← Every ratio with a given value is the simplest one scaled up · Proportion and Proportional Division

Every ratio with a given value is the simplest one scaled up · 12 practice problems

6.RP.A.16.RP.A.3

Generated variants — 12

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

Variant 1 easy answer: 15 : 25

Among the ratios whose value is $\frac{3}{5}$ , find the one whose two terms add to $40$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 3/5, we want the one whose two terms add to 40.

Givens

The value of the ratio is 3/5.
The two terms add to 40.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 3/5 in lowest terms is 3 to 5.

\frac{3}{5} = \frac{3}{5} \rightarrow 3 : 5

The shape is 3 to 5.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

3 + 5 = 8

Each scaling step adds 8.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 40, so divide by 8.

40 \div 8 = 5

Scale everything by 5.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

3 \times 5 : 5 \times 5 = 15 : 25

The ratio is 15 to 25.

Answer: 15 : 25

4 · Reviewdoes it hold up?

Both conditions hold: 15 plus 25 is 40, and 15 over 25 simplifies back to 3/5.

Another way: Listing 3 : 5, 6 : 10, 9 : 15 and watching the sums climb by 8 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 2 easy answer: 18 : 27

Among the ratios whose value is $\frac{2}{3}$ , find the one whose two terms add to $45$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 2/3, we want the one whose two terms add to 45.

Givens

The value of the ratio is 2/3.
The two terms add to 45.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 2/3 in lowest terms is 2 to 3.

\frac{2}{3} = \frac{2}{3} \rightarrow 2 : 3

The shape is 2 to 3.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

2 + 3 = 5

Each scaling step adds 5.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 45, so divide by 5.

45 \div 5 = 9

Scale everything by 9.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

2 \times 9 : 3 \times 9 = 18 : 27

The ratio is 18 to 27.

Answer: 18 : 27

4 · Reviewdoes it hold up?

Both conditions hold: 18 plus 27 is 45, and 18 over 27 simplifies back to 2/3.

Another way: Listing 2 : 3, 4 : 6, 6 : 9 and watching the sums climb by 5 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 3 easy answer: 24 : 28

Among the ratios whose value is $\frac{6}{7}$ , find the one whose two terms add to $52$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 6/7, we want the one whose two terms add to 52.

Givens

The value of the ratio is 6/7.
The two terms add to 52.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 6/7 in lowest terms is 6 to 7.

\frac{6}{7} = \frac{6}{7} \rightarrow 6 : 7

The shape is 6 to 7.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

6 + 7 = 13

Each scaling step adds 13.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 52, so divide by 13.

52 \div 13 = 4

Scale everything by 4.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

6 \times 4 : 7 \times 4 = 24 : 28

The ratio is 24 to 28.

Answer: 24 : 28

4 · Reviewdoes it hold up?

Both conditions hold: 24 plus 28 is 52, and 24 over 28 simplifies back to 6/7.

Another way: Listing 6 : 7, 12 : 14, 18 : 21 and watching the sums climb by 13 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 4 easy answer: 21 : 36

Among the ratios whose value is $\frac{7}{12}$ , find the one whose two terms add to $57$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 7/12, we want the one whose two terms add to 57.

Givens

The value of the ratio is 7/12.
The two terms add to 57.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 7/12 in lowest terms is 7 to 12.

\frac{7}{12} = \frac{7}{12} \rightarrow 7 : 12

The shape is 7 to 12.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

7 + 12 = 19

Each scaling step adds 19.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 57, so divide by 19.

57 \div 19 = 3

Scale everything by 3.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

7 \times 3 : 12 \times 3 = 21 : 36

The ratio is 21 to 36.

Answer: 21 : 36

4 · Reviewdoes it hold up?

Both conditions hold: 21 plus 36 is 57, and 21 over 36 simplifies back to 7/12.

Another way: Listing 7 : 12, 14 : 24, 21 : 36 and watching the sums climb by 19 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 5 medium answer: 28 : 36

Among the ratios whose value is $\frac{7}{9}$ , find the one whose two terms add to $64$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 7/9, we want the one whose two terms add to 64.

