← Express minutes as fractions of an hour · Elapsed Time and Base-Sixty Regrouping

Express minutes as fractions of an hour · 12 practice problems

5.MD.A.15.NF.A.15.NF.A.2

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 2 hours 40 minutes

To get to her grandmother's house, Mia rode a train for 2142\dfrac{1}{4} hours, rode a bus for 55 minutes, and walked for 13\dfrac{1}{3} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 2 and 1 over 4 hours by train, 5 minutes by bus, and 1 over 3 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 2142\frac{1}{4} hours.
  • Bus: 5 minutes.
  • Walk: 13\frac{1}{3} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 5 minutes is 5 sixtieths of an hour.
560=112 h\frac{5}{60} = \frac{1}{12}\ \text{h}
The bus leg is 112\frac{1}{12} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
2 whole hours is 8 4ths, plus the 1 already there.
214=942\frac{1}{4} = \frac{9}{4}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
3 is the smallest number all three denominators divide.
01+01+13\frac{0}{1} + \frac{0}{1} + \frac{1}{3}
Everything now counts 3ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
83=223 h\frac{8}{3} = 2\frac{2}{3}\ \text{h}
2 whole hours and 23\frac{2}{3} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
23\frac{2}{3} of 60 minutes gives the minutes part.
23×60=40\frac{2}{3} \times 60 = 40
The trip takes 2 hours 40 minutes.
Answer: 2 hours 40 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 135 min, the bus 5, the walk 20 -- 160 minutes in all, which is 2 h 40 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 160 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 3.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 2 easy answer: 3 hours 5 minutes

To get to her grandmother's house, Mia rode a train for 2342\dfrac{3}{4} hours, rode a bus for 1010 minutes, and walked for 16\dfrac{1}{6} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 2 and 3 over 4 hours by train, 10 minutes by bus, and 1 over 6 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 2342\frac{3}{4} hours.
  • Bus: 10 minutes.
  • Walk: 16\frac{1}{6} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 10 minutes is 10 sixtieths of an hour.
1060=16 h\frac{10}{60} = \frac{1}{6}\ \text{h}
The bus leg is 16\frac{1}{6} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
2 whole hours is 8 4ths, plus the 3 already there.
234=1142\frac{3}{4} = \frac{11}{4}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
12 is the smallest number all three denominators divide.
114+16+16\frac{11}{4} + \frac{1}{6} + \frac{1}{6}
Everything now counts 12ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
3712=3112 h\frac{37}{12} = 3\frac{1}{12}\ \text{h}
3 whole hours and 112\frac{1}{12} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
112\frac{1}{12} of 60 minutes gives the minutes part.
112×60=5\frac{1}{12} \times 60 = 5
The trip takes 3 hours 5 minutes.
Answer: 3 hours 5 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 165 min, the bus 10, the walk 10 -- 185 minutes in all, which is 3 h 5 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 185 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 12.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 3 easy answer: 2 hours 10 minutes

To get to her grandmother's house, Mia rode a train for 1341\dfrac{3}{4} hours, rode a bus for 1515 minutes, and walked for 16\dfrac{1}{6} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 1 and 3 over 4 hours by train, 15 minutes by bus, and 1 over 6 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 1341\frac{3}{4} hours.
  • Bus: 15 minutes.
  • Walk: 16\frac{1}{6} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 15 minutes is 15 sixtieths of an hour.
1560=14 h\frac{15}{60} = \frac{1}{4}\ \text{h}
The bus leg is 14\frac{1}{4} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
1 whole hours is 4 4ths, plus the 3 already there.
134=741\frac{3}{4} = \frac{7}{4}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
6 is the smallest number all three denominators divide.
76+16+16\frac{7}{6} + \frac{1}{6} + \frac{1}{6}
Everything now counts 6ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
136=216 h\frac{13}{6} = 2\frac{1}{6}\ \text{h}
2 whole hours and 16\frac{1}{6} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
16\frac{1}{6} of 60 minutes gives the minutes part.
16×60=10\frac{1}{6} \times 60 = 10
The trip takes 2 hours 10 minutes.
Answer: 2 hours 10 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 105 min, the bus 15, the walk 10 -- 130 minutes in all, which is 2 h 10 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 130 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 6.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 4 easy answer: 3 hours 15 minutes

