← Start where only one thing is unknown · Proportion and Proportional Division

Start where only one thing is unknown · 12 practice problems

7.RP.A.26.RP.A.3

Generated variants — 12

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

Variant 1 easy answer: 17 : 34 = 4 : 8

A proportion is to be built whose value is 0.50.5 and whose extremes multiply to 136136. Fill in the boxes.

□:34=□:□\square : 34 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 0.5, its second term is 34, and its outer terms multiply to 136. We want all three missing terms.

Givens
  • The value of each ratio is 0.5.
  • The second term is 34.
  • The extremes multiply to 136.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 34 with value 0.5, so the first term is 34 times 0.5.
34×0.5=1734 \times 0.5 = 17
The first term is 17.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 136.
136÷17=8136 \div 17 = 8
The last term is 8.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 8 times 0.5.
8×0.5=48 \times 0.5 = 4
The third term is 4.
Answer: 17 : 34 = 4 : 8
4 · Reviewdoes it hold up?

Both ratios have value 0.5, and the extremes 17 and 8 multiply to 136 -- as do the means, 34 and 4, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 2 easy answer: 10 : 20 = 11 : 22

A proportion is to be built whose value is 0.50.5 and whose extremes multiply to 220220. Fill in the boxes.

□:20=□:□\square : 20 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 0.5, its second term is 20, and its outer terms multiply to 220. We want all three missing terms.

Givens
  • The value of each ratio is 0.5.
  • The second term is 20.
  • The extremes multiply to 220.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 20 with value 0.5, so the first term is 20 times 0.5.
20×0.5=1020 \times 0.5 = 10
The first term is 10.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 220.
220÷10=22220 \div 10 = 22
The last term is 22.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 22 times 0.5.
22×0.5=1122 \times 0.5 = 11
The third term is 11.
Answer: 10 : 20 = 11 : 22
4 · Reviewdoes it hold up?

Both ratios have value 0.5, and the extremes 10 and 22 multiply to 220 -- as do the means, 20 and 11, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 3 easy answer: 30 : 20 = 18 : 12

A proportion is to be built whose value is 1.51.5 and whose extremes multiply to 360360. Fill in the boxes.

□:20=□:□\square : 20 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 1.5, its second term is 20, and its outer terms multiply to 360. We want all three missing terms.

Givens
  • The value of each ratio is 1.5.
  • The second term is 20.
  • The extremes multiply to 360.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 20 with value 1.5, so the first term is 20 times 1.5.
20×1.5=3020 \times 1.5 = 30
The first term is 30.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 360.
360÷30=12360 \div 30 = 12
The last term is 12.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 12 times 1.5.
12×1.5=1812 \times 1.5 = 18
The third term is 18.
Answer: 30 : 20 = 18 : 12
4 · Reviewdoes it hold up?

Both ratios have value 1.5, and the extremes 30 and 12 multiply to 360 -- as do the means, 20 and 18, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 4 easy answer: 17 : 34 = 13 : 26

A proportion is to be built whose value is 0.50.5 and whose extremes multiply to 442442. Fill in the boxes.

□:34=□:□\square : 34 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 0.5, its second term is 34, and its outer terms multiply to 442. We want all three missing terms.

Givens
  • The value of each ratio is 0.5.
  • The second term is 34.
  • The extremes multiply to 442.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 34 with value 0.5, so the first term is 34 times 0.5.
34×0.5=1734 \times 0.5 = 17
The first term is 17.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 442.
442÷17=26442 \div 17 = 26
The last term is 26.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 26 times 0.5.
26×0.5=1326 \times 0.5 = 13
The third term is 13.
Answer: 17 : 34 = 13 : 26
4 · Reviewdoes it hold up?

Both ratios have value 0.5, and the extremes 17 and 26 multiply to 442 -- as do the means, 34 and 13, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 5 medium answer: 70 : 28 = 25 : 10

A proportion is to be built whose value is 2.52.5 and whose extremes multiply to 700700. Fill in the boxes.

□:28=□:□\square : 28 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2.5, its second term is 28, and its outer terms multiply to 700. We want all three missing terms.