Givens

The value of the ratio is 7/9.
The two terms add to 64.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 7/9 in lowest terms is 7 to 9.

\frac{7}{9} = \frac{7}{9} \rightarrow 7 : 9

The shape is 7 to 9.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

7 + 9 = 16

Each scaling step adds 16.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 64, so divide by 16.

64 \div 16 = 4

Scale everything by 4.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

7 \times 4 : 9 \times 4 = 28 : 36

The ratio is 28 to 36.

Answer: 28 : 36

4 · Reviewdoes it hold up?

Both conditions hold: 28 plus 36 is 64, and 28 over 36 simplifies back to 7/9.

Another way: Listing 7 : 9, 14 : 18, 21 : 27 and watching the sums climb by 16 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 6 medium answer: 20 : 45

Among the ratios whose value is $\frac{4}{9}$ , find the one whose two terms add to $65$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 4/9, we want the one whose two terms add to 65.

Givens

The value of the ratio is 4/9.
The two terms add to 65.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 4/9 in lowest terms is 4 to 9.

\frac{4}{9} = \frac{4}{9} \rightarrow 4 : 9

The shape is 4 to 9.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

4 + 9 = 13

Each scaling step adds 13.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 65, so divide by 13.

65 \div 13 = 5

Scale everything by 5.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

4 \times 5 : 9 \times 5 = 20 : 45

The ratio is 20 to 45.

Answer: 20 : 45

4 · Reviewdoes it hold up?

Both conditions hold: 20 plus 45 is 65, and 20 over 45 simplifies back to 4/9.

Another way: Listing 4 : 9, 8 : 18, 12 : 27 and watching the sums climb by 13 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 7 medium answer: 24 : 42

Among the ratios whose value is $\frac{4}{7}$ , find the one whose two terms add to $66$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 4/7, we want the one whose two terms add to 66.

Givens

The value of the ratio is 4/7.
The two terms add to 66.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 4/7 in lowest terms is 4 to 7.

\frac{4}{7} = \frac{4}{7} \rightarrow 4 : 7

The shape is 4 to 7.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

4 + 7 = 11

Each scaling step adds 11.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 66, so divide by 11.

66 \div 11 = 6

Scale everything by 6.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

4 \times 6 : 7 \times 6 = 24 : 42

The ratio is 24 to 42.

Answer: 24 : 42

4 · Reviewdoes it hold up?

Both conditions hold: 24 plus 42 is 66, and 24 over 42 simplifies back to 4/7.

Another way: Listing 4 : 7, 8 : 14, 12 : 21 and watching the sums climb by 11 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 8 medium answer: 32 : 44

Among the ratios whose value is $\frac{8}{11}$ , find the one whose two terms add to $76$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 8/11, we want the one whose two terms add to 76.

Givens

The value of the ratio is 8/11.
The two terms add to 76.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 8/11 in lowest terms is 8 to 11.

\frac{8}{11} = \frac{8}{11} \rightarrow 8 : 11

The shape is 8 to 11.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

8 + 11 = 19

Each scaling step adds 19.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 76, so divide by 19.

76 \div 19 = 4

Scale everything by 4.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

8 \times 4 : 11 \times 4 = 32 : 44

The ratio is 32 to 44.

Answer: 32 : 44

4 · Reviewdoes it hold up?

Both conditions hold: 32 plus 44 is 76, and 32 over 44 simplifies back to 8/11.

Another way: Listing 8 : 11, 16 : 22, 24 : 33 and watching the sums climb by 19 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 9 hard answer: 30 : 48

Among the ratios whose value is $\frac{5}{8}$ , find the one whose two terms add to $78$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 5/8, we want the one whose two terms add to 78.

Givens

The value of the ratio is 5/8.
The two terms add to 78.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 5/8 in lowest terms is 5 to 8.

\frac{5}{8} = \frac{5}{8} \rightarrow 5 : 8

The shape is 5 to 8.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

5 + 8 = 13

Each scaling step adds 13.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 78, so divide by 13.

78 \div 13 = 6

Scale everything by 6.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

5 \times 6 : 8 \times 6 = 30 : 48

The ratio is 30 to 48.

Answer: 30 : 48

4 · Reviewdoes it hold up?

