Practice · Find the pair first, then let the ratio cut it · Sensim Math

Variant 1 easy

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $1 : 5$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 20 percent, dental clinics 16 percent and other 16 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 5. We want each of their percentages.

Givens

Pharmacies are 20 percent, dental clinics 16 percent, other 16 percent.
Family clinics to oriental clinics is 1 to 5.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 20 - 16 - 16 = 48

The two clinics share 48 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

1 to 5 means 6 equal parts, 1 of them family and 5 oriental.

48 \div 6 = 8

Each part is 8 percent.

3Give each its share

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

Family clinics take 1 parts and oriental clinics 5.

8 \times 1 = 8,\quad 8 \times 5 = 40

8 percent and 40 percent.

Answer: Family clinics 8%, oriental clinics 40%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 8 to 40 simplifies back to 1 to 5.

Another way: Splitting the 48 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 2 easy

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $1 : 7$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 20 percent, dental clinics 9 percent and other 15 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 7. We want each of their percentages.

Givens

Pharmacies are 20 percent, dental clinics 9 percent, other 15 percent.
Family clinics to oriental clinics is 1 to 7.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 20 - 9 - 15 = 56

The two clinics share 56 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

1 to 7 means 8 equal parts, 1 of them family and 7 oriental.

56 \div 8 = 7

Each part is 7 percent.

3Give each its share

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

Family clinics take 1 parts and oriental clinics 7.

7 \times 1 = 7,\quad 7 \times 7 = 49

7 percent and 49 percent.

Answer: Family clinics 7%, oriental clinics 49%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 7 to 49 simplifies back to 1 to 7.

Another way: Splitting the 56 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 3 easy

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $1 : 2$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 23 percent, dental clinics 9 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 2. We want each of their percentages.

Givens

Pharmacies are 23 percent, dental clinics 9 percent, other 5 percent.
Family clinics to oriental clinics is 1 to 2.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 23 - 9 - 5 = 63

The two clinics share 63 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

1 to 2 means 3 equal parts, 1 of them family and 2 oriental.

63 \div 3 = 21

Each part is 21 percent.

3Give each its share

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

Family clinics take 1 parts and oriental clinics 2.

21 \times 1 = 21,\quad 21 \times 2 = 42

21 percent and 42 percent.

Answer: Family clinics 21%, oriental clinics 42%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 21 to 42 simplifies back to 1 to 2.

Another way: Splitting the 63 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 4 easy

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $3 : 2$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 24 percent, dental clinics 12 percent and other 19 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 2. We want each of their percentages.

Givens

Pharmacies are 24 percent, dental clinics 12 percent, other 19 percent.
Family clinics to oriental clinics is 3 to 2.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 24 - 12 - 19 = 45

The two clinics share 45 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

3 to 2 means 5 equal parts, 3 of them family and 2 oriental.

45 \div 5 = 9

Each part is 9 percent.

3Give each its share

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

Family clinics take 3 parts and oriental clinics 2.

9 \times 3 = 27,\quad 9 \times 2 = 18

27 percent and 18 percent.

Answer: Family clinics 27%, oriental clinics 18%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 27 to 18 simplifies back to 3 to 2.

Another way: Splitting the 45 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 5 medium

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $7 : 4$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 30 percent, dental clinics 21 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 7 to 4. We want each of their percentages.

Givens

Pharmacies are 30 percent, dental clinics 21 percent, other 5 percent.
Family clinics to oriental clinics is 7 to 4.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 30 - 21 - 5 = 44

The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

7 to 4 means 11 equal parts, 7 of them family and 4 oriental.

44 \div 11 = 4

Each part is 4 percent.

3Give each its share

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

Family clinics take 7 parts and oriental clinics 4.

4 \times 7 = 28,\quad 4 \times 4 = 16

28 percent and 16 percent.

Answer: Family clinics 28%, oriental clinics 16%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 28 to 16 simplifies back to 7 to 4.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 6 medium

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $5 : 7$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 30 percent, dental clinics 11 percent and other 11 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 7. We want each of their percentages.

Givens

Pharmacies are 30 percent, dental clinics 11 percent, other 11 percent.
Family clinics to oriental clinics is 5 to 7.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 30 - 11 - 11 = 48

The two clinics share 48 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

5 to 7 means 12 equal parts, 5 of them family and 7 oriental.

48 \div 12 = 4

Each part is 4 percent.

3Give each its share

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

Family clinics take 5 parts and oriental clinics 7.

4 \times 5 = 20,\quad 4 \times 7 = 28

20 percent and 28 percent.

Answer: Family clinics 20%, oriental clinics 28%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 20 to 28 simplifies back to 5 to 7.

Another way: Splitting the 48 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 7 medium

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $3 : 1$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 36 percent, dental clinics 11 percent and other 9 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 1. We want each of their percentages.

Givens

Pharmacies are 36 percent, dental clinics 11 percent, other 9 percent.
Family clinics to oriental clinics is 3 to 1.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 36 - 11 - 9 = 44

The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

3 to 1 means 4 equal parts, 3 of them family and 1 oriental.

44 \div 4 = 11

Each part is 11 percent.

3Give each its share

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

Family clinics take 3 parts and oriental clinics 1.

11 \times 3 = 33,\quad 11 \times 1 = 11

33 percent and 11 percent.

