1. PART OF A WHOLE. Exercise 1. Verbal Problems Involving Fractions 41

Size: px

Start display at page:

Download "1. PART OF A WHOLE. Exercise 1. Verbal Problems Involving Fractions 41"

Clement Price
5 years ago
Views:

1 Verbal Problems Involving Fractions. PART OF A WHOLE A fraction represents a part of a whole. In dealing with fractional problems, we are usually dealing with a part of a quantity. Andrea and Danny ran for president of the ath Club. Andrea got votes, while Danny got the other 0. What part of the votes did Andrea receive? Andrea got votes out of. That is or of the votes. Exercise. In a class there are boys and girls. What part of the class is girls?. A team played 0 games and lost. What part of the games played did it win? 0 0. What part of an hour elapses between : p.m. and :0 p.m.?. A camp employs men, women, girls, and boys. In the middle of the summer, girls are fired and replaced by women. What part of the staff is then made up of women? 0

2 Chapter. There are three times as many seniors as juniors at a high school Junior-Senior dance. What part of the students present are juniors?. What part of a yard is ft. in.?. anorville High had a meeting of the Student Senate, which was attended by 0 freshmen, sophomores, juniors, and seniors. What part of the students present at the meeting were sophomores? 0. The Dobkin family budgets its monthly income as follows: for food, for rent, 0 for clothing, and for savings. What part is left for other expenses? 0 0

3 Verbal Problems Involving Fractions. FINDIN FRACTIONS OF FRACTIONS of. This involves multiply- any problems require you to find a fractional part of a fractional part, such as ing the fractions together, of is. of the employees of r. rown s firm earn over $0,000 per year. of the remainder earn between $,000 and $0,000. What part of the employees earns less than $,000 per year? earn over $0,000. of or earn between $,000 and $0,000. That accounts for + or of all employees. Therefore, the other earn less than $,000. A full bottle of isopropyl alcohol is left open in the school laboratory. If of the isopropyl alcohol evaporates in the first hours and of the remainder evaporates in the second hours, what part of the bottle is full at the end of hours? evaporates during the first hours. of or evaporates during the second hours. This accounts for of the isopropyl alcohol. Therefore, of the bottle is still full. Exercise. rs. Natt spent of the family income one year and divided the remainder between different savings banks. If she put $000 into each bank, what was the amount of her family income that year? $000 $,000 $,000 $,000 $000. After selling of the suits in his shop before Christmas, r. ross sold the remainder of the suits at the same price per suit after Christmas for $00. What was the income from the entire stock? $000 $00 $00 $00 $000

4 Chapter. Of this year s graduating seniors at South High, 0 will be going to college. Of these, will go to four-year colleges, while the rest will be going to two-year colleges. What part of the class will be going to two-year colleges?. 00 employees work for the etropolitan Transportation Company. of these are college graduates, while of the remainder are high school graduates. What part of the employees never graduated from high school? 0. Sue and Judy drove from New York to San Francisco, a distance of 000 miles. They covered 0 of the distance the first day and of the remaining distance the second day. How many miles were left to be driven?

5 Verbal Problems Involving Fractions. FINDIN WHOLE NUERS When a fractional part of a number is given and we wish to find the number representing the whole, it is often easiest to translate the words into mathematical symbols and solve the resulting equation. Norman buys a used car for $00, which is of the original price. Find the original price. 00 = x ultiply by. 000 = x $000 = x The gas gauge on ary s car reads full. She asks the gasoline attendant to fill the tank and finds she needs gallons. What is the capacity of her gas tank? of the tank is empty and requires gallons to fill. x = ultiply by. x = x = Exercise. Daniel spent $.0 for a ticket to the movies. This represents of his allowance for the week. What did he have left that week for other expenses? $.00 $.00 $. $. $.0. 0 seniors attended the prom. This represents of the class. How many seniors did not attend the prom? A resolution was passed by a ratio of :. If 00 people voted for the resolution, how many voted against it? r. Rich owns of a piece of property. If the value of his share is $,000, what is the total value of the property? $0,000 $,000 $,000 $0,000 $,000. The Stone family spends $00 per month for rent. This is of their total monthly income. Assuming that salaries remain constant, what is the Stone family income for one year? $ $000 $0,000 $,00 $,000

6 Chapter. SOLVIN WITH LETTERS When problems use letters in place of numbers, the same principles discussed earlier apply. If you are not sure which operations to use, replace the letters with numbers to determine the steps needed in the solution. It takes r. Cohen X days to paint his house. If he works for D days, what part of his house must still be painted? He has X - D days of painting left to do out of a total of X days; therefore, X - D is the correct X answer. Sue buys 00 stamps. X of these are 0-cent stamps. of the remainder are -cent stamps. How many -cent stamps does she buy? She buys 00 - X stamps that are not 0-cents stamps. of these are -cent stamps. Therefore, she buys 00 - X ( ) or 00 - X -cent stamps. John spent $X on the latest hit record album. This represents of his weekly allowance. What is his weekly allowance? Translate the sentence into an algebraic equation. Let A = weekly allowance X = A ultiply by. X = A

7 Verbal Problems Involving Fractions Exercise. A class contains boys and girls. What part of the class is boys? men agreed to rent a ski lodge for a total of D dollars. y the time they signed the contract, the price had increased by $00. Find the amount each man had to contribute as his total share. D D +00 D +00 D D. Of S students in ryant High, study French. of the remainder study Italian. How many of the students study Italian? S S S S S. r. and rs. Feldman took t dollars in travelers checks with them on a trip. During the first week, they spent of their money. During the second week, they spent of the remainder. How much did they have left at the end of the second week? t t t t t. Frank s gas tank was full. After putting in gallons of gasoline, the tank was full. What was the capacity of the tank.

Summer Math Packet for Entering Algebra 1 Honors Baker High School

Summer Math Packet for Entering Algebra 1 Honors Baker High School *You should be fluent in operations with fractions involved (multiplying, dividing, adding, and subtracting). *You should know all of