Practice · Subtract the overlap from total length · Sensim Math

Variant 1 easy

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $2\ \mathrm{m}\ 15\ \mathrm{cm}$ , the length from B to D is $2\ \mathrm{m}\ 45\ \mathrm{cm}$ , and the overlapping part from B to C is $1\ \mathrm{m}\ 5\ \mathrm{cm}$ .

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1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 2 m 15 cm, the span B to D is 2 m 45 cm, and the overlapping middle span B to C is 1 m 5 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 2 m 15 cm.
B to D = 2 m 45 cm.
Overlap B to C = 1 m 5 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

215\,\text{cm},\ 245\,\text{cm},\ 105\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

215 + 245 = 460 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (105 cm) to get the true length A-D.

460 - 105 = 355 \text{ cm} = 3\,\text{m}\ 55\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 3 m 55 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (2 m 15 cm or 2 m 45 cm) but less than their sum (4 m 60 cm); 3 m 55 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 215 - 105 = 110 cm; then A-D = A-B + B-D = 110 + 245 = 355 cm = 3 m 55 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 2 easy

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $4\ \mathrm{m}\ 60\ \mathrm{cm}$ , the length from B to D is $3\ \mathrm{m}\ 40\ \mathrm{cm}$ , and the overlapping part from B to C is $2\ \mathrm{m}\ 25\ \mathrm{cm}$ .

Your answer (check it yourself)

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1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 4 m 60 cm, the span B to D is 3 m 40 cm, and the overlapping middle span B to C is 2 m 25 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 4 m 60 cm.
B to D = 3 m 40 cm.
Overlap B to C = 2 m 25 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

460\,\text{cm},\ 340\,\text{cm},\ 225\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

460 + 340 = 800 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (225 cm) to get the true length A-D.

800 - 225 = 575 \text{ cm} = 5\,\text{m}\ 75\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 5 m 75 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (4 m 60 cm or 3 m 40 cm) but less than their sum (8 m 0 cm); 5 m 75 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 460 - 225 = 235 cm; then A-D = A-B + B-D = 235 + 340 = 575 cm = 5 m 75 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 3 medium

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $3\ \mathrm{m}\ 20\ \mathrm{cm}$ , the length from B to D is $2\ \mathrm{m}\ 70\ \mathrm{cm}$ , and the overlapping part from B to C is $1\ \mathrm{m}\ 30\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 3 m 20 cm, the span B to D is 2 m 70 cm, and the overlapping middle span B to C is 1 m 30 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 3 m 20 cm.
B to D = 2 m 70 cm.
Overlap B to C = 1 m 30 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

320\,\text{cm},\ 270\,\text{cm},\ 130\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

320 + 270 = 590 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (130 cm) to get the true length A-D.

590 - 130 = 460 \text{ cm} = 4\,\text{m}\ 60\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 4 m 60 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (3 m 20 cm or 2 m 70 cm) but less than their sum (5 m 90 cm); 4 m 60 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 320 - 130 = 190 cm; then A-D = A-B + B-D = 190 + 270 = 460 cm = 4 m 60 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 4 medium

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $3\ \mathrm{m}\ 75\ \mathrm{cm}$ , the length from B to D is $3\ \mathrm{m}\ 25\ \mathrm{cm}$ , and the overlapping part from B to C is $2\ \mathrm{m}\ 50\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 3 m 75 cm, the span B to D is 3 m 25 cm, and the overlapping middle span B to C is 2 m 50 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 3 m 75 cm.
B to D = 3 m 25 cm.
Overlap B to C = 2 m 50 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

375\,\text{cm},\ 325\,\text{cm},\ 250\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

375 + 325 = 700 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (250 cm) to get the true length A-D.

700 - 250 = 450 \text{ cm} = 4\,\text{m}\ 50\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 4 m 50 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (3 m 75 cm or 3 m 25 cm) but less than their sum (7 m 0 cm); 4 m 50 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 375 - 250 = 125 cm; then A-D = A-B + B-D = 125 + 325 = 450 cm = 4 m 50 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 5 medium

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $5\ \mathrm{m}\ 30\ \mathrm{cm}$ , the length from B to D is $4\ \mathrm{m}\ 80\ \mathrm{cm}$ , and the overlapping part from B to C is $3\ \mathrm{m}\ 60\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 5 m 30 cm, the span B to D is 4 m 80 cm, and the overlapping middle span B to C is 3 m 60 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 5 m 30 cm.
B to D = 4 m 80 cm.
Overlap B to C = 3 m 60 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

530\,\text{cm},\ 480\,\text{cm},\ 360\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

530 + 480 = 1010 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (360 cm) to get the true length A-D.

