Practice · The base of a percentage often has to be built before it can be used · Sensim Math

Variant 1 easy answer: 19.5%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$59$	$39$	$35$	$67$

Show solution

1 · Understandwhat's really being asked

Four schools sent 59, 39, 35, 67 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 59 students.
School B sent 39 students.
School C sent 35 students.
School D sent 67 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

59 + 39 + 35 + 67 = 200

200 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 39 students out of the 200.

\frac{39}{200}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{39}{200} \times 100 = 19.5

A 19.5 percent chance.

Answer: 19.5%

4 · Reviewdoes it hold up?

19.5 percent of 200 is 39, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 67 students, would answer a different question: the representative is drawn from all 200 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 2 easy answer: 15%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$78$	$45$	$69$	$108$

Show solution

1 · Understandwhat's really being asked

Four schools sent 78, 45, 69, 108 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 78 students.
School B sent 45 students.
School C sent 69 students.
School D sent 108 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

78 + 45 + 69 + 108 = 300

300 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 45 students out of the 300.

\frac{45}{300}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{45}{300} \times 100 = 15

A 15 percent chance.

Answer: 15%

4 · Reviewdoes it hold up?

15 percent of 300 is 45, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 108 students, would answer a different question: the representative is drawn from all 300 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 3 easy answer: 54%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$20$	$108$	$53$	$19$

Show solution

1 · Understandwhat's really being asked

Four schools sent 20, 108, 53, 19 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 20 students.
School B sent 108 students.
School C sent 53 students.
School D sent 19 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

20 + 108 + 53 + 19 = 200

200 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 108 students out of the 200.

\frac{108}{200}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{108}{200} \times 100 = 54

A 54 percent chance.

Answer: 54%

4 · Reviewdoes it hold up?

54 percent of 200 is 108, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 108 students, would answer a different question: the representative is drawn from all 200 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 4 easy answer: 38%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$36$	$114$	$79$	$71$

Show solution

1 · Understandwhat's really being asked

Four schools sent 36, 114, 79, 71 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 36 students.
School B sent 114 students.
School C sent 79 students.
School D sent 71 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

36 + 114 + 79 + 71 = 300

300 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 114 students out of the 300.

\frac{114}{300}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{114}{300} \times 100 = 38

A 38 percent chance.

Answer: 38%

4 · Reviewdoes it hold up?

38 percent of 300 is 114, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 114 students, would answer a different question: the representative is drawn from all 300 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 5 medium answer: 34.5%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$102$	$138$	$72$	$88$

Show solution

1 · Understandwhat's really being asked

Four schools sent 102, 138, 72, 88 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 102 students.
School B sent 138 students.
School C sent 72 students.
School D sent 88 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

102 + 138 + 72 + 88 = 400

400 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 138 students out of the 400.

\frac{138}{400}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{138}{400} \times 100 = 34.5

A 34.5 percent chance.

Answer: 34.5%

4 · Reviewdoes it hold up?

34.5 percent of 400 is 138, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 138 students, would answer a different question: the representative is drawn from all 400 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 6 medium answer: 33%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$144$	$99$	$22$	$35$

Show solution

1 · Understandwhat's really being asked

Four schools sent 144, 99, 22, 35 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 144 students.
School B sent 99 students.
School C sent 22 students.
School D sent 35 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

144 + 99 + 22 + 35 = 300

300 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 99 students out of the 300.

\frac{99}{300}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{99}{300} \times 100 = 33

A 33 percent chance.

Answer: 33%

4 · Reviewdoes it hold up?

33 percent of 300 is 99, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 144 students, would answer a different question: the representative is drawn from all 300 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 7 medium answer: 15%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$144$	$75$	$138$	$143$

Show solution

1 · Understandwhat's really being asked

Four schools sent 144, 75, 138, 143 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 144 students.
School B sent 75 students.
School C sent 138 students.
School D sent 143 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

144 + 75 + 138 + 143 = 500

500 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 75 students out of the 500.

\frac{75}{500}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{75}{500} \times 100 = 15

A 15 percent chance.

