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Maths Book 6 Decimals Part 1

Maths Book 6 Decimals Part 1. A maths programme to teach maths' skills for the primary years. Dennis Sparrow Educational Psychologist. Lesson 1: Reading and Writing Decimals. 1. Decimals are a special type of fraction.

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Maths Book 6 Decimals Part 1

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  1. Maths Book 6 Decimals Part 1 A maths programme to teach maths' skills for the primary years. Dennis Sparrow Educational Psychologist

  2. Lesson 1: Reading and Writing Decimals 1. Decimals are a special type of fraction. 2. Decimals are a fraction with a denominator that is a power of 10, e.g. 10, 100, 1 000,10 000. 3. Decimals do NOT have a written denominator, but use a place (decimal point) to show the number of parts. . Example 1: 10.5 This is one decimal place. It means there are 10 equal parts. Example 1: 10.55 This is two decimal places. It means there are 100 equal parts. Example 1: 10.555 This is three decimal place. It means there are 1000 equal parts.

  3. Lesson 1: Reading and Writing Decimals 4. Reading fractions with tenths and hundredths: examples: Exercise 1: Write these as tenths: examples: Exercise 2: Write these as hundredths:

  4. Lesson 1: Reading and Writing Decimals • 5. Writing fractions with tenths and hundredths: • example 1: 5 hundredths • 5 tells me the numerator is 5, hundredths tells me the denominator is 100. • example 2: 5 tenths • 5 tells me the numerator is 5, tenths tells me the denominator is 10. • Exercise 3: Convert these to fractions: • 8 tenths • 2 hundredths • Exercise 4: Name the denominator and numerator:

  5. Lesson 2: Reading Decimals Let’s learn another way to write tenths and hundredths. Rule 1. if there is one digit after the decimal we say tenths. Rule 2. A decimal point separates the whole number from the decimal part of the number Rule 3. If there are 2 digits after the decimal point we say hundredths. examples:    = 6 tenths = .6 = 60 hundredths = .60

  6. Lesson 2: Reading Decimals examples: = 9 tenths = 93 hundredths = 9 = 9 tenths = 93 = 93 hundredths

  7. Lesson 2: Reading Decimals The following are equivalent: = = 9 tenths = = 9 hundredths = = 9 hundredths Exercise 5: Write these as tenths, hundredths and fractions with a denominator of 10 or 100 as in the examples above: .03 .14 .30 .8 .50 .2 .58 .20 .41 .78

  8. Lesson 2: Reading Decimals Exercise 6: Complete these — does the decimal point say A = tenths or B = hundredths? .03 .14 .30 .8 .50 .2 .58 .20 .41 .78 .83 .22

  9. Lesson 3: More About Writing Decimals 1. Let’s learn more about writing decimals. 2. Read this fraction. 3. Does this fraction say A tenths or B hundredths? Answer B. 4. Now I want to write it as a Decimal. How to convert this farction to a decimal? Step 1: How many digits are there after the decimal point when the decimal is a hudnredth? 2 Step 2: What do we write after the decimal point? .73 Step 3:Does this decimal say 73 tenths or 73 hundredths? Answer: 73 hundredths Step 4: The decimal says point 73, decimal 73 or 73 hundredths.

  10. Lesson 3: More About Writing Decimals Exercise 7: Convert these fractions to decimals. 4/10 40/100 7/10 7/100

  11. Lesson 4: Writing Decimals - Hundredths Let’s learn to write special decimals. e.g. 2. Read this fraction. 7 hundredths 3. Let’s write 7 hundredths as a decimal..07 4. Let’s write lines after the decimal points. 5. How many digits after the decimal point? 2 (Yes, for hundredths) 6. So we draw 2 lines after the decimal point. . 7. We have 2 digits to fill in. 8. This fraction says 7 hundredths, so 7 goes in the in the hundredths place. 9.Remeber for hundredths we need 2 digits after the decimal point, so we use replace the line with a zero in the tenths place. 10. This decimal (.07)says 7 hundredths.

