Practice · Express minutes as fractions of an hour · Sensim Math

Variant 1 easy

To get to her grandmother's house, Mia rode a train for $2\dfrac{1}{4}$ hours, rode a bus for $5$ minutes, and walked for $\dfrac{1}{3}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $2\frac{1}{4}$ hours.
Bus: 5 minutes.
Walk: $\frac{1}{3}$ 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.

\frac{5}{60} = \frac{1}{12}\ \text{h}

The bus leg is

\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.

2\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.

\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.

\frac{8}{3} = 2\frac{2}{3}\ \text{h}

2 whole hours and

\frac{2}{3}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{2}{3}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $2\dfrac{3}{4}$ hours, rode a bus for $10$ minutes, and walked for $\dfrac{1}{6}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $2\frac{3}{4}$ hours.
Bus: 10 minutes.
Walk: $\frac{1}{6}$ 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.

\frac{10}{60} = \frac{1}{6}\ \text{h}

The bus leg is

\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.

2\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.

\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.

\frac{37}{12} = 3\frac{1}{12}\ \text{h}

3 whole hours and

\frac{1}{12}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{12}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $1\dfrac{3}{4}$ hours, rode a bus for $15$ minutes, and walked for $\dfrac{1}{6}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $1\frac{3}{4}$ hours.
Bus: 15 minutes.
Walk: $\frac{1}{6}$ 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.

\frac{15}{60} = \frac{1}{4}\ \text{h}

The bus leg is

\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.

1\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.

\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.

\frac{13}{6} = 2\frac{1}{6}\ \text{h}

2 whole hours and

\frac{1}{6}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{6}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $2\dfrac{5}{6}$ hours, rode a bus for $20$ minutes, and walked for $\dfrac{1}{12}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $2\frac{5}{6}$ hours.
Bus: 20 minutes.
Walk: $\frac{1}{12}$ 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.

\frac{20}{60} = \frac{1}{3}\ \text{h}

The bus leg is

\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.

2\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.

\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.

\frac{13}{4} = 3\frac{1}{4}\ \text{h}

3 whole hours and

\frac{1}{4}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{4}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $5\dfrac{1}{2}$ hours, rode a bus for $20$ minutes, and walked for $\dfrac{1}{4}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $5\frac{1}{2}$ hours.
Bus: 20 minutes.
Walk: $\frac{1}{4}$ 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.

\frac{20}{60} = \frac{1}{3}\ \text{h}

The bus leg is

\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.

5\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.

\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.

\frac{73}{12} = 6\frac{1}{12}\ \text{h}

6 whole hours and

\frac{1}{12}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{12}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $3\dfrac{1}{2}$ hours, rode a bus for $25$ minutes, and walked for $\dfrac{1}{4}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $3\frac{1}{2}$ hours.
Bus: 25 minutes.
Walk: $\frac{1}{4}$ 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.

\frac{25}{60} = \frac{5}{12}\ \text{h}

The bus leg is

\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.

3\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.

\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.

\frac{25}{6} = 4\frac{1}{6}\ \text{h}

4 whole hours and

\frac{1}{6}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{6}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $3\dfrac{1}{3}$ hours, rode a bus for $30$ minutes, and walked for $\dfrac{1}{2}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $3\frac{1}{3}$ hours.
Bus: 30 minutes.
Walk: $\frac{1}{2}$ 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.

\frac{30}{60} = \frac{1}{2}\ \text{h}

The bus leg is

\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.

3\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.

\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.

\frac{13}{3} = 4\frac{1}{3}\ \text{h}

4 whole hours and

\frac{1}{3}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{3}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $1\dfrac{5}{12}$ hours, rode a bus for $35$ minutes, and walked for $\dfrac{1}{3}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $1\frac{5}{12}$ hours.
Bus: 35 minutes.
Walk: $\frac{1}{3}$ 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.

\frac{35}{60} = \frac{7}{12}\ \text{h}

The bus leg is

\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.

1\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.

\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.

\frac{7}{3} = 2\frac{1}{3}\ \text{h}

2 whole hours and

\frac{1}{3}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{3}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $2\dfrac{2}{3}$ hours, rode a bus for $40$ minutes, and walked for $\dfrac{1}{12}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $2\frac{2}{3}$ hours.
Bus: 40 minutes.
Walk: $\frac{1}{12}$ 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.

\frac{40}{60} = \frac{2}{3}\ \text{h}

The bus leg is

\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.

2\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.

\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.

\frac{41}{12} = 3\frac{5}{12}\ \text{h}

3 whole hours and

\frac{5}{12}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{5}{12}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $4\dfrac{1}{6}$ hours, rode a bus for $45$ minutes, and walked for $\dfrac{1}{4}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $4\frac{1}{6}$ hours.
Bus: 45 minutes.
Walk: $\frac{1}{4}$ 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.

\frac{45}{60} = \frac{3}{4}\ \text{h}

The bus leg is

\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.

4\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.

\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.

\frac{31}{6} = 5\frac{1}{6}\ \text{h}

5 whole hours and

\frac{1}{6}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{6}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $1\dfrac{7}{12}$ hours, rode a bus for $50$ minutes, and walked for $\dfrac{1}{12}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $1\frac{7}{12}$ hours.
Bus: 50 minutes.
Walk: $\frac{1}{12}$ 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.

\frac{50}{60} = \frac{5}{6}\ \text{h}

The bus leg is

\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.

1\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.

\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.

\frac{5}{2} = 2\frac{1}{2}\ \text{h}

2 whole hours and

\frac{1}{2}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{1}{2}

of 60 minutes gives the minutes part.

\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

To get to her grandmother's house, Mia rode a train for $1\dfrac{11}{12}$ hours, rode a bus for $50$ minutes, and walked for $\dfrac{1}{6}$ hour. How long did the whole trip to her grandmother's house take, in hours and minutes?

Your answer (check it yourself)

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: $1\frac{11}{12}$ hours.
Bus: 50 minutes.
Walk: $\frac{1}{6}$ 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.

\frac{50}{60} = \frac{5}{6}\ \text{h}

The bus leg is

\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.

1\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.

\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.

\frac{35}{12} = 2\frac{11}{12}\ \text{h}

2 whole hours and

\frac{11}{12}

left over.

5Translate the leftover fraction back into minutes

#8 Analyze the Units 5.MD.A.1

\frac{11}{12}

of 60 minutes gives the minutes part.

\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.

Express minutes as fractions of an hour · 12 practice problems

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