← Eliminate to find two decimals from sum and difference · Find Two Unknowns from Sum and Difference

Eliminate to find two decimals from sum and difference · 10 practice problems

5.NBT.B.7

Generated variants — 10

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

Variant 1 easy answer: 5.28 and 2.17

Two decimal numbers have a sum of 7.457.45 and a difference of 3.113.11. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 7.45 and differ by 3.11. Find both numbers.

Givens
  • The two numbers add to 7.45.
  • The larger minus the smaller is 3.11.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 3.11.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 7.45, and the longer minus the shorter is 3.11. Adding these removes the shorter bar twice over and leaves two longer bars: 7.45 + 3.11 = 10.56 = two larger numbers.
7.45+3.11=10.56=2×(larger)7.45 + 3.11 = 10.56 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 10.56 is the larger number: 10.56 / 2 = 5.28.
10.56÷2=5.2810.56 \div 2 = 5.28
Two equal larger bars share 10.56 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 7.45 - 5.28 = 2.17. (Equivalently, 5.28 - 3.11 = 2.17.)
7.45−5.28=2.177.45 - 5.28 = 2.17
Once one number is known, the other is whatever is left of the sum.
Answer: 5.28 and 2.17
4 · Reviewdoes it hold up?

Check both clues: 5.28 + 2.17 = 7.45 (sum correct) and 5.28 - 2.17 = 3.11 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 7.45 - 3.11 = 4.34, equals two smaller numbers, so the smaller is 4.34 / 2 = 2.17 and the larger is 2.17 + 3.11 = 5.28 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 7.45 + 3.11, halving 10.56, and subtracting 7.45 - 5.28.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 2 easy answer: 5.67 and 2.93

Two decimal numbers have a sum of 8.608.60 and a difference of 2.742.74. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 8.60 and differ by 2.74. Find both numbers.

Givens
  • The two numbers add to 8.60.
  • The larger minus the smaller is 2.74.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 2.74.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 8.60, and the longer minus the shorter is 2.74. Adding these removes the shorter bar twice over and leaves two longer bars: 8.60 + 2.74 = 11.34 = two larger numbers.
8.60+2.74=11.34=2×(larger)8.60 + 2.74 = 11.34 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 11.34 is the larger number: 11.34 / 2 = 5.67.
11.34÷2=5.6711.34 \div 2 = 5.67
Two equal larger bars share 11.34 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 8.60 - 5.67 = 2.93. (Equivalently, 5.67 - 2.74 = 2.93.)
8.60−5.67=2.938.60 - 5.67 = 2.93
Once one number is known, the other is whatever is left of the sum.
Answer: 5.67 and 2.93
4 · Reviewdoes it hold up?

Check both clues: 5.67 + 2.93 = 8.60 (sum correct) and 5.67 - 2.93 = 2.74 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 8.60 - 2.74 = 5.86, equals two smaller numbers, so the smaller is 5.86 / 2 = 2.93 and the larger is 2.93 + 2.74 = 5.67 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 8.60 + 2.74, halving 11.34, and subtracting 8.60 - 5.67.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 3 easy answer: 6.36 and 2.69

Two decimal numbers have a sum of 9.059.05 and a difference of 3.673.67. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 9.05 and differ by 3.67. Find both numbers.

Givens
  • The two numbers add to 9.05.
  • The larger minus the smaller is 3.67.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 3.67.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 9.05, and the longer minus the shorter is 3.67. Adding these removes the shorter bar twice over and leaves two longer bars: 9.05 + 3.67 = 12.72 = two larger numbers.
9.05+3.67=12.72=2×(larger)9.05 + 3.67 = 12.72 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 12.72 is the larger number: 12.72 / 2 = 6.36.
12.72÷2=6.3612.72 \div 2 = 6.36
Two equal larger bars share 12.72 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 9.05 - 6.36 = 2.69. (Equivalently, 6.36 - 3.67 = 2.69.)
9.05−6.36=2.699.05 - 6.36 = 2.69
Once one number is known, the other is whatever is left of the sum.
Answer: 6.36 and 2.69
4 · Reviewdoes it hold up?