To get to her grandmother's house, Mia rode a train for 2562\dfrac{5}{6} hours, rode a bus for 2020 minutes, and walked for 112\dfrac{1}{12} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 2 and 5 over 6 hours by train, 20 minutes by bus, and 1 over 12 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 2562\frac{5}{6} hours.
  • Bus: 20 minutes.
  • Walk: 112\frac{1}{12} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 20 minutes is 20 sixtieths of an hour.
2060=13 h\frac{20}{60} = \frac{1}{3}\ \text{h}
The bus leg is 13\frac{1}{3} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
2 whole hours is 12 6ths, plus the 5 already there.
256=1762\frac{5}{6} = \frac{17}{6}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
4 is the smallest number all three denominators divide.
01+14+01\frac{0}{1} + \frac{1}{4} + \frac{0}{1}
Everything now counts 4ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
134=314 h\frac{13}{4} = 3\frac{1}{4}\ \text{h}
3 whole hours and 14\frac{1}{4} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
14\frac{1}{4} of 60 minutes gives the minutes part.
14×60=15\frac{1}{4} \times 60 = 15
The trip takes 3 hours 15 minutes.
Answer: 3 hours 15 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 170 min, the bus 20, the walk 5 -- 195 minutes in all, which is 3 h 15 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 195 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 4.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 5 medium answer: 6 hours 5 minutes

To get to her grandmother's house, Mia rode a train for 5125\dfrac{1}{2} hours, rode a bus for 2020 minutes, and walked for 14\dfrac{1}{4} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 5 and 1 over 2 hours by train, 20 minutes by bus, and 1 over 4 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 5125\frac{1}{2} hours.
  • Bus: 20 minutes.
  • Walk: 14\frac{1}{4} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 20 minutes is 20 sixtieths of an hour.
2060=13 h\frac{20}{60} = \frac{1}{3}\ \text{h}
The bus leg is 13\frac{1}{3} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
5 whole hours is 10 2ths, plus the 1 already there.
512=1125\frac{1}{2} = \frac{11}{2}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
12 is the smallest number all three denominators divide.
112+13+14\frac{11}{2} + \frac{1}{3} + \frac{1}{4}
Everything now counts 12ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
7312=6112 h\frac{73}{12} = 6\frac{1}{12}\ \text{h}
6 whole hours and 112\frac{1}{12} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
112\frac{1}{12} of 60 minutes gives the minutes part.
112×60=5\frac{1}{12} \times 60 = 5
The trip takes 6 hours 5 minutes.
Answer: 6 hours 5 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 330 min, the bus 20, the walk 15 -- 365 minutes in all, which is 6 h 5 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 365 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 12.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 6 medium answer: 4 hours 10 minutes

To get to her grandmother's house, Mia rode a train for 3123\dfrac{1}{2} hours, rode a bus for 2525 minutes, and walked for 14\dfrac{1}{4} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 3 and 1 over 2 hours by train, 25 minutes by bus, and 1 over 4 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 3123\frac{1}{2} hours.
  • Bus: 25 minutes.
  • Walk: 14\frac{1}{4} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 25 minutes is 25 sixtieths of an hour.
2560=512 h\frac{25}{60} = \frac{5}{12}\ \text{h}
The bus leg is 512\frac{5}{12} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
3 whole hours is 6 2ths, plus the 1 already there.
312=723\frac{1}{2} = \frac{7}{2}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
6 is the smallest number all three denominators divide.
72+01+16\frac{7}{2} + \frac{0}{1} + \frac{1}{6}
Everything now counts 6ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
256=416 h\frac{25}{6} = 4\frac{1}{6}\ \text{h}
4 whole hours and 16\frac{1}{6} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
16\frac{1}{6} of 60 minutes gives the minutes part.
16×60=10\frac{1}{6} \times 60 = 10
The trip takes 4 hours 10 minutes.
Answer: 4 hours 10 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 210 min, the bus 25, the walk 15 -- 250 minutes in all, which is 4 h 10 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 250 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 6.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 7 medium answer: 4 hours 20 minutes

