Practice · Read and compare multiple bars · Sensim Math

Variant 1 easy

The bar graph shows the population of three towns. Town A has $15$ people, Town B has $20$ people, and Town C has $25$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $10$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $15$ for Town A, $20$ for Town B, and $25$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 15, Town B = 20, Town C = 25. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 15 people.
Town B has 20 people.
Town C has 25 people.
The bars read 15, 20, and 25 against gridlines every 10 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 15, 20, and 25 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

15 + 20 + 25 = 60

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 20 of the 60 total people, so the fraction is

\frac{20}{60}

.

\dfrac{20}{60}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 20 and 60 are divisible by 20, so divide top and bottom by 20.

\dfrac{20}{60} = \dfrac{20 \div 20}{60 \div 20} = \dfrac{1}{3}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{1}{3}

4 · Reviewdoes it hold up?

Town B (20) over the total 60 is $\frac{1}{3}$ ; comparing 20 to one third of 60 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 2 easy

The bar graph shows the population of three towns. Town A has $25$ people, Town B has $35$ people, and Town C has $40$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $25$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $25$ for Town A, $35$ for Town B, and $40$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 25, Town B = 35, Town C = 40. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 25 people.
Town B has 35 people.
Town C has 40 people.
The bars read 25, 35, and 40 against gridlines every 25 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 25, 35, and 40 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

25 + 35 + 40 = 100

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 35 of the 100 total people, so the fraction is

\frac{35}{100}

.

\dfrac{35}{100}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 35 and 100 are divisible by 5, so divide top and bottom by 5.

\dfrac{35}{100} = \dfrac{35 \div 5}{100 \div 5} = \dfrac{7}{20}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{7}{20}

4 · Reviewdoes it hold up?

Town B (35) over the total 100 is $\frac{7}{20}$ ; comparing 35 to one third of 100 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 3 medium

The bar graph shows the population of three towns. Town A has $20$ people, Town B has $30$ people, and Town C has $50$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $20$ for Town A, $30$ for Town B, and $50$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 20, Town B = 30, Town C = 50. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 20 people.
Town B has 30 people.
Town C has 50 people.
The bars read 20, 30, and 50 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 20, 30, and 50 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

20 + 30 + 50 = 100

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 30 of the 100 total people, so the fraction is

\frac{30}{100}

.

\dfrac{30}{100}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 30 and 100 are divisible by 10, so divide top and bottom by 10.

\dfrac{30}{100} = \dfrac{30 \div 10}{100 \div 10} = \dfrac{3}{10}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{3}{10}

4 · Reviewdoes it hold up?

Town B (30) over the total 100 is $\frac{3}{10}$ ; comparing 30 to one third of 100 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 4 medium

The bar graph shows the population of three towns. Town A has $40$ people, Town B has $50$ people, and Town C has $60$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $40$ for Town A, $50$ for Town B, and $60$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 40, Town B = 50, Town C = 60. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 40 people.
Town B has 50 people.
Town C has 60 people.
The bars read 40, 50, and 60 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 40, 50, and 60 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

40 + 50 + 60 = 150

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 50 of the 150 total people, so the fraction is

\frac{50}{150}

.

\dfrac{50}{150}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 50 and 150 are divisible by 50, so divide top and bottom by 50.

\dfrac{50}{150} = \dfrac{50 \div 50}{150 \div 50} = \dfrac{1}{3}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{1}{3}

4 · Reviewdoes it hold up?

Town B (50) over the total 150 is $\frac{1}{3}$ ; comparing 50 to one third of 150 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 5 medium

The bar graph shows the population of three towns. Town A has $30$ people, Town B has $40$ people, and Town C has $60$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $30$ for Town A, $40$ for Town B, and $60$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 30, Town B = 40, Town C = 60. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 30 people.
Town B has 40 people.
Town C has 60 people.
The bars read 30, 40, and 60 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 30, 40, and 60 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

30 + 40 + 60 = 130

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 40 of the 130 total people, so the fraction is

\frac{40}{130}

.

\dfrac{40}{130}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 40 and 130 are divisible by 10, so divide top and bottom by 10.

\dfrac{40}{130} = \dfrac{40 \div 10}{130 \div 10} = \dfrac{4}{13}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{4}{13}

4 · Reviewdoes it hold up?