Check both clues: 6.36 + 2.69 = 9.05 (sum correct) and 6.36 - 2.69 = 3.67 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 9.05 - 3.67 = 5.38, equals two smaller numbers, so the smaller is 5.38 / 2 = 2.69 and the larger is 2.69 + 3.67 = 6.36 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 9.05 + 3.67, halving 12.72, and subtracting 9.05 - 6.36.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 4 medium answer: 6.60 and 3.20

Two decimal numbers have a sum of 9.809.80 and a difference of 3.403.40. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 9.80 and differ by 3.40. Find both numbers.

Givens
  • The two numbers add to 9.80.
  • The larger minus the smaller is 3.40.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 3.40.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 9.80, and the longer minus the shorter is 3.40. Adding these removes the shorter bar twice over and leaves two longer bars: 9.80 + 3.40 = 13.20 = two larger numbers.
9.80+3.40=13.20=2×(larger)9.80 + 3.40 = 13.20 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 13.20 is the larger number: 13.20 / 2 = 6.60.
13.20÷2=6.6013.20 \div 2 = 6.60
Two equal larger bars share 13.20 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 9.80 - 6.60 = 3.20. (Equivalently, 6.60 - 3.40 = 3.20.)
9.80−6.60=3.209.80 - 6.60 = 3.20
Once one number is known, the other is whatever is left of the sum.
Answer: 6.60 and 3.20
4 · Reviewdoes it hold up?

Check both clues: 6.60 + 3.20 = 9.80 (sum correct) and 6.60 - 3.20 = 3.40 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 9.80 - 3.40 = 6.40, equals two smaller numbers, so the smaller is 6.40 / 2 = 3.20 and the larger is 3.20 + 3.40 = 6.60 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 9.80 + 3.40, halving 13.20, and subtracting 9.80 - 6.60.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 5 medium answer: 7.86 and 3.36

Two decimal numbers have a sum of 11.2211.22 and a difference of 4.504.50. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 11.22 and differ by 4.50. Find both numbers.

Givens
  • The two numbers add to 11.22.
  • The larger minus the smaller is 4.50.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 4.50.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 11.22, and the longer minus the shorter is 4.50. Adding these removes the shorter bar twice over and leaves two longer bars: 11.22 + 4.50 = 15.72 = two larger numbers.
11.22+4.50=15.72=2×(larger)11.22 + 4.50 = 15.72 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 15.72 is the larger number: 15.72 / 2 = 7.86.
15.72÷2=7.8615.72 \div 2 = 7.86
Two equal larger bars share 15.72 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 11.22 - 7.86 = 3.36. (Equivalently, 7.86 - 4.50 = 3.36.)
11.22−7.86=3.3611.22 - 7.86 = 3.36
Once one number is known, the other is whatever is left of the sum.
Answer: 7.86 and 3.36
4 · Reviewdoes it hold up?

Check both clues: 7.86 + 3.36 = 11.22 (sum correct) and 7.86 - 3.36 = 4.50 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 11.22 - 4.50 = 6.72, equals two smaller numbers, so the smaller is 6.72 / 2 = 3.36 and the larger is 3.36 + 4.50 = 7.86 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 11.22 + 4.50, halving 15.72, and subtracting 11.22 - 7.86.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 6 medium answer: 9.07 and 3.39

Two decimal numbers have a sum of 12.4612.46 and a difference of 5.685.68. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 12.46 and differ by 5.68. Find both numbers.