To get to her grandmother's house, Mia rode a train for 3133\dfrac{1}{3} hours, rode a bus for 3030 minutes, and walked for 12\dfrac{1}{2} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 3 and 1 over 3 hours by train, 30 minutes by bus, and 1 over 2 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 3133\frac{1}{3} hours.
  • Bus: 30 minutes.
  • Walk: 12\frac{1}{2} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 30 minutes is 30 sixtieths of an hour.
3060=12 h\frac{30}{60} = \frac{1}{2}\ \text{h}
The bus leg is 12\frac{1}{2} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
3 whole hours is 9 3ths, plus the 1 already there.
313=1033\frac{1}{3} = \frac{10}{3}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
3 is the smallest number all three denominators divide.
103+13+13\frac{10}{3} + \frac{1}{3} + \frac{1}{3}
Everything now counts 3ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
133=413 h\frac{13}{3} = 4\frac{1}{3}\ \text{h}
4 whole hours and 13\frac{1}{3} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
13\frac{1}{3} of 60 minutes gives the minutes part.
13×60=20\frac{1}{3} \times 60 = 20
The trip takes 4 hours 20 minutes.
Answer: 4 hours 20 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 200 min, the bus 30, the walk 30 -- 260 minutes in all, which is 4 h 20 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 260 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 3.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 8 medium answer: 2 hours 20 minutes

To get to her grandmother's house, Mia rode a train for 15121\dfrac{5}{12} hours, rode a bus for 3535 minutes, and walked for 13\dfrac{1}{3} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 1 and 5 over 12 hours by train, 35 minutes by bus, and 1 over 3 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 15121\frac{5}{12} hours.
  • Bus: 35 minutes.
  • Walk: 13\frac{1}{3} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 35 minutes is 35 sixtieths of an hour.
3560=712 h\frac{35}{60} = \frac{7}{12}\ \text{h}
The bus leg is 712\frac{7}{12} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
1 whole hours is 12 12ths, plus the 5 already there.
1512=17121\frac{5}{12} = \frac{17}{12}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
3 is the smallest number all three denominators divide.
01+01+13\frac{0}{1} + \frac{0}{1} + \frac{1}{3}
Everything now counts 3ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
73=213 h\frac{7}{3} = 2\frac{1}{3}\ \text{h}
2 whole hours and 13\frac{1}{3} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
13\frac{1}{3} of 60 minutes gives the minutes part.
13×60=20\frac{1}{3} \times 60 = 20
The trip takes 2 hours 20 minutes.
Answer: 2 hours 20 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 85 min, the bus 35, the walk 20 -- 140 minutes in all, which is 2 h 20 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 140 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 3.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 9 hard answer: 3 hours 25 minutes

To get to her grandmother's house, Mia rode a train for 2232\dfrac{2}{3} hours, rode a bus for 4040 minutes, and walked for 112\dfrac{1}{12} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 2 and 2 over 3 hours by train, 40 minutes by bus, and 1 over 12 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 2232\frac{2}{3} hours.
  • Bus: 40 minutes.
  • Walk: 112\frac{1}{12} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 40 minutes is 40 sixtieths of an hour.
4060=23 h\frac{40}{60} = \frac{2}{3}\ \text{h}
The bus leg is 23\frac{2}{3} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
2 whole hours is 6 3ths, plus the 2 already there.
223=832\frac{2}{3} = \frac{8}{3}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
12 is the smallest number all three denominators divide.
83+23+112\frac{8}{3} + \frac{2}{3} + \frac{1}{12}
Everything now counts 12ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
4112=3512 h\frac{41}{12} = 3\frac{5}{12}\ \text{h}
3 whole hours and 512\frac{5}{12} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
512\frac{5}{12} of 60 minutes gives the minutes part.
512×60=25\frac{5}{12} \times 60 = 25
The trip takes 3 hours 25 minutes.
Answer: 3 hours 25 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 160 min, the bus 40, the walk 5 -- 205 minutes in all, which is 3 h 25 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 205 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 12.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 10 hard answer: 5 hours 10 minutes

To get to her grandmother's house, Mia rode a train for 4164\dfrac{1}{6} hours, rode a bus for 4545 minutes, and walked for 14\dfrac{1}{4} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 4 and 1 over 6 hours by train, 45 minutes by bus, and 1 over 4 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 4164\frac{1}{6} hours.
  • Bus: 45 minutes.
  • Walk: 14\frac{1}{4} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 45 minutes is 45 sixtieths of an hour.
4560=34 h\frac{45}{60} = \frac{3}{4}\ \text{h}
The bus leg is 34\frac{3}{4} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
4 whole hours is 24 6ths, plus the 1 already there.
416=2564\frac{1}{6} = \frac{25}{6}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
6 is the smallest number all three denominators divide.
256+12+16\frac{25}{6} + \frac{1}{2} + \frac{1}{6}
Everything now counts 6ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
316=516 h\frac{31}{6} = 5\frac{1}{6}\ \text{h}
5 whole hours and 16\frac{1}{6} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
16\frac{1}{6} of 60 minutes gives the minutes part.
16×60=10\frac{1}{6} \times 60 = 10
The trip takes 5 hours 10 minutes.
Answer: 5 hours 10 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 250 min, the bus 45, the walk 15 -- 310 minutes in all, which is 5 h 10 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 310 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 6.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 11 hard answer: 2 hours 30 minutes