Givens
  • The value of each ratio is 2.5.
  • The second term is 28.
  • The extremes multiply to 700.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 28 with value 2.5, so the first term is 28 times 2.5.
28×2.5=7028 \times 2.5 = 70
The first term is 70.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 700.
700÷70=10700 \div 70 = 10
The last term is 10.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 10 times 2.5.
10×2.5=2510 \times 2.5 = 25
The third term is 25.
Answer: 70 : 28 = 25 : 10
4 · Reviewdoes it hold up?

Both ratios have value 2.5, and the extremes 70 and 10 multiply to 700 -- as do the means, 28 and 25, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 6 medium answer: 19 : 38 = 19 : 38

A proportion is to be built whose value is 0.50.5 and whose extremes multiply to 722722. Fill in the boxes.

□:38=□:□\square : 38 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 0.5, its second term is 38, and its outer terms multiply to 722. We want all three missing terms.

Givens
  • The value of each ratio is 0.5.
  • The second term is 38.
  • The extremes multiply to 722.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 38 with value 0.5, so the first term is 38 times 0.5.
38×0.5=1938 \times 0.5 = 19
The first term is 19.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 722.
722÷19=38722 \div 19 = 38
The last term is 38.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 38 times 0.5.
38×0.5=1938 \times 0.5 = 19
The third term is 19.
Answer: 19 : 38 = 19 : 38
4 · Reviewdoes it hold up?

Both ratios have value 0.5, and the extremes 19 and 38 multiply to 722 -- as do the means, 38 and 19, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 7 medium answer: 32 : 16 = 70 : 35

A proportion is to be built whose value is 22 and whose extremes multiply to 11201120. Fill in the boxes.

□:16=□:□\square : 16 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2, its second term is 16, and its outer terms multiply to 1120. We want all three missing terms.

Givens
  • The value of each ratio is 2.
  • The second term is 16.
  • The extremes multiply to 1120.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 16 with value 2, so the first term is 16 times 2.
16×2=3216 \times 2 = 32
The first term is 32.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 1120.
1120÷32=351120 \div 32 = 35
The last term is 35.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 35 times 2.
35×2=7035 \times 2 = 70
The third term is 70.
Answer: 32 : 16 = 70 : 35
4 · Reviewdoes it hold up?

Both ratios have value 2, and the extremes 32 and 35 multiply to 1120 -- as do the means, 16 and 70, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 8 medium answer: 33 : 22 = 57 : 38

A proportion is to be built whose value is 1.51.5 and whose extremes multiply to 12541254. Fill in the boxes.

□:22=□:□\square : 22 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 1.5, its second term is 22, and its outer terms multiply to 1254. We want all three missing terms.

Givens
  • The value of each ratio is 1.5.
  • The second term is 22.
  • The extremes multiply to 1254.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 22 with value 1.5, so the first term is 22 times 1.5.
22×1.5=3322 \times 1.5 = 33
The first term is 33.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 1254.
1254÷33=381254 \div 33 = 38
The last term is 38.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 38 times 1.5.
38×1.5=5738 \times 1.5 = 57
The third term is 57.
Answer: 33 : 22 = 57 : 38
4 · Reviewdoes it hold up?

Both ratios have value 1.5, and the extremes 33 and 38 multiply to 1254 -- as do the means, 22 and 57, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 9 hard answer: 55 : 22 = 70 : 28

A proportion is to be built whose value is 2.52.5 and whose extremes multiply to 15401540. Fill in the boxes.

□:22=□:□\square : 22 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2.5, its second term is 22, and its outer terms multiply to 1540. We want all three missing terms.

Givens
  • The value of each ratio is 2.5.
  • The second term is 22.
  • The extremes multiply to 1540.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 22 with value 2.5, so the first term is 22 times 2.5.
22×2.5=5522 \times 2.5 = 55
The first term is 55.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 1540.
1540÷55=281540 \div 55 = 28
The last term is 28.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 28 times 2.5.
28×2.5=7028 \times 2.5 = 70
The third term is 70.
Answer: 55 : 22 = 70 : 28
4 · Reviewdoes it hold up?