Givens
  • The two numbers add to 12.46.
  • The larger minus the smaller is 5.68.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 5.68.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 12.46, and the longer minus the shorter is 5.68. Adding these removes the shorter bar twice over and leaves two longer bars: 12.46 + 5.68 = 18.14 = two larger numbers.
12.46+5.68=18.14=2×(larger)12.46 + 5.68 = 18.14 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 18.14 is the larger number: 18.14 / 2 = 9.07.
18.14÷2=9.0718.14 \div 2 = 9.07
Two equal larger bars share 18.14 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 12.46 - 9.07 = 3.39. (Equivalently, 9.07 - 5.68 = 3.39.)
12.46−9.07=3.3912.46 - 9.07 = 3.39
Once one number is known, the other is whatever is left of the sum.
Answer: 9.07 and 3.39
4 · Reviewdoes it hold up?

Check both clues: 9.07 + 3.39 = 12.46 (sum correct) and 9.07 - 3.39 = 5.68 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 12.46 - 5.68 = 6.78, equals two smaller numbers, so the smaller is 6.78 / 2 = 3.39 and the larger is 3.39 + 5.68 = 9.07 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 12.46 + 5.68, halving 18.14, and subtracting 12.46 - 9.07.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 7 medium answer: 9.73 and 4.17

Two decimal numbers have a sum of 13.9013.90 and a difference of 5.565.56. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 13.90 and differ by 5.56. Find both numbers.

Givens
  • The two numbers add to 13.90.
  • The larger minus the smaller is 5.56.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 5.56.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 13.90, and the longer minus the shorter is 5.56. Adding these removes the shorter bar twice over and leaves two longer bars: 13.90 + 5.56 = 19.46 = two larger numbers.
13.90+5.56=19.46=2×(larger)13.90 + 5.56 = 19.46 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 19.46 is the larger number: 19.46 / 2 = 9.73.
19.46÷2=9.7319.46 \div 2 = 9.73
Two equal larger bars share 19.46 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 13.90 - 9.73 = 4.17. (Equivalently, 9.73 - 5.56 = 4.17.)
13.90−9.73=4.1713.90 - 9.73 = 4.17
Once one number is known, the other is whatever is left of the sum.
Answer: 9.73 and 4.17
4 · Reviewdoes it hold up?

Check both clues: 9.73 + 4.17 = 13.90 (sum correct) and 9.73 - 4.17 = 5.56 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 13.90 - 5.56 = 8.34, equals two smaller numbers, so the smaller is 8.34 / 2 = 4.17 and the larger is 4.17 + 5.56 = 9.73 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 13.90 + 5.56, halving 19.46, and subtracting 13.90 - 9.73.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 8 hard answer: 10.63 and 4.37

Two decimal numbers have a sum of 15.0015.00 and a difference of 6.266.26. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 15.00 and differ by 6.26. Find both numbers.

Givens
  • The two numbers add to 15.00.
  • The larger minus the smaller is 6.26.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 6.26.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 15.00, and the longer minus the shorter is 6.26. Adding these removes the shorter bar twice over and leaves two longer bars: 15.00 + 6.26 = 21.26 = two larger numbers.
15.00+6.26=21.26=2×(larger)15.00 + 6.26 = 21.26 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 21.26 is the larger number: 21.26 / 2 = 10.63.
21.26÷2=10.6321.26 \div 2 = 10.63
Two equal larger bars share 21.26 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 15.00 - 10.63 = 4.37. (Equivalently, 10.63 - 6.26 = 4.37.)
15.00−10.63=4.3715.00 - 10.63 = 4.37
Once one number is known, the other is whatever is left of the sum.
Answer: 10.63 and 4.37
4 · Reviewdoes it hold up?

Check both clues: 10.63 + 4.37 = 15.00 (sum correct) and 10.63 - 4.37 = 6.26 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 15.00 - 6.26 = 8.74, equals two smaller numbers, so the smaller is 8.74 / 2 = 4.37 and the larger is 4.37 + 6.26 = 10.63 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 15.00 + 6.26, halving 21.26, and subtracting 15.00 - 10.63.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 9 hard answer: 13.40 and 3.38

Two decimal numbers have a sum of 16.7816.78 and a difference of 10.0210.02. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 16.78 and differ by 10.02. Find both numbers.