To get to her grandmother's house, Mia rode a train for 17121\dfrac{7}{12} hours, rode a bus for 5050 minutes, and walked for 112\dfrac{1}{12} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 1 and 7 over 12 hours by train, 50 minutes by bus, and 1 over 12 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 17121\frac{7}{12} hours.
  • Bus: 50 minutes.
  • Walk: 112\frac{1}{12} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 50 minutes is 50 sixtieths of an hour.
5060=56 h\frac{50}{60} = \frac{5}{6}\ \text{h}
The bus leg is 56\frac{5}{6} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
1 whole hours is 12 12ths, plus the 7 already there.
1712=19121\frac{7}{12} = \frac{19}{12}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
2 is the smallest number all three denominators divide.
01+01+01\frac{0}{1} + \frac{0}{1} + \frac{0}{1}
Everything now counts 2ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
52=212 h\frac{5}{2} = 2\frac{1}{2}\ \text{h}
2 whole hours and 12\frac{1}{2} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
12\frac{1}{2} of 60 minutes gives the minutes part.
12×60=30\frac{1}{2} \times 60 = 30
The trip takes 2 hours 30 minutes.
Answer: 2 hours 30 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 95 min, the bus 50, the walk 5 -- 150 minutes in all, which is 2 h 30 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 150 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 2.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.
Variant 12 hard answer: 2 hours 55 minutes

To get to her grandmother's house, Mia rode a train for 111121\dfrac{11}{12} hours, rode a bus for 5050 minutes, and walked for 16\dfrac{1}{6} hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Show solution
1 · Understandwhat's really being asked

Mia travels three ways: 1 and 11 over 12 hours by train, 50 minutes by bus, and 1 over 6 of an hour on foot. We need the total, given in hours and minutes.

Givens
  • Train: 111121\frac{11}{12} hours.
  • Bus: 50 minutes.
  • Walk: 16\frac{1}{6} hour.
Unknowns
  • The total travel time, in hours and minutes.
Constraints
  • Two legs are in hours and one is in minutes, so they cannot be added as they stand.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

Put every leg into hours first -- the bus leg is the only one that needs converting. Then it is a fraction addition, and the leftover fraction converts back into minutes at the end.

3 · Execute5 carry out the plan

1Make every part use the same unit

#8 Analyze the Units 5.MD.A.1
An hour is 60 minutes, so 50 minutes is 50 sixtieths of an hour.
5060=56 h\frac{50}{60} = \frac{5}{6}\ \text{h}
The bus leg is 56\frac{5}{6} of an hour.

2Write the train time as a single fraction

#7 Identify Subproblems 5.NF.A.1
1 whole hours is 12 12ths, plus the 11 already there.
11112=23121\frac{11}{12} = \frac{23}{12}
One improper fraction is easier to add than a mixed number.

3Give the fractions a common denominator

#7 Identify Subproblems 5.NF.A.1
12 is the smallest number all three denominators divide.
2312+56+16\frac{23}{12} + \frac{5}{6} + \frac{1}{6}
Everything now counts 12ths of an hour.

4Add the three times

#7 Identify Subproblems 5.NF.A.2
With one denominator, the numerators simply add.
3512=21112 h\frac{35}{12} = 2\frac{11}{12}\ \text{h}
2 whole hours and 1112\frac{11}{12} left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1
1112\frac{11}{12} of 60 minutes gives the minutes part.
1112×60=55\frac{11}{12} \times 60 = 55
The trip takes 2 hours 55 minutes.
Answer: 2 hours 55 minutes
4 · Reviewdoes it hold up?

Add in minutes as a check: the train is 115 min, the bus 50, the walk 10 -- 175 minutes in all, which is 2 h 55 min.

Another way: Converting everything to minutes first avoids fractions entirely and lands on the same 175 minutes; the fraction route is the one the unit asks for.

Standardsmin grade 5
  • 5.MD.A.1 Convert among different-sized standard measurement units within a given system — Converting the bus leg into hours and the remainder back into minutes.
  • 5.NF.A.1 Add and subtract fractions with unlike denominators — Putting all three legs over 12.
  • 5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Adding the three times into one total.
💡Takeaway. Mixed units cannot be added. Convert first, add second, and convert the leftover back at the end.