Fractions of an Area

Transcription

1 Fractions of an Area Describe and compare fractions as part of an area using words, objects, pictures, and symbols.. Circle the letter of each cake top that shows fourths. A. D. Each part of this rectangle is 4. All the parts cover the same area even though they don t all have the same shape. B. E. C. Answers will vary. For example:. a) Make this rectangular cake top red and 4 blue. Red Blue b) Write the fraction for the part that is not coloured. 4. Which fraction is greater? Tell how you know. a) 6 or 6 6 since is greater than b) 8 or since 7 is greater than 4. Join the dots in order from the. Is of cake top A the same as least to the greatest. of cake top B? Explain A B No, they are not equal areas. Even though they are both a cake, the area of of cake A is larger than the area of of cake B. 4 Answers Chapter : Fractions and Decimals Copyright 4 Nelson

2 Mixed Numbers and Improper Fractions Model, write, and compare improper fractions and mixed numbers.. The trapezoid is the whole. a) Colour trapezoids. 6 triangles make a whole hexagon. b) How many triangles did you colour? c) Write the improper fraction that describes how much is coloured.. The rhombus is the whole. So 8 triangles show 6 (a mixed number) or 8 6 (an improper fraction). a) Colour 4 rhombuses. b) Colour 7 rhombuses. c) Which is greater, 4 or 7? How do you know? 7 because more triangles are shaded than for 4 (or because more rhombuses are shaded).. The trapezoid is the whole. a) Colour 4 trapezoids. Then write the improper fraction. b) Colour trapezoids. Then write the mixed number. c) Which is greater, 4 or 4? How do you know? because 8 more triangles are shaded than for (or because 4 whole trapezoids are more than whole trapezoid). Copyright 4 Nelson Answers Chapter : Fractions and Decimals

3 Fractions of a Set Describe parts of sets using proper and improper fractions and mixed numbers. Use toothpicks, bread tags, or other counters to help you if necessary.. Liza is writing thank-you cards. They come in packages of 8. She has used 8 of a package. a) How many cards has she used? b) What improper fraction describes 8 of a package? 8 Mixed numbers and improper fractions can be used to describe parts of sets. For example, eggs come in cartons of. 4 eggs could be described as a mixed number,, or as an improper fraction, 4.. Mollie is putting pop cans in cartons. She puts cans in each carton. a) Write the mixed number that describes how many cartons she can fill with 7 cans. b) Write this amount as an improper fraction.. Write the mixed number for each improper fraction. Then draw pictures of toothpicks to show the mixed number as sets and parts of sets. a) b) 8 8 c) Arrange these numbers in order from least to greatest. a) 6,, 4, 8,, 4, 6, 8, b), 4, 4, 7, 4,, 7, 4, 6 Answers Chapter : Fractions and Decimals Copyright 4 Nelson

4 4 Decimal Tenths Write decimal tenths using words and symbols.. Complete the chart. Fraction Item of items Decimal Words pencils. two tenths erasers. three tenths crayons rulers glue sticks 4.4 four tenths. one tenth. zero tenths Decimals are a way to describe fractions. The fraction is written. and read two tenths. A decimal point separates the ones place from the fractional part. The means there is no whole amount and the is the numerator in the fraction.. Write each decimal as a fraction. a). b). c).. Write each fraction as a decimal. Then write it in words.. a) b) c) one tenth. zero tenths. five tenths 4. Draw and colour a design on the strip following the directions given. Answers will vary. For example: a) Put stars in less than 4 of the boxes. Write the decimal amount of stars.. c) Colour almost all of the boxes. Write the decimal amount of coloured boxes.. b) Put triangles in more than d) Write the decimals closest to of the boxes. Write the decimal..6. amount of triangles..6 Copyright 4 Nelson Answers Chapter : Fractions and Decimals 7

