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Good Afternoon!

Good Afternoon!. Today we will be learning about Converting decimals to fractions. Let’s warm up :. Divide:. 1) 57 ÷ 8. 1) 7.125. 2) 8.9825. 2) 35.93 ÷ 4. 3) 0.7222. 3) 13 ÷ 18. 4) 86.76 ÷ 15. 4) 5.784. 5) 94.42 ÷ 13. 5) 7.263.

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Good Afternoon!

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  1. Good Afternoon! Today we will be learning about Converting decimals to fractions Let’s warm up : Divide: 1) 57 ÷ 8 1) 7.125 2) 8.9825 2) 35.93 ÷ 4 3) 0.7222 3) 13 ÷ 18 4) 86.76 ÷ 15 4) 5.784 5) 94.42 ÷ 13 5) 7.263 CONFIDENTIAL

  2. Let’s first review what we learnt in the previous session before proceeding further. When we are given a long division to do, sometimes there will be numbers left over. These are known as Remainders. We can use the long division process to work out the answer toa number of decimal places. Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole number. If the divisor has a decimal in it, we can make it a whole number by moving the decimal point the appropriate number of places to the right. CONFIDENTIAL

  3. Review Divide: 5 ÷ 12. Round to the nearest hundredths place. Note: Since we must round to the hundredths place, we will carry the answer out 1 place beyond the hundredths place.) • Place the numbers in the division equation format. 12 5 0.4 • The dividend 5 is less than the divisor 12. Place a decimal point and bring it up to the quotient. 12 5.00 - 48 20 CONFIDENTIAL

  4. Review 0.416 12 5.000 • Add a 0 onto the dividend. Start dividing. The remainder is not zero, so add another zero to the dividend. - 48 20 - 12 80 - 72 8 The remainder is still not zero. The remainder continues to be 8. This is a repeating decimal. We need our answer rounded to the nearest hundredths place, so we are ready to round. 0.416 rounded to the nearest hundredths place is 0.42 CONFIDENTIAL

  5. Review We will saw another problem: Divide: 233.4 ÷ 4 • Place the numbers in the division equation format. 4 233.4 5 4 233.4 • Begin the division with 4 into 23 (since 4 cannot go into 2). This gives us 5 with a remainder of 3. - 20 3 CONFIDENTIAL

  6. Review 58 • Now bring down the next 3, so we must divide 33 by 4. This gives us 8 with a remainder of 1. 4 233.4 - 20 33 - 32 14 58.3 • Now bring down 4, so we must divide 14 by 4. Here, 4 occurs in the dividend after the decimal , so we put a decimal in the quotient after 8. This gives us 3 with a remainder of 2. 4 233.4 - 20 33 - 32 14 - 12 2 CONFIDENTIAL

  7. Review 58.35 4 233.40 • If after dividing you have a remainder, add a zero to the dividend and continue to divide until there is no remainder or the decimals recur. Now bring down the next 0, so we must divide 20 by 4. This gives us 5 with a remainder of 0. - 20 33 - 33 14 - 12 20 - 20 00 CONFIDENTIAL

  8. Let’s start Let us revise some terms before we proceed. FRACTION : A number that names part of a whole or part of a group. ¼ means 1 part of 4 parts, where 4 parts is the whole or group. DENOMINATOR: It is the number below the bar in a fraction. NUMERATOR: It is the number above the bar in a fraction. NUMERATOR ¼ FRACTION DENOMINATOR MIXED NUMBERS : A number named by a whole number and a fraction. CONFIDENTIAL

  9. So we see that, A fraction is based on the number into which the whole is divided (the denominator). The numerator (the top) is the PART, the denominator (the bottom) is the WHOLE. To convert a Decimal to a Fraction follow these steps: Step 1: • Count the decimal places • of the decimal starting from the decimal point. CONFIDENTIAL

  10. Step 2: • If there is one decimal place, place the number over 10. • If there are two decimal places, place the number over 100. • If there are three decimal places, • place the number over 1000. Step 3: • Simplify (or reduce) the fraction. CONFIDENTIAL

  11. Converting a Decimal to a Fraction with the help of a model Show the Decimal 0.45 with a model and express its equivalent fraction. Decimal 0.45 is represented by the pink portion shown in the grid. Here we see that, NUMERATOR Pink part: 45 DENOMINATOR Equal parts in all: 100 So, 45 of the area is pink. 100 CONFIDENTIAL

