This lesson explains how to read and work with decimals. Lesson # 1 – What Are Decimals? This lesson explains how to read and work with decimals. Problem: You work in a medical lab and you need to tell your coworker how much medicine you need. “I need two tenths of a gram of insulin.” Saying numbers correctly can ensure everyone is talking about the same thing.

0 < 0.1 < 1 (0.1 is between 0 and 1, so it is a decimal) 15 Minute Math – Decimals Lesson # 1 – What Are Decimals? Decimals are numbers that are less than 1 but greater than 0 0 < 0.1 < 1 (0.1 is between 0 and 1, so it is a decimal) They appear to the right of the decimal point whole number decimal 39.1 “39” is the whole number part “.1” is the decimal part “39.1” is read… “Thirty-nine and one tenth” “0.1” is the same thing as “.1”. “.1” is just a lazy way of writing the number.

15 Minute Math – Decimals Lesson # 1 – What Are Decimals? ten-thousandths ten-thousands hundredths thousandths thousands hundreds tens ones tenths 1 2 3 4 5 6 7 8 9 10,000. + 2,000. + 300. + 40. + 5. + .6 + .07 + .008 + .0009 12,345.6789 The “3” is in the hundreds column, so there are “3 hundreds”. If all the other numbers were a 0, then the number would be 00300.0000, which is 300 (three hundred.) The “7” is in the hundredths column, so there are “7 hundredths.” If every other number were a 0, then the number would be 00000.0700, which is 0.07 (seven hundredths.) Remember, decimals have a “th” at the end of their names.

15 Minute Math – Decimals Lesson # 1 – What Are Decimals? 2) Where you see the decimal point, say “and” To read a number… For example: 20.045 is read, “Twenty and forty-five thousandths.” 0.2 = 0.20 = 0.200 but… 0.2 = “two tenths” 0.20 = “twenty hundredths” 0.200 = “two hundred thousandths“ 4) Say the column name where the last number is 1) Read the whole number part 3) Read the decimal part tenths Extra zeroes to the far right of a decimal don’t change the value, but they do change how you pronounce the number. hundredths thousandths

15 Minute Math – Decimals Lesson # 1 – What Are Decimals? Try it yourself What numbers are these? Three and two hundredths = 3.02 Forty and two thousandth = Twelve and twelve hundredths = Eighty and eighty ten-thousands = How do you say these numbers? 37.03 = Thirty-seven and three hundredths 9.04 = 20.040 = 100.01 = Which of these are true: A) 2.01 = 2.010 B) 2.01 = 2.001 C) 2.001 = 2.100 D) 2.10 = 2.010 E) 2.10 = 2.100 F) 2.0010 = 2.001 Click for answers: Forty and two thousandth = 40.002 Twelve and twelve hundredths = 12.12 Eighty and eighty ten-thousands = 80.0080 9.04 = nine and four hundredths 20.040 = twenty and forty thousands 100.01 = one hundred and one hundredth A, E, and F are true End of Lesson 1

15 Minute Math – Decimals Lesson # 2 – Addition & Subtraction This lesson explains how to add and subtract numbers that have a decimal point. Problem: You need to take 3 grams of pain medication. You’ve already taken 0.75 grams of pain medication from a multi-purpose formula. How much more medication do you need? 3.00 -0.75 2.25 When adding and subtracting numbers with decimal points, ALWAYS line up the decimal points!

15 Minute Math – Decimals Lesson # 2 – Addition & Subtraction Line up the decimals points Put zeroes in the blank spaces to help you see what you’re adding 24.3 + 18.45  24.30 18.62 – 3.8  18.62 +18.45 - 3.80 42.75 14.82 1 7 / 1 When adding, don’t forget to carry when numbers add up to more than 10. When subtracting, don’t forget to borrow if the top number is smaller than the bottom number.

For example, $15 can also be written as $15.00 15 Minute Math – Decimals Lesson # 2 – Addition & Subtraction All numbers have a decimal point, even if you can’t see it. For example, $15 can also be written as $15.00 20 + 4.02  20.00 100 – 25.783  100.000 + 4.02 - 25.783 24.02 74.217 9 9 9 9 1 / / / / / Even if you don’t see the decimal point, it’s actually at the end. 100 = 100. = 100.00 Remember when you’re borrowing, you can’t borrow from nothing (zero). Make sure you borrow all the way over to the first non-zero number you find.

15 Minute Math – Decimals Lesson # 2 – Addition & Subtraction Try it yourself 2.89 + 1.5 = 20.6 + 10.9 = 3.13 + 9 = 20 + 8.2 = 9.373 + 3.34 = 9 + 2.8 = 12.99 – 8.1 = 19 – 3.2 = 2.933 – 1.2 = 8.4 – 5.555 = 20 – 2.5 = 100 – 2.66 = Click for answers: 2.89 + 1.5 = 4.39 20.6 + 10.9 = 31.5 3.13 + 9 = 12.13 20 + 8.2 = 28.2 9.373 + 3.34 = 12.713 9 + 2.8 = 11.8 12.99 – 8.1 = 4.89 19 – 3.2 = 15.8 2.933 – 1.2 = 1.733 8.4 – 5.555 = 2.845 20 – 2.5 = 17.5 100 – 2.66 = 97.34 End of Lesson 2

15 Minute Math – Decimals Lesson # 3 – Multiplication This lesson explains how to multiply numbers that have a decimal point. Problem: You need to buy 12 cans of paint costing $5.29 each. How much will you pay? 5.29 × 12 63.48 When multiplying numbers with decimal points, count the total number of numbers to the right of the decimal point in the problem and make sure the answer has the same number!