  12. Lesson 4: Writing Decimals - Hundredths Exercise 8: Write these fractions as decimals. Draw 1 line for tenths and 2 lines for hundredths, then replace with zeroes or digits. 4/100 5/100 7/100 50/100 7/10 5/10 2/10 2/100 8/100 3/100 3/10 23/100

  13. Lesson 5: Reading Mixed Decimals 1. Let’s learn about reading mixed decimals. e.g.2.4 2. It has a whole number, a decimal point and a decimal. 3. The number on the left of the decimal point is a whole number 2. 6. The number on the right of the decimal point is the decimal. .4 7. The mixed decimal is said 2 whole and 4 tenths OR 2 and 4 tenths. examples: 1.1 = 1 whole and 1 tenth 3.34 = 3 whole and 34 hundredths 6.30 = 6 whole and 30 hundredths Exercise 9: Write these mixed decimals as whole numbers + tenths or hundredths, as in the examples above. 5.5 14.2 16.43 7.40 19.23 11.16

  14. Lesson 6: Writing Mixed Decimals from Mixed Fractions Let’s learn to write this mixed Fraction as a mixed decimal e.g. 3 6/10 2. Look at this side. This is a whole number. 3. Remember numbers on the left side of the decimal point are whole numbers 4. We enter 3 on the left hand side of the decimal point. 3. 5. We enter 6 on the Right Hand Side of the decimal point 3.6 So, 3 6/10 = 3.6 examples: 1 1/10 = 1.1 3 34/100 = 3.34 6 30/100 = 6.30 Exercise 10: Write these mixed fractions as decimals. 5 43/100 5 6/10 8 17/100 20 34/100

  15. Lesson 7: Reading Mixed Decimals - Words 1. When we WRITE mixed decimals we use a decimal point to separate the whole number from the decimal. 2. When we READ a mixed decimal we use AND to separate the whole number from the decimal. e.g. 6 AND 30 hundredthsis how to read a mixed decimal. 3. It has a whole number and a decimal. 4. It is written 6.30 5. We say AND or POINT when we come to the decimal point. 6. The number on the left is the whole number. 7. The number on the right of the AND or POINT is the decimal. Exercise 11: Read these 4 mixed fractions as decimals, and write your answers. 5.43 8.5 19.23 47.7

  16. Lesson 8: Writing Mixed Decimals from Words e.g. 3 AND 6 tenths = 3.6 1. This is a WHOLE number. 2. Remember numbers on the Left of the AND are a whole number. 3. We enter 3 on the this side of the decimal. 3. 4. This fraction tells about TENTHS, Therefore this has 1 digit after the decimal point. 4. We enter the 6 on this side of the decimal point. 3.6 e.g. 4 AND 43 hundredths = 4.43 1.This fraction tells about HUNDREDTHS, therefore this has 2 digits after the decimal point. Exercise 12: Write these mixed fractions as decimals. 4 and 43 hundredths 5 and 43 hundredths 8 and 5 tenths 19 and 23 hundredths 47 and 7tenths

  17. Lesson 9: Equivalent Decimals – Adding Zeroes Rule 1: When we write a zero AFTER a decimal point, we don’t change the value of the number. example: .3 1. Now I will write a zero after the decimal. .30 2. .3 = .30 tenths hundredths 3. I changed .3 to .30 by adding a 0 after the last digit. 4. I am going to use fractions to show that 3 tenths equals 30 hundredths. .3 = .30

  18. Lesson 9: Equivalent Decimals – Adding Zeroes Remember the rule, when we multiply by a fraction that is equivalent to 1, we don’t change the value of the number. 5. So, now I will work out what equals 6. I must multiply the numerator by 10 to end with 30. 7. I must now multiply the denominator by the same number, 10, and end up with 100. 8. Remember, since I multiplied 3 tenths by a fraction equivalent to 1 (10/10), I didn’t change the value of this number.

  19. Lesson 9: Equivalent Decimals – Adding Zeroes Remember the rule, when we multiply by a fraction that is equivalent to 1, we don’t change the value of the number. 5. So, now I will work out what equals 6. I must multiply the numerator by 10 to end with 30. 7. I must now multiply the denominator by the same number, 10, and end up with 100. 8. Remember, since I multiplied 3 tenths by a fraction equivalent to 1 (10/10), I didn’t change the value of this number.

  20. Lesson 9: Equivalent Decimals – Adding Zeroes 9. 3 tenths times 10 tenths equals 30 hundredths, therefore: .3 = .30 and 3 tenths = 30 hundredths Exercise 13: Write the equivalent fractions to prove each of these tenths are equivalent to hundredths (ie .9 = .90) .9 .2 .8 .6

  21. Lesson 10: Equivalent Decimals – Removing Zeroes A new rule. If we erase zeros AT THE END of a decimal, we don’t change the value of the decimal. example:.50 says 50 hundredths 1. Now I will erase the zero at the end of the decimal. .50 = .5 hundredths tenths 2. I changed 50 hundredths to 5 tenths by erasing the zero. 3. Now I am going to use fractions to show that 50 hundredths equals 5 tenths.

