Problem
Read and compare multiple bars
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.
Measurement & data
Your answer
Watch out Many students stop at 40/130 without simplifying it to lowest terms — the fraction still needs to be reduced to 4/13.
How to solve
Strategy Identify Subproblems — This breaks into two 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.
1STEP 1
Read the three bar heights
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.
3.MD.B.3Identify Subproblems2STEP 2
Find the total population
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.
3.MD.B.3Identify Subproblems3STEP 3
Write Town B as a fraction of the total
Town B has 40 of the 130 total people, so the fraction is 40/130.
40/130
The part (Town B) over the whole (all towns) is the fraction that lives in B.
3.NF.A.1Analyze The UnitsTown B holds 40 of the total 130 people, so the fraction of the whole population that lives in Town B is 40/130.
Why?
The whole population is the total number of people, and Town B's 40 is the part of it we want, so the fraction is that part written over the whole.
Why?
The three towns together are the whole population with no person left out and nobody counted twice, so their counts add to give the total of 130.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
A fraction tells how many of the whole's equal shares the part fills, and each person is one equal share, so Town B's 40 people are 40 of the 130 shares, which is 40/130.
Why?
Every person pairs with exactly one equal share of the population, so counting the people counts the shares, giving 130 shares in all with 40 of them in Town B.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
4STEP 4
Simplify the fraction
Both 40 and 130 are divisible by 10, so divide top and bottom by 10.
40/130 = (40 ÷ 10)/(130 ÷ 10) = 4/13
Dividing numerator and denominator by the same number keeps the fraction equal but simpler.
3.NF.A.1Analyze The UnitsAnswer
4/13
Town B (40) is a bit less than a third of the total 130, and 4/13 is a little under 1/3 (since 4 is a bit under 13/3 = about 4.3), so the fraction is the right size.
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 the three bar heights
- Find the total population
- Write Town B as a fraction of the total
- Simplify the fraction
Where next?
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