Eliminate to find two decimals from sum and difference
5.NBT.B.7
Generated variants — 10
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
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Understand
Two decimal numbers add up to 15.00 and differ by 6.26. Find both numbers.
- The two numbers add to 15.00.
- The larger minus the smaller is 6.26.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 6.26.
Plan
#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.
Execute
Review
Check both clues: 10.63 + 4.37 = 15.00 (sum correct) and 10.63 - 4.37 = 6.26 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 15.00 + 6.26, halving 21.26, and subtracting 15.00 - 10.63.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
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Understand
Two decimal numbers add up to 12.46 and differ by 5.68. Find both numbers.
- The two numbers add to 12.46.
- The larger minus the smaller is 5.68.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 5.68.
Plan
#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.
Execute
Review
Check both clues: 9.07 + 3.39 = 12.46 (sum correct) and 9.07 - 3.39 = 5.68 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 12.46 + 5.68, halving 18.14, and subtracting 12.46 - 9.07.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 16.78 and differ by 10.02. Find both numbers.
- The two numbers add to 16.78.
- The larger minus the smaller is 10.02.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 10.02.
Plan
#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.
Execute
Review
Check both clues: 13.40 + 3.38 = 16.78 (sum correct) and 13.40 - 3.38 = 10.02 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 16.78 + 10.02, halving 26.80, and subtracting 16.78 - 13.40.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
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Understand
Two decimal numbers add up to 8.60 and differ by 2.74. Find both numbers.
- The two numbers add to 8.60.
- The larger minus the smaller is 2.74.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 2.74.
Plan
#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.
Execute
Review
Check both clues: 5.67 + 2.93 = 8.60 (sum correct) and 5.67 - 2.93 = 2.74 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 8.60 + 2.74, halving 11.34, and subtracting 8.60 - 5.67.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 7.45 and differ by 3.11. Find both numbers.
- The two numbers add to 7.45.
- The larger minus the smaller is 3.11.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 3.11.
Plan
#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.
Execute
Review
Check both clues: 5.28 + 2.17 = 7.45 (sum correct) and 5.28 - 2.17 = 3.11 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 7.45 + 3.11, halving 10.56, and subtracting 7.45 - 5.28.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 9.05 and differ by 3.67. Find both numbers.
- The two numbers add to 9.05.
- The larger minus the smaller is 3.67.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 3.67.
Plan
#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.
Execute
Review
Check both clues: 6.36 + 2.69 = 9.05 (sum correct) and 6.36 - 2.69 = 3.67 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 9.05 + 3.67, halving 12.72, and subtracting 9.05 - 6.36.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 13.90 and differ by 5.56. Find both numbers.
- The two numbers add to 13.90.
- The larger minus the smaller is 5.56.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 5.56.
Plan
#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.
Execute
Review
Check both clues: 9.73 + 4.17 = 13.90 (sum correct) and 9.73 - 4.17 = 5.56 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 13.90 + 5.56, halving 19.46, and subtracting 13.90 - 9.73.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 20.34 and differ by 8.88. Find both numbers.
- The two numbers add to 20.34.
- The larger minus the smaller is 8.88.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 8.88.
Plan
#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.
Execute
Review
Check both clues: 14.61 + 5.73 = 20.34 (sum correct) and 14.61 - 5.73 = 8.88 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 20.34 + 8.88, halving 29.22, and subtracting 20.34 - 14.61.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 11.22 and differ by 4.50. Find both numbers.
- The two numbers add to 11.22.
- The larger minus the smaller is 4.50.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 4.50.
Plan
#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.
Execute
Review
Check both clues: 7.86 + 3.36 = 11.22 (sum correct) and 7.86 - 3.36 = 4.50 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 11.22 + 4.50, halving 15.72, and subtracting 11.22 - 7.86.
Two decimal numbers have a sum of and a difference of . Find each of the two numbers.
Show solution
Understand
Two decimal numbers add up to 9.80 and differ by 3.40. Find both numbers.
- The two numbers add to 9.80.
- The larger minus the smaller is 3.40.
- The larger number and the smaller number.
- Both are decimals; the larger one is bigger than the smaller by 3.40.
Plan
#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.
Execute
Review
Check both clues: 6.60 + 3.20 = 9.80 (sum correct) and 6.60 - 3.20 = 3.40 (difference correct). Both match the givens.
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.
Standards · min grade 5
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths — Computing 9.80 + 3.40, halving 13.20, and subtracting 9.80 - 6.60.