  22. Lesson 10: Equivalent Decimals – Removing Zeroes Remember the rule, when we multiply by a fraction that is equivalent to 1, we don’t change the value of the number. 4. We are going to solve the problem from this side because this is where the ? are.. 5. I must multiply the numerator by 10 to end with 50. 6. I must multiply the denominator by 10 to end with 100. 7. 10/10 = 1, therefore 5 tenths times 10 tenths (i.e. 1) equals 50 hundredths. 8. Therefore .50 = .5

  23. Lesson 11: Equivalent Decimals – Wholes Rule: When we write zero after a decimal we don’t change the value of the number. Rule: When changing a whole number to a mixed decimal we usually use 2 zeroes after the decimal point. example:5 1. First write in the decimal point. 5. 2. Then write 2 zeroes after the decimal point. 5.00 3. We changed a whole number, 5, to a mixed decimal, 5 and 0 hundredths.

  24. Lesson 11: Equivalent Decimals – Wholes Exercise 14: Convert these whole numbers to mixed numbers with 2 decimal places. 36 2 67 12 22 130 3 16 48 713 5 14 Remember the Rule: When changing a whole number to a mixed decimal we usually add 2 zeroes after the decimal point. 4.Let’s prove this by changing the mixed decimals 5.00 back to the whole number 5 5. Erase the 2 zeroes and the decimal point. 5 6. There are no digits to the right of the decimal point. 7. Therefore the mixed decimal 5.00 is equivalent to the whole number 5.

  25. Lesson 11: Equivalent Decimals – Wholes Exercise 15: Convert these mixed decimals to whole numbers with 0 decimal places and no decimal point. 22.00 100.00 8.00 67.00 12.00 90.00 200.00 130.00 40.00 713.00

  26. Lesson 12: Decimal Point Alignment Here's a Rule: when we add and subtract decimals, we must line up the decimal points directly beneath one another. example:4.2 + 3.6 1. Now I can add the decimals. 2. Put the decinal point beleow the line and in line with the other decimal points. 3. Now I’ll add 2 + 6 = 8. 4. I’ll enter 8 in the tenths column 5. Now I can add the whole numbers 4 + 3 = 7. 6. The answer is 7.8 or 7 and 8 tenths.

  27. Lesson 12: Decimal Point Alignment A subtraction example: 0.69 - 0.58 1.Align the decimal point. Now I can subtract the decimals. 2. Now I’ll subtract 9 - 8 = 1. 3, I’ll enter 1 in the hundredths column 4. Now I can subtract the tenths 6 — 5 and enter 1 in the tenths column. 5. Now I can subtract the whole numbers 0 — 0 = 0 and enter 0 in the answer. 6. The answer is 0.11 or 0 and 11 hundredths. Exercise 16: add or subtract these decimals and write the answer in tenths or hundredths form. 12.78 +33.11 12.3 – 10.2

  28. Lesson 13: Adding and Subtracting Decimals Remember the Rule: when we add and subtract decimals, we must line up the decimal points directly beneath one another. example: 12.46 - 10.2 - New Rule: To add and subtract decimals, we need the same number of decimal points AFTER the decimal point. 1. So we must add a zero to the hundredth place 2. Now there is the same number of digits after each decimal point. - 3. Therefore we can solve the problem.

  29. Lesson 13: Adding and Subtracting Decimals Exercise 17: Add or subtract these decimals. 12.46 – 10 8.1 — 2.73 8 — 2.7 41.34 — 21.1 23.2- 4.62 6.32-4 94.06- 51.0 56 + 23.55 0.65- 0.3 10 528.5 + 34.34 1.2 — 1 423 + 322.90 46.42 + 40.22 54.42 + 42 231.01 — 126.7 532 + 102 18.23 — 8.21

  30. Lesson 14: Adding and Subtracting Decimals Using Regrouping and Renaming • Remember this rule: adding and subtracting decimals is the same as adding and subtracting any numbers except, when we add and subtract decimals, we must line up the decimal points directly beneath one another. • example:4.5 + 3.7 = ? • 5 tenths + 7 tenths is 12 tenths. • We’ll re-name 12 as 2 tenths • and 1 one whole. • 2. We enter the 2 in the tenths column and the 1 above the ones column • 3. Now we add 4 + 3 and the 1 that was re-namedin the one’s column. • 3. Therefore we can solve the problem. • 4.5 + 3.7 = 8.2

  31. Lesson 14: Adding and Subtracting Decimals Using Regrouping and Renaming Exercise 18: Add or subtract these decimals and write.