Both conditions hold: 30 plus 48 is 78, and 30 over 48 simplifies back to 5/8.

Another way: Listing 5 : 8, 10 : 16, 15 : 24 and watching the sums climb by 13 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 10 hard answer: 36 : 48

Among the ratios whose value is $\frac{3}{4}$ , find the one whose two terms add to $84$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 3/4, we want the one whose two terms add to 84.

Givens

The value of the ratio is 3/4.
The two terms add to 84.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 3/4 in lowest terms is 3 to 4.

\frac{3}{4} = \frac{3}{4} \rightarrow 3 : 4

The shape is 3 to 4.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

3 + 4 = 7

Each scaling step adds 7.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 84, so divide by 7.

84 \div 7 = 12

Scale everything by 12.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

3 \times 12 : 4 \times 12 = 36 : 48

The ratio is 36 to 48.

Answer: 36 : 48

4 · Reviewdoes it hold up?

Both conditions hold: 36 plus 48 is 84, and 36 over 48 simplifies back to 3/4.

Another way: Listing 3 : 4, 6 : 8, 9 : 12 and watching the sums climb by 7 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 11 hard answer: 40 : 48

Among the ratios whose value is $\frac{5}{6}$ , find the one whose two terms add to $88$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 5/6, we want the one whose two terms add to 88.

Givens

The value of the ratio is 5/6.
The two terms add to 88.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 5/6 in lowest terms is 5 to 6.

\frac{5}{6} = \frac{5}{6} \rightarrow 5 : 6

The shape is 5 to 6.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

5 + 6 = 11

Each scaling step adds 11.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 88, so divide by 11.

88 \div 11 = 8

Scale everything by 8.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

5 \times 8 : 6 \times 8 = 40 : 48

The ratio is 40 to 48.

Answer: 40 : 48

4 · Reviewdoes it hold up?

Both conditions hold: 40 plus 48 is 88, and 40 over 48 simplifies back to 5/6.

Another way: Listing 5 : 6, 10 : 12, 15 : 18 and watching the sums climb by 11 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.

Variant 12 hard answer: 45 : 50

Among the ratios whose value is $\frac{9}{10}$ , find the one whose two terms add to $95$ .

Show solution

1 · Understandwhat's really being asked

Of all the ratios worth 9/10, we want the one whose two terms add to 95.

Givens

The value of the ratio is 9/10.
The two terms add to 95.

Unknowns

The two terms of the ratio.

Constraints

Infinitely many ratios share the value; only one has that sum.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems#13 Convert to Algebra

The value alone allows any number of ratios, because scaling both terms leaves it unchanged. Write the simplest one, see what its terms add to, and scale until that sum is the one asked for.

3 · Execute4 carry out the plan

1Write the simplest ratio

#5 Look for a Pattern 6.RP.A.1

A value of 9/10 in lowest terms is 9 to 10.

\frac{9}{10} = \frac{9}{10} \rightarrow 9 : 10

The shape is 9 to 10.

2Add its terms

#7 Identify Subproblems 6.RP.A.3

That sum is what one unit of scaling is worth.

9 + 10 = 19

Each scaling step adds 19.

3Find the scale factor

#13 Convert to Algebra 6.RP.A.3

The real sum is 95, so divide by 19.

95 \div 19 = 5

Scale everything by 5.

4Scale both terms

#5 Look for a Pattern 6.RP.A.1

Multiplying both by the same number leaves the value alone.

9 \times 5 : 10 \times 5 = 45 : 50

The ratio is 45 to 50.

Answer: 45 : 50

4 · Reviewdoes it hold up?

Both conditions hold: 45 plus 50 is 95, and 45 over 50 simplifies back to 9/10.

Another way: Listing 9 : 10, 18 : 20, 27 : 30 and watching the sums climb by 19 arrives at the same place, one step at a time.

Standardsmin grade 6

6.RP.A.1 Understand ratio concepts and use ratio language — Writing the value as a ratio in lowest terms and scaling it.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Relating the sum of the terms to the scale factor.

💡Takeaway. A ratio's value says its shape. One more fact -- a sum or a difference -- says how big it is.