Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Paolo helped in the community garden for
2(3)/(4) hours this week. That was
1(5)/(6) equal-length shifts, because Paolo stopped early one day when it started to rain.
How long is a single shift? hours

Paolo helped in the community garden for $2 \frac{3}{4}$ hours this week. That was $1 \frac{5}{6}$ equal-length shifts, because Paolo stopped early one day when it started to rain. $\newline$ How long is a single shift? $\newline$ hours

View step-by-step help

View step-by-step help

GCF and LCM: word problems

Full solution

Q. Paolo helped in the community garden for

2 \frac{3}{4}

hours this week. That was

1 \frac{5}{6}

equal-length shifts, because Paolo stopped early one day when it started to rain.

\newline

How long is a single shift?

\newline

hours

Convert to Improper Fractions: Convert the mixed numbers to improper fractions to make the calculations easier. $\newline$ $2\left(\frac{3}{4}\right)$ hours can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and then placing the result over the original denominator. $\newline$ $2\left(\frac{3}{4}\right) = \left(2 \times 4 + 3\right)/4 = \left(8 + 3\right)/4 = \frac{11}{4}$ hours. $\newline$ $1\left(\frac{5}{6}\right)$ shifts can be converted in the same way. $\newline$ $1\left(\frac{5}{6}\right) = \left(1 \times 6 + 5\right)/6 = \left(6 + 5\right)/6 = \frac{11}{6}$ shifts.
Calculate Total Time Worked: To find the length of a single shift, divide the total hours worked by the number of shifts. $\newline$ We have $\frac{11}{4}$ hours for the total time worked and $\frac{11}{6}$ shifts. $\newline$ $(\frac{11}{4}) \div (\frac{11}{6}) = (\frac{11}{4}) \times (\frac{6}{11}) = \frac{11 \times 6}{4 \times 11}.$
Simplify Expression: Simplify the expression by canceling out the common factors. $\newline$ The number $11$ in the numerator and denominator cancels out, as does one factor of $2$ in the $6$ and $4$ . $\newline$ This leaves us with $\frac{6}{4}$ after canceling out $11$ , and then we simplify $\frac{6}{4}$ by dividing both the numerator and the denominator by $2$ . $\newline$ $\frac{6}{4} = \frac{(6/2)}{(4/2)} = \frac{3}{2}.$
Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary. $\newline$ $\frac{3}{2}$ hours is the same as $1\frac{1}{2}$ hours or $1.5$ hours. $\newline$ So, a single shift is $1\frac{1}{2}$ hours long.

More problems from GCF and LCM: word problems

Question

The Huffman Corporation would like to donate

15

20

printers to local schools. The corporation would like to make sure that each school receives the same set of computers and printers, with none left over. What is the greatest number of schools that The Huffman Corporation can donate to?

\newline

\_\_\_\_

Posted 2 months ago

Question

What is the greatest common factor of

2

14

\newline

Posted 2 months ago

Question

What is the least common multiple of

6

12

\newline

Posted 2 months ago

Question

Which numbers are factors of

20

? Select all that apply.

\newline

17

\newline

5

\newline

9

\newline

7

Posted 25 days ago

Question

Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Posted 2 months ago

Question

What is the greatest common factor of

35 y^{4}, 14 y^{4}

63 y^{4}

Posted 4 months ago

Question

What is the greatest common factor of

60 \mathrm{w}, 36 w^{2}

24 w^{4}

Posted 1 month ago

Question

Find the greatest common factor of

75

8

21

Posted 4 months ago

Question

Find the greatest common factor of

110

40

120

Posted 4 months ago

Question

What is the greatest common factor of

6 a, 8 a^{2}

14

Posted 4 months ago