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← 4-1 · Read and compare multiple bars · Read and Scale a Data Graph

Read and compare multiple bars · 8 practice problems

3.MD.B.3

Generated variants — 8

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

Variant 1 answer: 1/3

The bar graph shows the population of three towns. Town A has 4040 people, Town B has 5050 people, and Town C has 6060 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 4040 for Town A, 5050 for Town B, and 6060 for Town C.

Population by Town (people) 0 50 100 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
40+50+60=15040 + 50 + 60 = 150
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 50 of the 150 total people, so the fraction is 50/150.
50150\dfrac{50}{150}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 50 and 150 are divisible by 50, so divide top and bottom by 50.
50150=50÷50150÷50=13\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: 1/3

Review

Town B (50) over the total 150 is 1/3; comparing 50 to one third of 150 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 7/20

The bar graph shows the population of three towns. Town A has 5050 people, Town B has 7070 people, and Town C has 8080 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 5050 for Town A, 7070 for Town B, and 8080 for Town C.

Population by Town (people) 0 50 100 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
50+70+80=20050 + 70 + 80 = 200
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 70 of the 200 total people, so the fraction is 70/200.
70200\dfrac{70}{200}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 70 and 200 are divisible by 10, so divide top and bottom by 10.
70200=70÷10200÷10=720\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: 7/20

Review

Town B (70) over the total 200 is 7/20; comparing 70 to one third of 200 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 1/5

The bar graph shows the population of three towns. Town A has 4545 people, Town B has 3030 people, and Town C has 7575 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 4545 for Town A, 3030 for Town B, and 7575 for Town C.

Population by Town (people) 0 50 100 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
45+30+75=15045 + 30 + 75 = 150
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 30 of the 150 total people, so the fraction is 30/150.
30150\dfrac{30}{150}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 30 and 150 are divisible by 30, so divide top and bottom by 30.
30150=30÷30150÷30=15\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: 1/5

Review

Town B (30) over the total 150 is 1/5; comparing 30 to one third of 150 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 4/13

The bar graph shows the population of three towns. Town A has 3030 people, Town B has 4040 people, and Town C has 6060 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 3030 for Town A, 4040 for Town B, and 6060 for Town C.

Population by Town (people) 0 50 100 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
30+40+60=13030 + 40 + 60 = 130
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 40 of the 130 total people, so the fraction is 40/130.
40130\dfrac{40}{130}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 40 and 130 are divisible by 10, so divide top and bottom by 10.
40130=40÷10130÷10=413\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: 4/13

Review

Town B (40) over the total 130 is 4/13; comparing 40 to one third of 130 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 2/5

The bar graph shows the population of three towns. Town A has 6060 people, Town B has 8080 people, and Town C has 6060 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 6060 for Town A, 8080 for Town B, and 6060 for Town C.

Population by Town (people) 0 50 100 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
60+80+60=20060 + 80 + 60 = 200
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 80 of the 200 total people, so the fraction is 80/200.
80200\dfrac{80}{200}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 80 and 200 are divisible by 40, so divide top and bottom by 40.
80200=80÷40200÷40=25\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: 2/5

Review

Town B (80) over the total 200 is 2/5; comparing 80 to one third of 200 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 3/10

The bar graph shows the population of three towns. Town A has 2020 people, Town B has 3030 people, and Town C has 5050 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 5050 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 2020 for Town A, 3030 for Town B, and 5050 for Town C.

Population by Town (people) 0 50 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
20+30+50=10020 + 30 + 50 = 100
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 30 of the 100 total people, so the fraction is 30/100.
30100\dfrac{30}{100}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 30 and 100 are divisible by 10, so divide top and bottom by 10.
30100=30÷10100÷10=310\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: 3/10

Review

Town B (30) over the total 100 is 3/10; comparing 30 to one third of 100 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 7/20

The bar graph shows the population of three towns. Town A has 2525 people, Town B has 3535 people, and Town C has 4040 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 2525 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 2525 for Town A, 3535 for Town B, and 4040 for Town C.

Population by Town (people) 0 25 50 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
25+35+40=10025 + 35 + 40 = 100
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 35 of the 100 total people, so the fraction is 35/100.
35100\dfrac{35}{100}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 35 and 100 are divisible by 5, so divide top and bottom by 5.
35100=35÷5100÷5=720\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: 7/20

Review

Town B (35) over the total 100 is 7/20; comparing 35 to one third of 100 confirms the fraction is the right size.

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

Standards · min 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.
💡 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 answer: 1/3

The bar graph shows the population of three towns. Town A has 1515 people, Town B has 2020 people, and Town C has 2525 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 1010 people. The horizontal axis lists Towns A, B, and C in order. The bar heights are 1515 for Town A, 2020 for Town B, and 2525 for Town C.

Population by Town (people) 0 10 20 30 A B C Town
Show solution

Understand

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.

Plan

#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.

Execute

#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.
#7 Identify Subproblems 3.MD.B.3
Add the three town populations to get the whole.
15+20+25=6015 + 20 + 25 = 60
The total is just all the people in the three towns added together.
#8 Analyze the Units 3.NF.A.1
Town B has 20 of the 60 total people, so the fraction is 20/60.
2060\dfrac{20}{60}
The part (Town B) over the whole (all towns) is the fraction that lives in B.
#8 Analyze the Units 3.NF.A.1
Both 20 and 60 are divisible by 20, so divide top and bottom by 20.
2060=20÷2060÷20=13\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: 1/3

Review

Town B (20) over the total 60 is 1/3; comparing 20 to one third of 60 confirms the fraction is the right size.

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

Standards · min 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.
💡 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!