  12. Express 0.75 as a fraction Step 1:Write down the decimal. 0.75 1 x 100 Step 2:Multiply both top and bottom by 100 (because there were 2 digits after the decimal place). 0.75 = 75 1 100 x 100 CONFIDENTIAL

  13. ÷ 25 Step 3:Reduce the fraction. 75 = 3 100 4 Answer = 3 4 ÷ 25 Note:75 is called a decimal fraction and 3 is called a common fraction ! 1004 Convert 0.235 to a simple fraction. 47 200 CONFIDENTIAL

  14. Repeating decimal Express 5.233233…… as a fraction Step 1: Let x = 5.233233. Call this equation #1. Step 2: Count how many numbers there are in the repeating part. In this example, the repeating part is 233. So there are 3 numbers in the repeating part. Step 3: Multiply both sides by 1000, because 1000 has 3 zeroes. We get 1000x = 5233.233233... Call this equation #2. CONFIDENTIAL

  15. Step 4: Subtract equation #1 from equation #2. 1000x = 5233.233233 x = 5.233233 999x = 5228 Solving for x, we get x = 5228. 999 7858 999 Convert 7.865865……… to a simple fraction. CONFIDENTIAL

  16. BREAK CONFIDENTIAL

  17. GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/06-01-07-squirrel.html CONFIDENTIAL

  18. Assignments Express the following decimals as a fraction: 2) 31 20 1) 0.4 2) 1.55 • 2 • 5 3) 2.274 4) 0.4573 3) 1137 500 4) 4573 10000 CONFIDENTIAL

  19. Express the following repeating decimals as a fraction: 5) 245 33 6) 5451 999 5) 7.4242 6) 5.456456 7) 418 111 7) 3.765765 8) 9.2323 8) 914 99 CONFIDENTIAL

  20. 9) Show the Decimal 0.07 with a model and express its equivalent fraction. Decimal 0.07 is represented by the pink portion shown in the grid. Here we see that, NUMERATOR Pink part: 7 DENOMINATOR Equal parts in all: 100 9) So, 7 of the area is pink. 100 CONFIDENTIAL

  21. 10) Express 1.392392…… as a fraction. 10) 1392 999 CONFIDENTIAL

  22. Very Good! Let's Review So we saw that, A fraction is based on the number into which the whole is divided (the denominator). The numerator (the top) is the PART, the denominator (the bottom) is the WHOLE. To convert a Decimal to a Fraction follow these steps: Step 1: • Count the decimal places, of the decimal starting from the decimal point. Step 2: • If there is one decimal place, place the number over 10. • If there are two decimal places, place the number over 100. • If there are three decimal places, place the number over 1000. Step 3: • Simplify (or reduce) the fraction. CONFIDENTIAL

  23. Review Converting a Decimal to a Fraction with the help of a model Show the Decimal 0.45 with a model and express its equivalent fraction. Decimal 0.45 is represented by the pink portion shown in the grid. Here we see that, NUMERATOR Pink part: 45 DENOMINATOR Equal parts in all: 100 So, 45 of the area is pink. 100 CONFIDENTIAL

  24. Review Express 0.75 as a fraction Step 1:Write down the decimal. 0.75 1 x 100 Step 2:Multiply both top and bottom by 100 (because there were 2 digits after the decimal place). 0.75 = 75 1 100 x 100 CONFIDENTIAL

  25. Review ÷ 25 Step 3:Reduce the fraction. 75 = 3 100 4 Answer = 3 4 ÷ 25 Note:75 is called a decimal fraction and 3 is called a common fraction ! 1004 CONFIDENTIAL

  26. Review Repeating decimal Express 5.233233…… as a fraction Step 1: Let x = 5.233233. Call this equation #1. Step 2: Count how many numbers there are in the repeating part. In this example, the repeating part is 233. So there are 3 numbers in the repeating part. Step 3: Multiply both sides by 1000, because 1000 has 3 zeroes. We get 1000x = 5233.233233... Call this equation #2. Step 4: Subtract equation #1 from equation #2. 1000x = 5233.233233 x = 5.233233 999x = 5228 Solving for x, we get x = 5228. 999 CONFIDENTIAL

  27. You have done a nice job. See you in the next session. CONFIDENTIAL

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