This is a complete lesson with instruction & exercises for 5th grade about multiplying decimals by decimals. The interpretation for multiplying a decimal by a decimal is to think of it as taking a fractional part of a decimal number (the symbol × translates to "of"). The lesson compares multiplication by a decimal to scaling & shrinking a stick. Lastly, it shows the common shortcut to decimal multiplication (multiply as if there were no decimal points; the answer has as many decimals as the factors have in total.) In the video below, I explain the rule for multiplying decimals (put as many decimal digits in the answer as there are in the factors.) I explain where this rule comes from, using fraction multiplication. The lesson continues below the video. You have learned to think of
multiplication by a whole number, such as 3 × 4 or 8 × 0.6, as repeated Example. 0.1 × 80 means finding one-tenth “of” 80. That is simply 8. Example. 0.4 × 80 means finding four-tenths “of” 80. Since one-tenth of 80 is 8, then 0.4 of 80 is four times as much, or 32. Example. 0.02 × 3,000 means finding two-hundredths of 3,000. Since one-hundredth of 3,000 is 30, then 0.02 of 3,000 is two times as much, or 60. 1. Write as a multiplication using a decimal, and solve. Remember, "of" translates into "×". Use the
2. Solve. Use the top problem in each box to help you solve the bottom one.
3. Answer. You do not have to calculate. a. You have learned that 0.1 × 246 means one-tenth of 246. b. Also, 0.1 × 0.8 means one-tenth of 0.8. c. Will the result of 1.9 × 928 be more or less than 928?
4. The stick is being shrunk. How long will it be in pixels? Compare the problems.
Let’s expand this stick (40 px) to be 1.2 times as long: →We can write a multiplication: 1.2 × =To calculate how long it is in pixels, let’s first figure out what 0.2 of 40 is. 5. The red stick is 50 pixels long. It is being expanded or shrunk. Fill in the blanks.
6. Tell if the resulting stick after being "multiplied" will be shorter or longer than the original.
7. Fill in Anita’s reasoning.
8. Multiply first as if there were NO decimal points. Then add the decimal point to the answer.
9. Multiply.
10. Solve.
Potatoes cost $1.20 / kg. If you buy 23 kilograms, you multiply 23 × $1.20 to find the total price. If you buy 0.8 kg, you do the same: multiply the price by 0.8. To find 0.8 × $1.20, first multiply without the decimal point: 8 × 120 = 960. The factors have Note that the answer also makes sense: 0.8 kg
of potatoes should cost a bit less than 1 kg of 11. Find the total cost. Write a multiplication. a. Ribbon costs $1.10 per meter, and you buy 0.4 meters. b. Nuts cost $8 per pound. You buy 0.3 pounds. c. A phone call costs $7 per hour. You talk for 1.2 hours. d. Lace costs $2.20 per meter, and you buy 1.5 meters. You can make worksheets for decimal multiplication here. This lesson is taken from Maria Miller's book Math Mammoth Decimals 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller. It addresses the Common Core Standard for 5th grade 5.NBT.7. Math Mammoth Decimals 2A self-teaching worktext for 5th-6th grade that covers the four operations with decimals up to three decimal digits, concentrating on decimal multiplication and division. The book also covers place value, comparing, rounding, addition and subtraction of decimals. There are a lot of mental math problems. Download ($6.25). Also available as a printed copy. => Learn more and see the free samples! When any given number greater than 0 is multiplied by a fraction greater than 1?When a positive whole number is multiplied by a fraction greater than 1, the product is greater than the whole number. When a positive whole number is multiplied by a fraction between 0 and 1, the product is less than the whole number.
How can multiplying by a whole number result in a product less than one?Whenever you multiply a positive number by a positive factor less than 1, the product will be smaller than the original number. For example, \frac 12 \times\frac 34 = \frac 38. Both factors are less than 1, and the product is less than both factors.
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