Givens
  • The two numbers add to 16.78.
  • The larger minus the smaller is 10.02.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 10.02.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 16.78, and the longer minus the shorter is 10.02. Adding these removes the shorter bar twice over and leaves two longer bars: 16.78 + 10.02 = 26.80 = two larger numbers.
16.78+10.02=26.80=2×(larger)16.78 + 10.02 = 26.80 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 26.80 is the larger number: 26.80 / 2 = 13.40.
26.80÷2=13.4026.80 \div 2 = 13.40
Two equal larger bars share 26.80 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 16.78 - 13.40 = 3.38. (Equivalently, 13.40 - 10.02 = 3.38.)
16.78−13.40=3.3816.78 - 13.40 = 3.38
Once one number is known, the other is whatever is left of the sum.
Answer: 13.40 and 3.38
4 · Reviewdoes it hold up?

Check both clues: 13.40 + 3.38 = 16.78 (sum correct) and 13.40 - 3.38 = 10.02 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 16.78 - 10.02 = 6.76, equals two smaller numbers, so the smaller is 6.76 / 2 = 3.38 and the larger is 3.38 + 10.02 = 13.40 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 16.78 + 10.02, halving 26.80, and subtracting 16.78 - 13.40.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!
Variant 10 hard answer: 14.61 and 5.73

Two decimal numbers have a sum of 20.3420.34 and a difference of 8.888.88. Find each of the two numbers.

Show solution
1 · Understandwhat's really being asked

Two decimal numbers add up to 20.34 and differ by 8.88. Find both numbers.

Givens
  • The two numbers add to 20.34.
  • The larger minus the smaller is 8.88.
Unknowns
  • The larger number and the smaller number.
Constraints
  • Both are decimals; the larger one is bigger than the smaller by 8.88.
2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #15 Organize Information in More Ways

Picture the two numbers as two bars. The sum is both bars together; the difference is the extra piece on the longer bar. Adding sum and difference gives two copies of the larger number, which is the classic sum-and-difference (bar model) method.

3 · Execute3 carry out the plan

1Add sum and difference to get twice the larger

#1 Draw a Diagram 5.NBT.B.7
In a bar model, the longer bar plus the shorter bar is 20.34, and the longer minus the shorter is 8.88. Adding these removes the shorter bar twice over and leaves two longer bars: 20.34 + 8.88 = 29.22 = two larger numbers.
20.34+8.88=29.22=2×(larger)20.34 + 8.88 = 29.22 = 2 \times (\text{larger})
Sum plus difference doubles the bigger number - a bar-model staple.

2Find the larger number

#1 Draw a Diagram 5.NBT.B.7
Half of 29.22 is the larger number: 29.22 / 2 = 14.61.
29.22÷2=14.6129.22 \div 2 = 14.61
Two equal larger bars share 29.22 evenly, so split it in half.

3Find the smaller number

#15 Organize Information in More Ways 5.NBT.B.7
Subtract the larger from the total to get the smaller: 20.34 - 14.61 = 5.73. (Equivalently, 14.61 - 8.88 = 5.73.)
20.34−14.61=5.7320.34 - 14.61 = 5.73
Once one number is known, the other is whatever is left of the sum.
Answer: 14.61 and 5.73
4 · Reviewdoes it hold up?

Check both clues: 14.61 + 5.73 = 20.34 (sum correct) and 14.61 - 5.73 = 8.88 (difference correct). Both match the givens.

Another way: Subtract instead: sum minus difference, 20.34 - 8.88 = 11.46, equals two smaller numbers, so the smaller is 11.46 / 2 = 5.73 and the larger is 5.73 + 8.88 = 14.61 - same pair.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 20.34 + 8.88, halving 29.22, and subtracting 20.34 - 14.61.
💡Takeaway. Sum plus difference is two of the bigger number - cut it in half and the rest falls out!