2/3 of the students at Lamar High School are girls. Of those girls, 2/3 sing in the school choir. What fraction of students at Lamar High School are girls in choir?
If $2/3$ of the students in the school are girls, then there are $(2/3) \times 3/3=2/3$ of the total number of students who are girls. Because $(2/3)(1/3)=2/9$, $\boxed{\frac{2}{9}}$ of the students at Lamar High School are girls in choir.
twenty-four pencils are in a package. The students use 3/8 of the pencils. How many did they use?
Responses
A 8 pencils8 pencils
B 9 pencils9 pencils
C 12 pencils12 pencils
D 18 pencils
To find out how many pencils were used, we need to find $3/8$ of the total number of pencils.
To do this, we can multiply the total number of pencils by $3/8$.
$3/8 \cdot 24 = (3 \cdot 24)/8 = 72/8 = \boxed{9 \text{ pencils}}$
So the students used 9 pencils.
At West High School, 2/5 of the students play a sport. Of the students who play a sport, 1/4 play football. What fraction of the students at West High School play football?
To find the fraction of students at West High School who play football, we need to multiply the fraction of students who play a sport by the fraction of sport players who play football.
Fraction of students who play a sport: 2/5
Fraction of sport players who play football: 1/4
Multiplying these fractions, we get:
(2/5) * (1/4) = 2/20 = 1/10
Therefore, the fraction of students at West High School who play football is 1/10.
What is the value of the expression -13(21 4/9)?
Responses
278 7/9
B 8 1/4
C -278 7/9
D -34 1/4
To find the value of the expression $-13(21 \frac{4}{9})$, we need to first convert the mixed number $21 \frac{4}{9}$ to an improper fraction.
$21 \frac{4}{9} = \frac{21 \cdot 9 + 4}{9} = \frac{189 + 4}{9} = \frac{193}{9}$
Now, we can multiply $-13$ by $\frac{193}{9}$:
$-13 \cdot \frac{193}{9} = \frac{-13 \cdot 193}{9} = \frac{-2509}{9}$
This cannot be simplified further, so the value of the expression is $\boxed{-278 \frac{7}{9}}$, which is option C.
If a bookshelf is 28 1/81 inches long, how many 1 7/8 inch thick books will it hold?
respones
A 52 books52 books
B 35 books35 books
C 15 books15 books
D 48 books
To find out how many 1 7/8 inch thick books the bookshelf can hold, we need to divide the length of the bookshelf by the thickness of each book.
The length of the bookshelf is given as 28 1/81 inches.
The thickness of each book is given as 1 7/8 inches.
To divide the two fractions, we need to convert them to improper fractions.
28 1/81 = (28 * 81 + 1) / 81 = 2269 / 81
1 7/8 = (1 * 8 + 7) / 8 = 15 / 8
Now, we can divide 2269/81 by 15/8:
(2269/81) / (15/8) = (2269/81) * (8/15) = (2269 * 8) / (81 * 15) = 18152 / 1215
Simplifying further:
18152 / 1215 = 52 / 3
Therefore, the bookshelf can hold 52/3 books. Since we can't have a fraction of a book, we need to round this number down to the nearest whole number.
Hence, the bookshelf can hold $\boxed{17}$ books (option C).
A library loans out 3 books every day for a week and no books are returned. The following equation is written to represent the situation:
(−3)⋅7=−21
Which of the following best explains the meaning of −21 in the equation?
Responses
A Books were loaned out for −21 days.Books were loaned out for negative 21 days.
B The library now has −21 books.The library now has negative 21 books.
C The change in the number of books at the library over the course of the week was −21.The change in the number of books at the library over the course of the week was negative 21.
D The number of books loaned per day was −21.