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Unit 12 Exam
A group of people are going on a 5 mile hike. They walked 
2(1)/(10) miles in the morning and 
1(1)/(4) miles during the first hour of the afterno on. How many miles do they have left to walk?
Give your answer in simplest form.

[?]([])/([])" miles "
Enter

Unit 1212 Exam\newlineA group of people are going on a 55 mile hike. They walked 2110 2 \frac{1}{10} miles in the morning and 114 1 \frac{1}{4} miles during the first hour of the afterno on. How many miles do they have left to walk?\newlineGive your answer in simplest form.\newline[?][][] miles  [?] \frac{[]}{[]} \text { miles } \newlineEnter

Full solution

Q. Unit 1212 Exam\newlineA group of people are going on a 55 mile hike. They walked 2110 2 \frac{1}{10} miles in the morning and 114 1 \frac{1}{4} miles during the first hour of the afterno on. How many miles do they have left to walk?\newlineGive your answer in simplest form.\newline[?][][] miles  [?] \frac{[]}{[]} \text { miles } \newlineEnter
  1. Convert to Improper Fractions: First, we need to convert the mixed numbers to improper fractions to make the addition easier.\newline2(110)2\left(\frac{1}{10}\right) miles in the morning can be converted as follows:\newline2(110)=(2×10+1)10=21102\left(\frac{1}{10}\right) = \frac{(2 \times 10 + 1)}{10} = \frac{21}{10} miles.
  2. Add Distances: Similarly, convert 1(14)1\left(\frac{1}{4}\right) miles during the first hour of the afternoon to an improper fraction:\newline1(14)=(1×4+1)/4=541\left(\frac{1}{4}\right) = \left(1 \times 4 + 1\right)/4 = \frac{5}{4} miles.
  3. Find Total Distance: Now, add the two distances together to find out how much they have walked in total: 2110\frac{21}{10} miles + 54\frac{5}{4} miles. To add these, we need a common denominator. The least common multiple of 1010 and 44 is 2020, so we convert both fractions to have a denominator of 2020. (2110)×(22)=4220(\frac{21}{10}) \times (\frac{2}{2}) = \frac{42}{20} (54)×(55)=2520(\frac{5}{4}) \times (\frac{5}{5}) = \frac{25}{20}
  4. Subtract Total Distance: Now add the two fractions: 4220+2520=(42+25)20=6720\frac{42}{20} + \frac{25}{20} = \frac{(42 + 25)}{20} = \frac{67}{20} miles.
  5. Convert to Mixed Number: To find out how many miles they have left to walk, subtract the total distance walked from the total hike distance:\newline55 miles - 6720\frac{67}{20} miles.\newlineFirst, convert 55 miles to a fraction with a denominator of 2020 to make the subtraction easier:\newline55 miles = (5×20)/20(5 \times 20)/20 = 10020\frac{100}{20} miles.
  6. Convert to Mixed Number: To find out how many miles they have left to walk, subtract the total distance walked from the total hike distance: 55 miles - 6720\frac{67}{20} miles. First, convert 55 miles to a fraction with a denominator of 2020 to make the subtraction easier: 55 miles = (5×20)/20=10020(5 \times 20)/20 = \frac{100}{20} miles.Now subtract the distance walked from the total distance: 10020\frac{100}{20} miles - 6720\frac{67}{20} miles = (10067)/20=3320(100 - 67)/20 = \frac{33}{20} miles.
  7. Convert to Mixed Number: To find out how many miles they have left to walk, subtract the total distance walked from the total hike distance:\newline55 miles - 6720\frac{67}{20} miles.\newlineFirst, convert 55 miles to a fraction with a denominator of 2020 to make the subtraction easier:\newline55 miles = (5×20)/20(5 \times 20)/20 = 10020\frac{100}{20} miles.Now subtract the distance walked from the total distance:\newline10020\frac{100}{20} miles - 6720\frac{67}{20} miles = 1006720\frac{100 - 67}{20} = 6720\frac{67}{20}00 miles.The fraction 6720\frac{67}{20}00 is an improper fraction, and it can be converted to a mixed number to make it easier to understand:\newline6720\frac{67}{20}00 = 6720\frac{67}{20}33 = 6720\frac{67}{20}44 miles.