How do you cast nines?

Answer 1

Casting nines is a method of checking the accuracy of math calculations in addition,subtraction, multiplication and division. It is a "quick check" which flags wronganswers. A great many mistakes in calculation are the result of careless errors andpeople's reluctance to spend time checking their work. Casting nines is quick and easy,once mastered, and many students consider it a game. In many cases, students wholearn and apply this technique will get better grades and have more fun in math. Whenteachers don't have to deal with careless errors, it is possible to move on more quicklyto new math concepts. Warning: This checking method has one limitation. It canoccasionally fail to flag a wrong answer. This happens when a zero is added or left out,when there is a transposition such as 3,528 instead of 3,582, and in some other cases.To cast nines from a number, add the digits:17 1 + 7 = 8 8 is the result of casting the nines.If the sum of the digits is nine, cast (throw away) the nine. It becomes a zero.36 3 + 6 = 9 9 - 9 = 0 0 is the result of casting the nines.If the sum of the digits is more than nine, cast the nines. You will always end up withjust one digit when this is completed: 0, 1, 2, 3, 4, 5, 6, 7, or 8.28 2 + 8 = 10 10 - 9 = 1 1 is the result of casting the ninesInstead of subtracting the nine from a two-digit number as shown above, you may addthe two digits. The result is the same.28 2 + 8 = 10 1 + 0 = 1 1 is the result of casting the ninesHere is an example of casting nines from a large number:5,628 5 + 6 = 11, 1 + 1 (from the 11) = 22 (from the 5 + 6) + 2 (the next digit in 5,628) = 44 (from the 2 + 2 above) + 8 (next digit) = 12, 1 + 2 (from 12) = 33 is the result of casting nines from 5,628To speed up casting nines from large numbers, look for and cross out nines orcombinations which equal nine. Add the remaining digits. For example:5,629,384,2725,629,384,272 Cross out any nines.5,629,384,272 Cross out any combinations which make 9: 5+2+2, 6+3, 7+2Then add any digits still not crossed out: 8 + 4 = 12, 1 + 2 (from the 12) = 33 is the result of casting nines from 5,629,384,272.Once you are able to cast nines from any number, use it to check problems as shown on the next page.Casting NinesAdditionCast nines from both addends and add the one-digit results for the "check number"(circled). Cast nines from the sum. The results must match or the answer is wrong.addend 38 cast nines from 38: 3 + 8 = 11, 1 + 1 = 2addend +76 cast nines from 76: 7 + 6 = 13, 1 + 3 = + 4sum 114 add the two digits to get check number 6Then cast nines from the sum, 114: 1 + 1 = 2 + 4 = 6. This must match the checknumber. If there is no match, thoroughly check the problem to locate and fix the error.MultiplicationCast nines from the multiplicand and the multiplier and multiply the one-digit results forthe "check number" (circled). Cast nines from the product. The results must match.multiplicand 78 cast nines from 78: 7 + 8 = 15, 1 + 5 = 6multiplier x 8 cast nines from 8 (no nines to cast) = x 8product 624 multiply the two digits 48Cast nines from the 48 to get the 1-digit check number: 4 + 8 = 12, 1 + 2= 3Then cast nines from the product, 624: 6 + 2 = 8 + 4 = 12, 1 + 2 (from the 12) = 3SubtractionCast nines from the minuend and the subtrahend. Subtract for the "check number"(circled). Cast nines from the difference. The result must equal the check number.minuend 53 cast nines from 53: 5 + 3 = 8subtrahend - 38 cast nines from 38: 3 + 8 = 11, 1 + 1 = - 2difference 15 subtract the two digits to get check number 6Then cast nines from the difference, 15: 1 + 5 = 6. This must match the check number.In subtraction, the one-digit result on the bottom (subtrahend) may be larger than that on the top (minuend). If this occurs, add a nine to the minuend so subtraction is possible, asshown below. Continue as shown above.minuend 93 cast nines from 93: 3 + 9 =12subtrahend - 44 cast nines from 44: 4 + 4 = - 8 - 8difference 49 subtract the two digits for check number can't do 4DivisionCast nines from the dividend to get the "check number" (circled). Cast nines from thequotient. Cast nines from the divisor. Cast nines from the remainder. Multiply the onedigitresults as is done normally in checking division: quotient times divisor plusremainder. The result must equal the check number.Cast 9's from dividend, 89, for 8 , the check number.quotient 14 r5 remainder quotient 14, 1 + 4 = 5 times divisor 6 = 30 (3 + 0 = 3)divisor 6 ) 89 dividend plus remainder 5 = 8. This matches check number.© 1995 Susan C. Anthony - Reproducible for use with students