5 Decimal Tenths Greater Than Model, write, and compare decimal tenths greater than. Use the metre sticks on the side of the page to help you.. Find. m on the metre sticks. a) What does the in. m tell you? one whole metre The drawing below shows metre sticks end-to-end. The decimal marked A is. m. This represents whole metres and tenth of a metre, or whole metres and decimetre ( dm). b) What does the in. m tell you? c) Write. in words. five tenths of a metre or five decimetres d) How many decimetres is. m? e) Write. m as a mixed number.. Write a decimal for each mixed number. Then find each length in metres on the metre stick. The first one is done for you. a) 4 d) 6 b) e) 8 c) f) one metre and five tenths dm. Write each measurement in metres using decimals. a) one metre four decimetres.4 m b) twenty-five decimetres. m c) two metres eight decimetres.8 m 4. Arrange these measurements from longest to shortest.. m,. m,. m,.8 m,. m,. m. m,. m,. m,.8 m,. m,. m. m m m m e b f A d c dm m 8 Answers Chapter : Fractions and Decimals Copyright 4 Nelson

6 6 Adding Decimal Tenths Add decimals in tenths. Use the number line on the side of the page to help you with the questions.. a) Find. on the number line. Add. to it. What is the answer? b) Find.6 on the number line. Add. to it. What is the answer? c) Find. on the number line. Add.8 to it. What is the answer?..8.7 To add decimals, use the number line. For example, to add. and.: Start at.. (It s marked A.) Jump. from. to 4.. (It s marked B.) That s wholes added. Jump. more from 4. to.. (It s marked C.) That s tenth added..... Add the lengths. a). m and.8 m e). cm and.8 cm 4. m 6. m b). km and.4 km f) 4. m and. m 4.4 m. m c) 4. m and. m g).7 dm and.7 dm. m.4 m d).8 m and.6 m. Larry walked. km and then ran. km. How far did he go?.7 km.4 m 4. Find 4 different pairs of decimal tenths that add to 4.. Answers will vary. For example,. +.,. +.,. +., Find 4 different pairs of decimal tenths that add to 6.. Answers will vary. For example, 6. +.,. +., 4. +.,. +.. A BC Copyright 4 Nelson Answers Chapter : Fractions and Decimals

7 7 Subtracting Decimal Tenths Subtract decimals in tenths. Use the number line on the side of the page to help you. To answer the riddle What happens to a duck when it flies upside down? : find each difference use the code below to match each difference with a letter Count on to subtract decimal tenths. To subtract..6: Find.6 on the number line. (It s marked A.) Count to.. (It s marked B.). That s 4 tenths. Count from. to.. (It s marked C.) That s another tenths. 4 tenths and tenths is 7 tenths, or.7. So Code A C I U Q T K S P I T Q U A C K S U P The difference between the lengths of the front foot and the back foot of a skunk is. cm. Circle the letter of the lengths the feet could be. A. 4. cm and. cm C.. cm and. cm B.. cm and. cm D.. cm and. cm. A black bear s front foot is 4. cm long. A grizzly bear s front foot is. cm long. What is the difference between the lengths of their front feet? Use a ruler to help you.. cm A B C Answers Chapter : Fractions and Decimals Copyright 4 Nelson

8 8 Communicate About Decimal Operations Use a model to explain how to add and subtract decimals.. These base ten blocks show the difference between. and Check the answer by adding.8 and =.... These base ten blocks show the difference between 4. and.6. Base ten blocks are useful for modelling addition and subtraction of decimal tens. tens rod is dm (decimetre). unit cube is cm, or. dm.. Communication Checklist Did you show all your steps? Did you put the steps in order? Did you explain your thinking? Did you use math language? = a) Write an explanation using a diagram to show how the difference is found. Use the Communication Checklist to check your explanation. b) What is the difference? c) What could you add to check? d) Check = and.. These base ten blocks show the sum of.6 and.7. a) How many rods are there altogether? b) How many cubes are there altogether? c) Express the number of cubes in part b) as rods and cubes. d) What is the sum of.6 and.7? 4. rod, cubes Copyright 4 Nelson Answers Chapter : Fractions and Decimals