  32. Lesson 14: Adding and Subtracting Decimals Using Regrouping and Renaming Exercise 18: Add or subtract these decimals and write.

  33. Lesson 15: Rewriting Decimals - Thousandths New rule: If there are 3 digits after the decimal point we say thousandths. example:8.4 1. Read this as 8 and 4 tenths. 2. Let’s re-write this so it tells about thousandths. 8.4 = 8.400 Exercise 19: Rewrite these mixed decimals so they tell about thousandths.

  34. Lesson 16: Rounding Off New rule: If the digit to the right of the number being rounded is 5 or greater, add 1 to the number in the Rounded Place. example: 3.4675 1. Let’s round off to the nearest hundredth. 2. 1st we draw a line right after the number to be rounded off (hundredths in this case, so we draw a line after the second digit after the decimal place). 3.4675 3. Now look at the number to the right of this line. The number is 7 (greater than or equal to 5) so we add 1 to the number to the left of this line (6). 4. We rewrite the 6 as a 7 So 3.4675 = 3.47 (to hundredths)

  35. Lesson 16: Rounding Off Exercise 20: Round these numbers to: (a) hundredths 7.6423, 0.346, 2.34, 0.4825, 0.482, 19.208, 9.300 (b) tenths 7.6423, 0.346, 2.345, 2.45, 1.55, 8.72, 22.00, 100.00, 8.00, 67.00, 12.00, 90.00, 200.00, 130.00, 40.00, 713.00, 19.208, 5.10, 9.300, 9.03, 9.43, 7.05, (c) ones 7.6423, 0.346, 2.345, 2.45, 1.55, 8.72, 12.3, 22.7, 19.2, 19.02, 6.32,9.0, 22.00, 100.00, 8.00, 67.00, 12.00, 90.00, 200.00, 130.00, 40.00, 713.00, 19.208, 5.10, 9.300, 9.3, 9.03, 9.43, 7.0, 4.3,

  36. Lesson 17: Decimal Point Placement – Multiplying Decimals New rule: When multiplying 2 or more decimals, we count the places AFTER decimal point in both (or more) numbers. example: 32. 1 x 0.4 1. 32.1 has 1 place after the decimal point. 2. 0.4 has 1 place after the decimal point. 3. There are 2 places in the answer. 4. We complete the multiplication as for any number. 5. To place the decimal point in the answer, we count 2 places to the left, from the last digit in the answer.

  37. Lesson 17: Decimal Point Placement – Multiplying Decimals Exercise 21: multiply the following decimals:

  38. Lesson 18:Powers of 10 Rules about multiplying by tens, hundreds and thousands: Rule 1: When multiply x 10 you move the decimal point ONE place to the right. Rule 2: When multiply x 100 you move the decimal point TWO places to the right. Rule 3: When multiply x 1000 you move the decimal point THREE places to the right. example: 8.45 x 10 = 84.5 8.458 x 100 = 845.8 8.458 x 1000 = 8458 If the number does not have enough decimal places, we add 2 or 3 zeroes.

  39. Lesson 18:Powers of 10 example: 8.4 x 1000 = 8.400 x 1000 =8400. Exercise 22: Multiply these numbers by 10, 100, 1000:

  40. Lesson 18:Powers of 10 example: 8.4 x 1000 = 8.400 x 1000 =8400. Exercise 22: Multiply these numbers by 10, 100, 1000:

  41. Lesson 18:Powers of 10 example: 8.4 x 1000 = 8.400 x 1000 =8400. Exercise 22: Multiply these numbers by 10, 100, 1000:

  42. Lesson 19: Dividing Decimals by a Whole Number Rule 1: When we divide decimals we must line up the decimal points. Rule 2: When dividing decimals, we do exactly what we do to divide any numbers, after we have lined up the decimal points Example:

  43. Lesson 19: Dividing Decimals by a Whole Number Exercise 23: Divide these numbers. Line up the decimal points first.

  44. Lesson 19: Dividing Decimals by a Whole Number Rule 3: When dividing a whole number, we must convert it to a decimal. We do this by putting 2 zeroes after the decimal point. Example:

  45. Now go to Lesson 1 Book 6 Decimals Part 2

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