Practice · Spend the small cards on the divisor and the rest look after themselves · Sensim Math

Variant 1 easy

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 4, 5, 6 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 4, 5, 6.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 4, 5 and 6 make the largest number when the biggest is in front.

6.54

The dividend is 6.54.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

6.54 \div 1.2 = 5.45

The largest quotient is 5.45.

Answer: 5.45

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.19, so 5.45 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 2 easy

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 3, 4, 5, 6, 7 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 3, 4, 5, 6, 7.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 3 and 4, and the smaller one goes in front to keep the divisor low.

3.4

The divisor is 3.4.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 5, 6 and 7 make the largest number when the biggest is in front.

7.65

The dividend is 7.65.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

7.65 \div 3.4 = 2.25

The largest quotient is 2.25.

Answer: 2.25

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.45, so 2.25 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 3 easy

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 6, 7, 8 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 6, 7, 8.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 6, 7 and 8 make the largest number when the biggest is in front.

8.76

The dividend is 8.76.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

8.76 \div 1.2 = 7.3

The largest quotient is 7.3.

Answer: 7.3

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.14, so 7.3 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 4 easy

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 4, 6, 8 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 4, 6, 8.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 4, 6 and 8 make the largest number when the biggest is in front.

8.64

The dividend is 8.64.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

8.64 \div 1.2 = 7.2

The largest quotient is 7.2.

Answer: 7.2

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.14, so 7.2 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 5 medium

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 3, 7, 8 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 3, 7, 8.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 3, 7 and 8 make the largest number when the biggest is in front.

8.73

The dividend is 8.73.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

8.73 \div 1.2 = 7.275

The largest quotient is 7.275.

Answer: 7.275

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.14, so 7.275 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 6 medium

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 4, 5, 7, 8 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 4, 5, 7, 8.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 4, and the smaller one goes in front to keep the divisor low.

1.4

The divisor is 1.4.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 5, 7 and 8 make the largest number when the biggest is in front.

8.75

The dividend is 8.75.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

8.75 \div 1.4 = 6.25

The largest quotient is 6.25.

Answer: 6.25

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.17, so 6.25 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 7 hard

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 3, 6, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 3, 6, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 3, 6 and 9 make the largest number when the biggest is in front.

9.63

The dividend is 9.63.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.63 \div 1.2 = 8.025

The largest quotient is 8.025.

Answer: 8.025

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.13, so 8.025 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 8 hard

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 4, 7, 8, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 4, 7, 8, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 4, and the smaller one goes in front to keep the divisor low.

1.4

The divisor is 1.4.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 7, 8 and 9 make the largest number when the biggest is in front.

9.87

The dividend is 9.87.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.87 \div 1.4 = 7.05

The largest quotient is 7.05.

Answer: 7.05

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.15, so 7.05 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 9 medium

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 3, 5, 7, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 3, 5, 7, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 3, and the smaller one goes in front to keep the divisor low.

1.3

The divisor is 1.3.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 5, 7 and 9 make the largest number when the biggest is in front.

9.75

The dividend is 9.75.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.75 \div 1.3 = 7.5

The largest quotient is 7.5.

Answer: 7.5

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.14, so 7.5 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 10 hard

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 2, 5, 6, 7, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 2, 5, 6, 7, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 2 and 5, and the smaller one goes in front to keep the divisor low.

2.5

The divisor is 2.5.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 6, 7 and 9 make the largest number when the biggest is in front.

9.76

The dividend is 9.76.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.76 \div 2.5 = 3.904

The largest quotient is 3.904.

Answer: 3.904

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.26, so 3.904 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 11 medium

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 2, 5, 6, 8, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 2, 5, 6, 8, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 2 and 5, and the smaller one goes in front to keep the divisor low.

2.5

The divisor is 2.5.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 6, 8 and 9 make the largest number when the biggest is in front.

9.86

The dividend is 9.86.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.86 \div 2.5 = 3.944

The largest quotient is 3.944.

Answer: 3.944

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.26, so 3.944 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Variant 12 hard

Using each of the five number cards exactly once, make the division (a number with two decimal places) $\div$ (a number with one decimal place) whose quotient is as large as possible, and find that quotient.

Your answer

Show solution

1 · Understandwhat's really being asked

The cards 1, 2, 5, 7, 9 fill five places: three in a number with two decimal places and two in a number with one. We want the largest quotient.

Givens

The cards are 1, 2, 5, 7, 9.
Each card is used exactly once.
The dividend has two decimal places and the divisor one.

Unknowns

The largest quotient that can be made.

Constraints

The five cards must fill all five places.

2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #8 Analyze the Units#2 Make a Systematic List

A big quotient wants a big dividend and a small divisor. Check whether those two aims compete: the divisor needs two cards, and spending the two smallest there leaves the three largest for the dividend -- so they do not.

3 · Execute4 carry out the plan

1Say what makes a quotient large

#8 Analyze the Units 6.NS.B.3

More on top and less underneath both push it up.

\frac{\text{large}}{\text{small}}

Two things to arrange.

2Give the divisor the smallest cards

#3 Eliminate Possibilities 6.EE.B.8

The two smallest are 1 and 2, and the smaller one goes in front to keep the divisor low.

1.2

The divisor is 1.2.

3Build the dividend from what is left

#2 Make a Systematic List 6.EE.B.8

The remaining cards 5, 7 and 9 make the largest number when the biggest is in front.

9.75

The dividend is 9.75.

4Divide

#8 Analyze the Units 6.NS.B.3

Both numbers are as favourable as the cards allow.

9.75 \div 1.2 = 8.125

The largest quotient is 8.125.

Answer: 8.125

4 · Reviewdoes it hold up?

The other extreme is far away: the smallest quotient these cards can make is about 0.13, so 8.125 really is at the top of the range.

Another way: Swapping any one card between the two numbers makes the dividend smaller or the divisor bigger, and either way the quotient drops -- which is the check that the two aims do not compete.

Standardsmin grade 6

6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing one decimal by another.
6.EE.B.8 Write and graph inequalities of the form x>c or x<c — Comparing arrangements to find the largest.

💡Takeaway. Ask what makes the answer big, then check whether the two ways of doing it get in each other's way.

Spend the small cards on the divisor and the rest look after themselves · 12 practice problems

Generated variants — 12

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