Town B (40) over the total 130 is $\frac{4}{13}$ ; comparing 40 to one third of 130 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 6 medium

The bar graph shows the population of three towns. Town A has $45$ people, Town B has $30$ people, and Town C has $75$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $45$ for Town A, $30$ for Town B, and $75$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 45, Town B = 30, Town C = 75. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 45 people.
Town B has 30 people.
Town C has 75 people.
The bars read 45, 30, and 75 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 45, 30, and 75 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

45 + 30 + 75 = 150

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 30 of the 150 total people, so the fraction is

\frac{30}{150}

.

\dfrac{30}{150}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 30 and 150 are divisible by 30, so divide top and bottom by 30.

\dfrac{30}{150} = \dfrac{30 \div 30}{150 \div 30} = \dfrac{1}{5}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{1}{5}

4 · Reviewdoes it hold up?

Town B (30) over the total 150 is $\frac{1}{5}$ ; comparing 30 to one third of 150 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 7 hard

The bar graph shows the population of three towns. Town A has $50$ people, Town B has $70$ people, and Town C has $80$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $50$ for Town A, $70$ for Town B, and $80$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 50, Town B = 70, Town C = 80. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 50 people.
Town B has 70 people.
Town C has 80 people.
The bars read 50, 70, and 80 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 50, 70, and 80 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

50 + 70 + 80 = 200

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 70 of the 200 total people, so the fraction is

\frac{70}{200}

.

\dfrac{70}{200}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 70 and 200 are divisible by 10, so divide top and bottom by 10.

\dfrac{70}{200} = \dfrac{70 \div 10}{200 \div 10} = \dfrac{7}{20}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{7}{20}

4 · Reviewdoes it hold up?

Town B (70) over the total 200 is $\frac{7}{20}$ ; comparing 70 to one third of 200 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Variant 8 hard

The bar graph shows the population of three towns. Town A has $60$ people, Town B has $80$ people, and Town C has $60$ people.

Write, as a fraction, the part of the total population that lives in Town B.

The vertical axis shows population (number of people), with gridlines drawn every $50$ people. The horizontal axis lists Towns A, B, and C in order. The bar heights are $60$ for Town A, $80$ for Town B, and $60$ for Town C.

Your answer

Show solution

1 · Understandwhat's really being asked

A bar graph gives the populations of three towns: Town A = 60, Town B = 80, Town C = 60. We must write, as a fraction, the part of the total population that lives in Town B.

Givens

Town A has 60 people.
Town B has 80 people.
Town C has 60 people.
The bars read 60, 80, and 60 against gridlines every 50 people.

Unknowns

The fraction of the total population that lives in Town B.

Constraints

The 'total' is the sum of all three towns.
The answer must be expressed as a fraction.

2 · Planchoose the strategy

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

This breaks into small steps: first find the total population (a sum), then write Town B's count over that total as a fraction and simplify. Checking the units (people over people) confirms the fraction is a pure part-of-whole ratio.

3 · Execute4 carry out the plan

1Read the three bar heights

#7 Identify Subproblems 3.MD.B.3

From the bar graph the populations are 60, 80, and 60 people for Towns A, B, and C.

Each bar's height against the scaled axis gives that town's number of people.

2Find the total population

#7 Identify Subproblems 3.MD.B.3

Add the three town populations to get the whole.

60 + 80 + 60 = 200

The total is just all the people in the three towns added together.

3Write Town B as a fraction of the total

#8 Analyze the Units 3.NF.A.1

Town B has 80 of the 200 total people, so the fraction is

\frac{80}{200}

.

\dfrac{80}{200}

The part (Town B) over the whole (all towns) is the fraction that lives in B.

4Simplify the fraction

#8 Analyze the Units 3.NF.A.1

Both 80 and 200 are divisible by 40, so divide top and bottom by 40.

\dfrac{80}{200} = \dfrac{80 \div 40}{200 \div 40} = \dfrac{2}{5}

Dividing numerator and denominator by the same number keeps the fraction equal but simpler.

Answer:

\frac{2}{5}

4 · Reviewdoes it hold up?

Town B (80) over the total 200 is $\frac{2}{5}$ ; comparing 80 to one third of 200 confirms the fraction is the right size.

Another way: Organize the information differently (tool 15): list the parts as a ratio, reduce it, and read off Town B's share of the whole.

Standardsmin grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the town populations from the bar graph and summing them.
3.NF.A.1 Understand a fraction as quantity formed by parts of a whole — Expressing Town B's population as a part of the whole total and simplifying.

💡Takeaway. Add up all the bars for the whole, then put one bar over that total - it's just part-over-whole fractions you learned in Grade 3!

Read and compare multiple bars · 8 practice problems

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