Both ratios have value 2.5, and the extremes 55 and 28 multiply to 1540 -- as do the means, 22 and 70, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 10 hard answer: 72 : 36 = 58 : 29

A proportion is to be built whose value is 22 and whose extremes multiply to 20882088. Fill in the boxes.

□:36=□:□\square : 36 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2, its second term is 36, and its outer terms multiply to 2088. We want all three missing terms.

Givens
  • The value of each ratio is 2.
  • The second term is 36.
  • The extremes multiply to 2088.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 36 with value 2, so the first term is 36 times 2.
36×2=7236 \times 2 = 72
The first term is 72.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 2088.
2088÷72=292088 \div 72 = 29
The last term is 29.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 29 times 2.
29×2=5829 \times 2 = 58
The third term is 58.
Answer: 72 : 36 = 58 : 29
4 · Reviewdoes it hold up?

Both ratios have value 2, and the extremes 72 and 29 multiply to 2088 -- as do the means, 36 and 58, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 11 hard answer: 68 : 34 = 72 : 36

A proportion is to be built whose value is 22 and whose extremes multiply to 24482448. Fill in the boxes.

□:34=□:□\square : 34 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2, its second term is 34, and its outer terms multiply to 2448. We want all three missing terms.

Givens
  • The value of each ratio is 2.
  • The second term is 34.
  • The extremes multiply to 2448.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 34 with value 2, so the first term is 34 times 2.
34×2=6834 \times 2 = 68
The first term is 68.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 2448.
2448÷68=362448 \div 68 = 36
The last term is 36.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 36 times 2.
36×2=7236 \times 2 = 72
The third term is 72.
Answer: 68 : 34 = 72 : 36
4 · Reviewdoes it hold up?

Both ratios have value 2, and the extremes 68 and 36 multiply to 2448 -- as do the means, 34 and 72, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.
Variant 12 hard answer: 90 : 36 = 95 : 38

A proportion is to be built whose value is 2.52.5 and whose extremes multiply to 34203420. Fill in the boxes.

□:36=□:□\square : 36 = \square : \square

Show solution
1 · Understandwhat's really being asked

A proportion has value 2.5, its second term is 36, and its outer terms multiply to 3420. We want all three missing terms.

Givens
  • The value of each ratio is 2.5.
  • The second term is 36.
  • The extremes multiply to 3420.
Unknowns
  • The first, third and fourth terms.
Constraints
  • The extremes are the first and last terms, not the middle two.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #13 Convert to Algebra#7 Identify Subproblems

Three blanks and two facts, so nothing can be done all at once. Start at the ratio that already has a term printed: there the value fixes the partner, and every later step then has only one unknown too.

3 · Execute3 carry out the plan

1Use the printed term

#3 Eliminate Possibilities 6.RP.A.3
The first ratio is something to 36 with value 2.5, so the first term is 36 times 2.5.
36×2.5=9036 \times 2.5 = 90
The first term is 90.

2Use the extremes

#13 Convert to Algebra 7.RP.A.2
The extremes are the first and last terms, and they multiply to 3420.
3420÷90=383420 \div 90 = 38
The last term is 38.

3Use the value again

#7 Identify Subproblems 6.RP.A.3
The second ratio has the same value, so its first term is 38 times 2.5.
38×2.5=9538 \times 2.5 = 95
The third term is 95.
Answer: 90 : 36 = 95 : 38
4 · Reviewdoes it hold up?

Both ratios have value 2.5, and the extremes 90 and 38 multiply to 3420 -- as do the means, 36 and 95, which is what makes it a proportion.

Another way: Starting from the extremes' product alone leaves two unknowns in one equation and cannot get going; the printed term is what makes the first step possible.

Standardsmin grade 7
  • 7.RP.A.2 Recognize and represent proportional relationships between quantities — Using the equality of the two products in a proportion.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Getting each term from the ratio's value.
💡Takeaway. With several blanks, look for the one place a single fact settles something. Fill that in and the rest follow.