Answer: 15%

4 · Reviewdoes it hold up?

15 percent of 500 is 75, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 144 students, would answer a different question: the representative is drawn from all 500 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 8 medium answer: 5%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$22$	$15$	$107$	$156$

Show solution

1 · Understandwhat's really being asked

Four schools sent 22, 15, 107, 156 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 22 students.
School B sent 15 students.
School C sent 107 students.
School D sent 156 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

22 + 15 + 107 + 156 = 300

300 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 15 students out of the 300.

\frac{15}{300}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{15}{300} \times 100 = 5

A 5 percent chance.

Answer: 5%

4 · Reviewdoes it hold up?

5 percent of 300 is 15, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 156 students, would answer a different question: the representative is drawn from all 300 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 9 hard answer: 24.6%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$149$	$123$	$26$	$202$

Show solution

1 · Understandwhat's really being asked

Four schools sent 149, 123, 26, 202 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 149 students.
School B sent 123 students.
School C sent 26 students.
School D sent 202 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

149 + 123 + 26 + 202 = 500

500 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 123 students out of the 500.

\frac{123}{500}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{123}{500} \times 100 = 24.6

A 24.6 percent chance.

Answer: 24.6%

4 · Reviewdoes it hold up?

24.6 percent of 500 is 123, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 202 students, would answer a different question: the representative is drawn from all 500 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 10 hard answer: 17.8%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$22$	$89$	$116$	$273$

Show solution

1 · Understandwhat's really being asked

Four schools sent 22, 89, 116, 273 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 22 students.
School B sent 89 students.
School C sent 116 students.
School D sent 273 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

22 + 89 + 116 + 273 = 500

500 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 89 students out of the 500.

\frac{89}{500}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{89}{500} \times 100 = 17.8

A 17.8 percent chance.

Answer: 17.8%

4 · Reviewdoes it hold up?

17.8 percent of 500 is 89, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 273 students, would answer a different question: the representative is drawn from all 500 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 11 hard answer: 17%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$58$	$85$	$36$	$321$

Show solution

1 · Understandwhat's really being asked

Four schools sent 58, 85, 36, 321 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 58 students.
School B sent 85 students.
School C sent 36 students.
School D sent 321 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

58 + 85 + 36 + 321 = 500

500 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 85 students out of the 500.

\frac{85}{500}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{85}{500} \times 100 = 17

A 17 percent chance.

Answer: 17%

4 · Reviewdoes it hold up?

17 percent of 500 is 85, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 321 students, would answer a different question: the representative is drawn from all 500 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

Variant 12 hard answer: 5.2%

The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?

School	A	B	C	D
Students	$54$	$26$	$94$	$326$

Show solution

1 · Understandwhat's really being asked

Four schools sent 54, 26, 94, 326 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.

Givens

School A sent 54 students.
School B sent 26 students.
School C sent 94 students.
School D sent 326 students.

Unknowns

The percent chance the representative comes from school B.

Constraints

Every student is equally likely to be chosen.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#2 Make a Systematic List

A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.

3 · Execute3 carry out the plan

1Total all four schools

#2 Make a Systematic List 6.RP.A.3

Every student is a candidate, so the whole is everyone.

54 + 26 + 94 + 326 = 500

500 students in all.

2Write B's share as a fraction

#7 Identify Subproblems 6.RP.A.3

School B's 26 students out of the 500.

\frac{26}{500}

Part over whole.

3Turn it into a percent

#8 Analyze the Units 6.RP.A.3

Multiply the share by 100.

\frac{26}{500} \times 100 = 5.2

A 5.2 percent chance.

Answer: 5.2%

4 · Reviewdoes it hold up?

5.2 percent of 500 is 26, which is exactly school B's column -- so the percentage and the count agree.

Another way: Comparing B only with the largest school, 326 students, would answer a different question: the representative is drawn from all 500 students, not from that school alone.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.

💡Takeaway. Before you can take a percentage you need the whole. Sometimes you have to add it up yourself.

The base of a percentage often has to be built before it can be used · 12 practice problems

Generated variants — 12

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