have more than one line of symmetry. Regular polygons have as many lines of symmetry as they do sides. 3 sides 3 lines of symmetry 5 sides 5 lines of symmetry Figures that look the same more than once during a full turn have rotational symmetry. A C C A C B B B A Regular polygons have reflective symmetry and rotational symmetry. Find all the lines of symmetry in each figure A regular hexagon has how many lines of symmetry? 5. Which of these letters has rotational symmetry? (Circle one). S U B T R A C T Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 5

6 Reading and Ordering Decimal Numbers Lesson We can use bills and coins to represent value. Each in the chart below is one tenth of the value of the to its left. tens ones tenths hundredths thousandths tenthousandths. $0 bills $ bills dimes pennies mills To compare or order decimal numbers:. Line up the decimal points Compare the digits starting in the tenths s, and then in each to the right Arrange from least to greatest Remove any unnecessary zeros , 0.45, 0.457, 0.5 Use words to name each number Round each decimal number to the nearest whole number Compare Arrange in order from least to greatest. 0.03, 0.03, 0.003, Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5

7 Using Percent to Name Part of a Group Lesson Percent means per hundred. Like fractions, percents can be used to name part of a group. To name part of a group using percent:. Find the fraction that names the part of the group. 2. Change the fraction to a percent by multiplying by 00%. 3. Check for reasonableness. Example: If 9 of the 20 students read for an hour each night, what percent of the students read for an hour each night?. The fraction described is Multiply by 00% % = 900% 20 = 45% 3. The answer is reasonable because 9 out of 20 is a little less than 2 and 45% is a little less than 50%, which equals 2. To make the division easier, cancel if possible % = 45% Remember to write the percent symbol.. If 8 of the 30 yearbook members are teenagers, then what percent of the yearbook members are teenagers? % = 2. If 2 out of 50 pieces of apple were eaten by David, then what percent of the pieces of apple did David eat? 3. Sixteen out of 20 is what percent? 4. Eight out of 25 is what percent? % 5. If one fourth of the people drank water at lunch, then what percent of the people drank water at lunch? = Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 7

8 Schedules Lesson A schedule is used to arrange events by time period. It shows when events are planned to happen. You might use a schedule to choose a bus route, or to organize your day. We often show a schedule in a table. Spelling Bee Round 9:5 a.m. Theater Performance 2:40 p.m. Number Sense :00 a.m. Math Computation 3:30 p.m. Science Investigations :45 a.m. Reading Comprehension 4:00 p.m. Lunch Break 2:45 p.m. Creative Writing 4:40 p.m. Spelling Bee Round 2 :05 p.m. History Bee 5:45 p.m. Music Theory 2:00 p.m. Awards Ceremony 6:45 p.m.. Mrs. Brisbee s class is going to compete in an academic competition. Above are the times for each event. The school is 35 minutes from the competition. If Mrs. Brisbee s class wants to arrive 5 minutes before the first event, when should they leave the school? Remember to write a.m. or p.m. 2. Five of Mrs. Brisbee s students will compete in the Theater Performance and Reading Comprehension events. How much time is scheduled between the start of the two events? Flight Departure Time Flight Arrival Time Flt. 327 to New York 8:4 a.m. Flt. 025 from Houston 8:2 a.m. Flt. 590 to Miami 9:23 a.m. Flt. 62 from Seattle 8:58 a.m. Flt. 226 to Chicago 0:02 a.m. Flt. 38 from Baltimore 9:43 a.m. Flt. 86 to Los Angeles 0:35 a.m. Flt. 74 from Phoenix 0:29 a.m. 3. The table above shows arrival and departure times for flights into and out of Atlanta. Efraim is traveling from Houston to Chicago. His flight arrives from Houston at 8:2 a.m. What time does his plane depart for Chicago? 4. Trevia is traveling from Baltimore to Los Angeles. How much time is scheduled between the arrival and departure times? 8 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5

9 Multiplying Decimal Numbers Lesson To multiply decimal numbers:. Multiply the numbers. 2. Count the digits to the right of the decimal points in the factors. 3. Put the same number of digits to the right of the decimal point in the answer. Examples: digits 7 0 digits digits digits 0. 4 digit 2. 8 digit digits 0. 6 digit digits Multiply = = = = 9. What is the area of this square? Remember to write the units..7 cm Saxon Math Intermediate 5 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. 9

10 Multiply Decimal Numbers: Using Zeros as Placeholders Lesson 0 0 When we multiply decimal numbers, we count the digits to the right of the decimal points in the factors. We put the same number of digits to the right of the decimal point in the answer. Sometimes there are fewer digits in the answer than we need, so we fill the empty s to the left with zeros. Examples: Multiply We count a total of 3 digits to the right of the decimal points in the factors. There are only 2 digits in the answer, so we use a zero to the left of the 9 as a holder before writing the decimal point = = = = 9. What is the area of this rectangle? Remember to write the units. 0.0 m 0.08 m 20 Harcourt Achieve Inc. and Stephen Hake. All rights reserved. Saxon Math Intermediate 5