Answer:
A and E (top left and bottom middle)
Step-by-step explanation:
Unit rates are found when a ratio has a denominator of 1. For the sake of simplicity, I will give the options in the image letter designations. A, B, and C are the top three from left to right, and D, E, and F are the bottom 3 from left to right.
A
[tex]\frac{9}{5} miles:\frac{5}{6}hour[/tex]
Because ratios can be written as fractions, this ratio can be written:
[tex]\frac{\frac{9}{5}}{\frac{5}{6}}[/tex]
That's a mess! Another way to divide fractions is to multiply by the reciprocal of the denominator:
[tex]\frac{9}{5}*\frac{6}{5}[/tex]
Since none of the terms can be cross-cancelled, multiply!
[tex]=\frac{54}{25}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!
B
[tex]4miles:3\frac{1}{3}hours[/tex]
Start by turning the mixed number into an improper fraction:
[tex]3\frac{1}{3}=\frac{10}{3}[/tex]
Now compare by multiplying 4 over 1 by the reciprocal of 10 thirds:
[tex]\frac{4}{1}*\frac{3}{10}[/tex]
Cross-cancel and multiply:
[tex]=\frac{2}{5}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
C
[tex]2\frac{1}{2} miles:3hours[/tex]
Convert the mixed number into an improper fraction:
[tex]2\frac{1}{2} =\frac{5}{2}[/tex]
Multiply by the reciprocal of 3:
[tex]\frac{5}{2}*\frac{1}{3}[/tex]
Multiply!
[tex]\frac{5}{6}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
D
[tex]\frac{9}{5} miles :3hours[/tex]
Multiply by the reciprocal of 3:
[tex]\frac{9}{5}*\frac{1}{3}[/tex]
Cross cancel and multiply!
[tex]=\frac{3}{5}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
E
[tex]7 miles :\frac{3}{4}hour[/tex]
Multiply by the reciprocal of 3 fourths:
[tex]\frac{7}{1}*\frac{4}{3}[/tex]
Multiply:
[tex]=\frac{28}{3}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!
F
[tex]\frac{1}{3}mile:2\frac{3}{8}hours[/tex]
Convert the mixed number into an improper fraction:
[tex]2\frac{3}{8}=\frac{19}{8}[/tex]
Multiply one third by the reciprocal of 19 eighths:
[tex]\frac{1}{3}*\frac{8}{19}[/tex]
Multiply!
[tex]=\frac{8}{57}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