Answer: Family clinics 33%, oriental clinics 11%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 33 to 11 simplifies back to 3 to 1.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 8 medium

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $3 : 1$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 40 percent, dental clinics 10 percent and other 6 percent. Family and oriental clinics are unlabelled and stand in the ratio 3 to 1. We want each of their percentages.

Givens

Pharmacies are 40 percent, dental clinics 10 percent, other 6 percent.
Family clinics to oriental clinics is 3 to 1.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 40 - 10 - 6 = 44

The two clinics share 44 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

3 to 1 means 4 equal parts, 3 of them family and 1 oriental.

44 \div 4 = 11

Each part is 11 percent.

3Give each its share

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

Family clinics take 3 parts and oriental clinics 1.

11 \times 3 = 33,\quad 11 \times 1 = 11

33 percent and 11 percent.

Answer: Family clinics 33%, oriental clinics 11%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 33 to 11 simplifies back to 3 to 1.

Another way: Splitting the 44 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 9 hard

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $1 : 2$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 41 percent, dental clinics 21 percent and other 17 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 2. We want each of their percentages.

Givens

Pharmacies are 41 percent, dental clinics 21 percent, other 17 percent.
Family clinics to oriental clinics is 1 to 2.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 41 - 21 - 17 = 21

The two clinics share 21 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

1 to 2 means 3 equal parts, 1 of them family and 2 oriental.

21 \div 3 = 7

Each part is 7 percent.

3Give each its share

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

Family clinics take 1 parts and oriental clinics 2.

7 \times 1 = 7,\quad 7 \times 2 = 14

7 percent and 14 percent.

Answer: Family clinics 7%, oriental clinics 14%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 7 to 14 simplifies back to 1 to 2.

Another way: Splitting the 21 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 10 hard

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $5 : 3$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 42 percent, dental clinics 13 percent and other 5 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 3. We want each of their percentages.

Givens

Pharmacies are 42 percent, dental clinics 13 percent, other 5 percent.
Family clinics to oriental clinics is 5 to 3.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 42 - 13 - 5 = 40

The two clinics share 40 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

5 to 3 means 8 equal parts, 5 of them family and 3 oriental.

40 \div 8 = 5

Each part is 5 percent.

3Give each its share

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

Family clinics take 5 parts and oriental clinics 3.

5 \times 5 = 25,\quad 5 \times 3 = 15

25 percent and 15 percent.

Answer: Family clinics 25%, oriental clinics 15%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 25 to 15 simplifies back to 5 to 3.

Another way: Splitting the 40 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 11 hard

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $1 : 6$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 45 percent, dental clinics 10 percent and other 3 percent. Family and oriental clinics are unlabelled and stand in the ratio 1 to 6. We want each of their percentages.

Givens

Pharmacies are 45 percent, dental clinics 10 percent, other 3 percent.
Family clinics to oriental clinics is 1 to 6.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 45 - 10 - 3 = 42

The two clinics share 42 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

1 to 6 means 7 equal parts, 1 of them family and 6 oriental.

42 \div 7 = 6

Each part is 6 percent.

3Give each its share

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

Family clinics take 1 parts and oriental clinics 6.

6 \times 1 = 6,\quad 6 \times 6 = 36

6 percent and 36 percent.

Answer: Family clinics 6%, oriental clinics 36%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 6 to 36 simplifies back to 1 to 6.

Another way: Splitting the 42 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Variant 12 hard

The bar graph shows the medical facilities in a city. If the number of family clinics to oriental clinics is $5 : 1$ , what percent of the total is each?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A bar graph gives pharmacies 48 percent, dental clinics 15 percent and other 19 percent. Family and oriental clinics are unlabelled and stand in the ratio 5 to 1. We want each of their percentages.

Givens

Pharmacies are 48 percent, dental clinics 15 percent, other 19 percent.
Family clinics to oriental clinics is 5 to 1.

Unknowns

The percentage for family clinics and for oriental clinics.

Constraints

The five sections together are 100 percent.

2 · Planchoose the strategy

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

Neither unlabelled section can be found by itself. Their total can: it is whatever the labelled sections leave. Find that first, and the ratio then says how to cut it.

3 · Execute3 carry out the plan

1Find what the two share between them

#16 Count the Complement 6.RP.A.3

The five sections make 100 percent, so subtract the three that are labelled.

100 - 48 - 15 - 19 = 18

The two clinics share 18 percent.

2Cut it in the given ratio

#7 Identify Subproblems 6.RP.A.3

5 to 1 means 6 equal parts, 5 of them family and 1 oriental.

18 \div 6 = 3

Each part is 3 percent.

3Give each its share

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

Family clinics take 5 parts and oriental clinics 1.

3 \times 5 = 15,\quad 3 \times 1 = 3

15 percent and 3 percent.

Answer: Family clinics 15%, oriental clinics 3%

4 · Reviewdoes it hold up?

All five add to 100 percent, and 15 to 3 simplifies back to 5 to 1.

Another way: Splitting the 18 percent by eye and adjusting until the ratio comes out right lands in the same place, after several guesses.

Standardsmin grade 6

6.RP.A.3 Use ratio and rate reasoning to solve problems — Dividing a leftover percentage in a given ratio.

💡Takeaway. When two things are missing, look for what they add up to. A ratio can only cut something you already have.

Find the pair first, then let the ratio cut it · 12 practice problems

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