9 Decimal Hundredths Less Than or Equal to Write hundredths as decimals using words and symbols.. Write each fraction as a decimal and in words. a) b) 4 c)., hundredths.4, 4 hundredths., hundredths hundredths of this grid is shaded. This is. or. 68 hundredths of this grid is not shaded. This is.68 or 68.. Order the decimals in Question from least to greatest..4,.,.. Write each decimal as a fraction. 7 8 a). b).7 c).8 4. Write the decimal from Question that is closest to each number. a).8 b).7 c).. Describe using fractions, decimals, and words. 8 a) E,.8, 8 hundredths b) t 7,.7, 7 hundredths c) c,., hundredths d) Etc e) part not shaded 8,., hundredths,.8, 8 hundredths Answers Chapter : Fractions and Decimals Copyright 4 Nelson

10 Add and Subtract Hundredths Add and subtract decimal hundredths using grids and calculators.. This grid shows.4.. a) What is the sum?.7 b) Explain how you know. shaded altogether.. This grid shows.4.. a) What is the difference?. b) Explain how you know. are not stroked out. 7 squares are shaded squares A grid can be used to add decimal hundredths. Shade the number of squares equal to each decimal number. Then count all the shaded squares. (See Question.) A grid can be used to subtract decimal hundredths. One way is to shade the number of squares equal to the greater decimal number. Stroke out the number of shaded squares that is equal to the lesser number. Then count the shaded squares that didn t get stroked out. (See Question.). Add or subtract using the grids provided. If you have a calculator, check your answers. a).8.44 =.6 c).. =.74 e).7. =.6 b).. =. d).66. =.44 f).8.8 =.76 Copyright 4 Nelson Answers Chapter : Fractions and Decimals

11 Relating Fractions and Decimals Explore, model, and calculate how fractions and decimals are related.. a) Shade. as a decimal hundredth. b) Shade 4. 4 as a decimal hundredth.7 c) Shade. as a decimal hundredth The grid is 4 shaded. This is hundredths of the grid, or.. 4. You can check by dividing the numerator by the denominator 4 using a calculator.. d) Shade. as a decimal hundredth.4 e) Shade. as a decimal hundredth.6 If you have a calculator, check that each decimal hundredth is correct. Divide the numerator of each fraction by its denominator. f) Shade 4. 4 as a decimal hundredth.8 4 Answers Chapter : Fractions and Decimals Copyright 4 Nelson

12 Test Yourself Page Circle the correct answer.. Which statement does not describe this rectangle? A. 4 of the rectangle is shaded. B. of the rectangle is not shaded. C. Each section is 4 of the whole area even though the sections are not the same shape. D. 4 of the rectangle is not shaded.. Which is a mixed number that describes the amount of hexagons that are shaded? E. 7 G. F. 8 H.. Juice boxes come in packages of. John has 4 juice boxes. Which fraction shows how many packages he has? A. packages B. 4 packages C. packages D. 4 packages 4. Which of the following correctly describes this set of pattern blocks? E.. of the set are trapezoids. F. The triangles and hexagons are more than. of the set. G. 4. of the set are rhombuses. H. The rhombuses and trapezoids are more than.4 of the set.. Which of the following shows the decimal amount shaded? A.. C.. B.. D.. Copyright 4 Nelson Answers Chapter : Fractions and Decimals

13 Test Yourself Page Circle the correct answer. 6. What is the sum of.8 and 4.? E. 8. F. 7. G. 7. H What is the difference between. and.7? A. 8. B.. C.. D.. 8. What operation is shown by these base ten blocks? E.... G.... F.... H What is as a decimal? A.. B.. C.. D... What operation is shown on this grid? E F G H What operation is shown on this grid? A B C..7.. D Which decimal represents 4 on a calculator or on a grid? E..4 F.. G..4 H..4 6 Answers Chapter : Fractions and Decimals Copyright 4 Nelson