Annexing O's to the Right of a Decimal We can annex as many O's to the right of a decimal as we please, and the form, but not the value is changed. Have the pupil state a principle now, in his own words. NOTE.-Do as much of this work by inspection, as possible. Don't, however, look for the impossible in oral work, as some teachers do. Reducing Decimals to a Common Denominator. At first, the pupil need only know that he may do this by Annexing O's to the right of each decimal until all have the same number of decimal figures. EXAMPLE: Reduce .5, .04, and .025 to a common denominator. .025 .500 .040 Simply write the number with most decimal figures first. Write the others under it and fill in with O's, as shown. The pupil from this can readily see that O's annexed to the right of a decimal do not change its value. ADDITION OF DECIMALS. There is just one thing to keep in mind here and that is: Write the numbers so that the decimal points are in a column. This is not even new to the child, for his work with United States money has made him familiar with it. EXAMPLE: Add 3.702, 2.3, 143.275, 60.756, 73.0046, 2736, .0042. NOTE. Since the O's in an addition do not affect the result, there is nothing new in the addition. It is an easy matter to explain to the child, or let him explain, why the numbers should be written with the decimal points in a column. It places units of the same value in a column. SUBTRACTION OF DECIMALS. Remember: Write the numbers so that the decimal point of the subtrahend is directly under the decimal point in the minuend. Then subtract as in integers, placing a decimal point in the remainder, directly under the decimal points above. EXAMPLE: From 42.375 take 5.025. WORK: 42.375 - 5.025 37.350 For convenience, at first, it is well to write the decimals with a common denominator, before subtracting. EXAMPLE: From 7.5 take .002. WORK: 7.500 - .002 7.498 Write a number of examples in this way, until the pupil becomes familiar with the principle. After that, he need not actually write the O's to make a common denominator. He may imagine them written. MULTIPLICATION OF DECIMALS. Perhaps the simplest way to help the child to know the place of the decimal point in the product, is the one given here: Ask him to find the product of the common fractions, and. 18 × 3 = 18. Now, let him write the fractions as decimals, and multiply. He gets 15. He will see at once where to put the decimal point to make it hundredths, .15. Give other examples like: He will see that, in order to write the 21 as a decimal fraction, whose denominator is thousandths, he must put a 0 before the 2, and the decimal point before that. After drill on these, the pupil is ready to tell you, or to be told (it matters little, as he is ready to remember it), that The product always has as many decimal places as both the multiplicand and multiplier. Another Way: For those who prefer it, the reason for the position of the decimal point in the product may be explained as in the following: EXAMPLE: Multiply 27.3 by 14. WORK: 27.3 × 14 109.2 273.0 382.2 EXPLANATION: We multiply the 3 tenths by 4 and get 12 tenths, or, 1 and 2 tenths. We write the 2 tenths. Multiplying 7 by 4, we get 28; 28+ 1 = 29. Write the 9. Multiplying 2 by 4, we get 8; 8+2=10. Write the 10. = Multiplying the 3 tenths by 10, we get 30 tenths; 30 tenths 3, and 0 tenths. Write 0 in tenths' place. Multiplying 7 by 10, we get 70. 70+3=73. Write 3. Multiplying 2 by 10, we get 20. 20+7=27. Write 27. After adding, we find we have 1 decimal place in the product. By using a few examples like this, the truth of the fact regarding the place of the decimal point in the product, may be established. NOTE. The explanation by means of the use of both common fractions and decimals, is to be preferred in most cases. Older and more matured pupils may grasp the latter plan. pupils will have difficulty with it for a time. 1. .025 .4 =? EXAMPLES. 2. 4.25 × 1.9. =? Young |