Answer:
15a) True 15b) False 15c) True
16)[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
Step-by-step explanation:
*Rewriting the question with Retrieved missing information:
15. Mr. Clements painted his barn for hours in the morning. He painted his barn [tex]3\frac{3}{5}[/tex] hours in the morning. He painted the barn for [tex]5\frac{3}{4}[/tex] hours in the afternoon.Select True or False for each statement.
15a. A common denominator of the mixed numbers is 20.
15b. The amount of time spent painting in the morning can be rewritten as [tex]3\frac{15}{20}[/tex]
15c. Mr. Clements spent [tex]2\frac{3}{20}[/tex]
hours longer painting in the afternoon than the morning.
16. Tom exercised:
[tex]\frac{4}{5}[/tex]
hour on Monday and
[tex]\frac{5}{6}[/tex]
hour on Tuesday. Part A. Complete the calculations below to write equivalent fractions with a common denominator.
15a) True
Turning the Mixed Numbers into Improper ones:
He painted the his barn:
[tex]3\frac{3}{5}=\frac{18}{5}[/tex] Keep the denominator, and for the numerator multiply the denominator 5 by 3 and add 3 = 18. (In the morning).
[tex]5\frac{3}{4}=\frac{23}{4}[/tex] (In the afternoon)
The Prime factorization [tex]\frac{23}{4},\frac{18}{5}[/tex] help us to obtain the common denomination, i.e. 20
15b) False
This is a matter of simplification. In this mixed number, the fraction can be simplified this way:
[tex]3\frac{15}{20}=3\frac{15:5}{20:5}\Rightarrow 3\frac{3}{4}[/tex]
15c) True
Subtracting the working hours, knowing the common denominator by prime factorization is 20.
For Mixed Numbers:
[tex]5\frac{3}{4}-3\frac{3}{5}=5\frac{15}{20}-3\frac{12}{20}=2\frac{3}{20}[/tex]
For the same mixed numbers turned into improper fractions:
[tex]\frac{23}{4}-\frac{18}{5}=\frac{115-72}{20}=\frac{43}{20}[/tex]
Notice that:
[tex]2\frac{3}{20}==\frac{43}{20}=2.15[/tex]
16A
Equivalent fractions are fractions multiplied by a same constant, on the numerator and denominator:
[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