15 Minute Math – Decimals Lesson # 3 – Multiplication Don’t worry about the decimal until you’re done multiplying everything First multiply, and then count up the places to the right of the decimal point and put the decimal in the answer. 3.51 x 1.4  351 ×14 1404 +3510 4914 first, multiply 351 by 4 then, multiply 351 by 10 then, add up the numbers last, since there are a total of 3 decimal places in the problem, start from the right and move the decimal 3 places to the left in the answer (the problem has 3 decimal places and so does the answer) 3 decimal places  4.914 So, 3.51 x 1.4 = 4.914!

15 Minute Math – Decimals Lesson # 3 – Multiplication Remember to only count numbers to the RIGHT of the decimal point. 2.3 × 0.0002  23 × 2 46 Sometimes you may see .00046 instead of 0.00046. Both are right, but it’s more common to put a 0 in the ones place.  0.00046 5 decimal places 5 decimal places So, 2.3 x 0.0002 = 0.00046!

15 Minute Math – Decimals Lesson # 3 – Multiplication There are some shortcuts you can take if you’re multiplying by a multiple of 10. Multiples of 10 are things like 10, 100, 1000 and also things like 0.1, 0.01, 0.001, etc. shift the decimal left 4 places (if you move the decimal point right (don’t see the decimal point it’s at the end) 2 spaces (100 has 2 0’s) 297 × 0.0001 = 0.0297 2.309 × 100 = 230.9 Try not to think about if you’re moving the decimal to the right or the left. Think if you need to make the number larger (because you’re multiplying by a number bigger than 1) or if you need to make the number smaller (because you’re multiplying by a number between 0 and 1). Then move the decimal point in the direction that will make the number bigger or smaller. 4 decimal places

15 Minute Math – Decimals Lesson # 3 – Multiplication Try it yourself 27.2 × 9.2 = 3.2904 × 0.22 = 62.5 × 12.8 = 38 × 0.25 = 0.034 × 0.026 = 8.02 × 2.1 = 2.04 × 0.001 = 589 × 100 = 10.2 × 1.2 = 0.34 × 0.5 = 5.89 × 100 = 9.9999 × 0.01 = Click for answers: 27.2 × 9.2 = 250.24 3.2904 × 0.22 = 0.723888 62.5 × 12.8 = 800 38 × 0.25 = 9.5 0.034 × 0.026 = 0.000884 8.02 × 2.1 = 16.842 2.04 × 0.001 = 0.00204 589 × 100 = 58,900 10.2 × 1.2 = 12.24 0.34 × 0.5 = 0.17 5.89 × 100 = 589 9.9999 × 0.01 = 0.099999 End of Lesson 3

This lesson explains how to divide numbers that have a decimal point. 15 Minute Math – Decimals Lesson # 4 – Division This lesson explains how to divide numbers that have a decimal point. Problem: A wall measures 96.5 inches tall. You need to install 3.25 inch tall siding panels. How many panels do you need? 26.5 3.25|96.5 When dividing numbers with decimal points, decimal point placement is key.

15 Minute Math – Decimals Lesson # 4 – Division Remind yourself of the steps you need to take when dividing Divide Multiply Subtract Bring down one more number and do it again 8 21|172263 -168 4 42 8203 21|172263 -168 42 -42 06 - 0 63 -63

15 Minute Math – Decimals Lesson # 4 – Division Step 1 - Move the decimal of the divisor (outside the house) as far to the right as you can Step 2 - Move the decimal of the dividend (inside the house) by the same number of spaces Step 3 - Move the decimal straight up onto the answer line Step 4 - Divide like normal Problem 8.91 ÷ 3.3 Steps 1 & 2  3.3 |8.91  33 |89.1 Step 3 . 33 |89.1 Step 4 2.7 33 |89.1 - 66 231 - 231 Think of the division sign, | , like a house. With all division problems, the first number goes inside the house (the 8.91) and the second goes outside the house (3.3). If you forget, think about a problem you know. 10 ÷ 2 = 5. You wouldn’t say 10 | 2. To work it out you’d say 2 |10 (2 goes into 10.)

15 Minute Math – Decimals Lesson # 4 – Division Problem 8.91 ÷ 0.33 Steps 1 & 2  0.33 |8.91  33 |891. Step 3 . 33 |891. Step 4 27. 33 |891. - 66 231 - 231 Move the decimal 2 places to the right Problem 8.91 ÷ 0.0033 Steps 1 & 2  0.0033 |8.91  33 |89100. Step 3 . 33 |89100. Step 4 2700. 33 |89100. - 66 231 - 231 Move the decimal 2 places to the right Fill in the empty spaces with zeroes

15 Minute Math – Decimals Lesson # 4 – Division Try it yourself 3.2 ÷ 64 = 60.8 ÷ 19 = 187.53 ÷ 3 = 3.2 ÷ 6.4 = 60.8 ÷ 0.19 = 187.53 ÷ 0.03 = 32 ÷ 6.4 = 0.608 ÷ 0.19 = 18753 ÷ 0.3 = 32 ÷ 0.00064 = 608 ÷ 1.9 = 0.0018753 ÷ 0.3 = Click for answers: 3.2 ÷ 64 = 0.05 60.8 ÷ 19 = 3.2 187.53 ÷ 3 = 62.51 3.2 ÷ 6.4 = 0.5 60.8 ÷ 0.19 = 320 187.53 ÷ 0.03 = 6251 32 ÷ 6.4 = 5 0.608 ÷ 0.19 = 3.2 18753 ÷ 0.3 = 62510 32 ÷ 0.00064 = 50000 608 ÷ 1.9 = 320 0.0018753 ÷ 0.3 = 0.006251 End of Lesson 4