1010 - 360 = 650 \text{ cm} = 6\,\text{m}\ 50\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 6 m 50 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (5 m 30 cm or 4 m 80 cm) but less than their sum (10 m 10 cm); 6 m 50 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 530 - 360 = 170 cm; then A-D = A-B + B-D = 170 + 480 = 650 cm = 6 m 50 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 6 medium

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $2\ \mathrm{m}\ 55\ \mathrm{cm}$ , the length from B to D is $2\ \mathrm{m}\ 89\ \mathrm{cm}$ , and the overlapping part from B to C is $1\ \mathrm{m}\ 50\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 2 m 55 cm, the span B to D is 2 m 89 cm, and the overlapping middle span B to C is 1 m 50 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 2 m 55 cm.
B to D = 2 m 89 cm.
Overlap B to C = 1 m 50 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

255\,\text{cm},\ 289\,\text{cm},\ 150\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

255 + 289 = 544 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (150 cm) to get the true length A-D.

544 - 150 = 394 \text{ cm} = 3\,\text{m}\ 94\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 3 m 94 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (2 m 55 cm or 2 m 89 cm) but less than their sum (5 m 44 cm); 3 m 94 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 255 - 150 = 105 cm; then A-D = A-B + B-D = 105 + 289 = 394 cm = 3 m 94 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 7 hard

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $2\ \mathrm{m}\ 90\ \mathrm{cm}$ , the length from B to D is $3\ \mathrm{m}\ 10\ \mathrm{cm}$ , and the overlapping part from B to C is $1\ \mathrm{m}\ 95\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 2 m 90 cm, the span B to D is 3 m 10 cm, and the overlapping middle span B to C is 1 m 95 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 2 m 90 cm.
B to D = 3 m 10 cm.
Overlap B to C = 1 m 95 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

290\,\text{cm},\ 310\,\text{cm},\ 195\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

290 + 310 = 600 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (195 cm) to get the true length A-D.

600 - 195 = 405 \text{ cm} = 4\,\text{m}\ 5\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 4 m 5 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (2 m 90 cm or 3 m 10 cm) but less than their sum (6 m 0 cm); 4 m 5 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 290 - 195 = 95 cm; then A-D = A-B + B-D = 95 + 310 = 405 cm = 4 m 5 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Variant 8 hard

Find the length from A to D in meters and centimeters.

On a single straight line the four points A, B, C, D are marked in order from left to right. The length from A to C is $1\ \mathrm{m}\ 80\ \mathrm{cm}$ , the length from B to D is $1\ \mathrm{m}\ 95\ \mathrm{cm}$ , and the overlapping part from B to C is $1\ \mathrm{m}\ 10\ \mathrm{cm}$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Four points A, B, C, D lie in order on a line. The span A to C is 1 m 80 cm, the span B to D is 1 m 95 cm, and the overlapping middle span B to C is 1 m 10 cm. Find the full length from A to D in meters and centimeters.

Givens

A, B, C, D are in order from left to right on one straight line.
A to C = 1 m 80 cm.
B to D = 1 m 95 cm.
Overlap B to C = 1 m 10 cm.

Unknowns

The length from A to D in meters and centimeters.

Constraints

1 m = 100 cm.
Adding A-C and B-D counts the middle overlap B-C twice, so it must be subtracted once.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The picture shows two overlapping spans whose overlap is B-C. Adding the two spans double-counts the overlap, so A-D = (A-C) + (B-D) - (B-C). Work in centimeters, then convert back.

3 · Execute3 carry out the plan

1Convert all spans to centimeters

#1 Draw a Diagram 2.MD.B.5

Write each length in centimeters so they can be combined.

180\,\text{cm},\ 195\,\text{cm},\ 110\,\text{cm}

Same-unit lengths add and subtract cleanly.

2Add the two overlapping spans

#7 Identify Subproblems 2.MD.A.4

Add A-C and B-D; this counts the middle part B-C twice.

180 + 195 = 375 \text{ cm}

Combining the two measured pieces gives a total that includes the overlap region twice.

3Subtract the double-counted overlap

#7 Identify Subproblems 2.MD.B.5

Remove one copy of the overlap B-C (110 cm) to get the true length A-D.

375 - 110 = 265 \text{ cm} = 2\,\text{m}\ 65\,\text{cm}

Taking out the part counted twice leaves the full stretch from A to D exactly once.

Answer: 2 m 65 cm

4 · Reviewdoes it hold up?

A-D should be longer than either single span (1 m 80 cm or 1 m 95 cm) but less than their sum (3 m 75 cm); 2 m 65 cm fits between, so it is reasonable.

Another way: Subproblems by segments (tool 7): A-B = (A-C) - (B-C) = 180 - 110 = 70 cm; then A-D = A-B + B-D = 70 + 195 = 265 cm = 2 m 65 cm.

Standardsmin grade 2

2.MD.B.5 Solve word problems involving lengths using same units — Adding and subtracting same-unit lengths to find A to D.
2.MD.A.4 Measure to determine how much longer one object is than another — Reasoning about the overlapping spans and the doubly counted middle part.

💡Takeaway. When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!

Subtract the overlap from total length · 8 practice problems

Generated variants — 8

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