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Find the extreme decimal satisfying an inequality · 10 practice problems

5.NBT.B.74.NF.C.7

Generated variants — 10

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

Variant 1 answer: 5.02

Find the greatest number with two decimal places that can go in the □\square.

□+3.25<9.82−1.54\square + 3.25 < 9.82 - 1.54

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 3.25 stays less than 9.82 - 1.54.

Givens
  • The inequality is box + 3.25 < 9.82 - 1.54.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 9.82 - 1.54 = 8.28. So the inequality becomes box + 3.25 < 8.28.
9.82−1.54=8.289.82 - 1.54 = 8.28
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 3.25 from both sides to undo the addition: box < 8.28 - 3.25 = 5.03.
□<8.28−3.25=5.03\square < 8.28 - 3.25 = 5.03
Undo the +3.25 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 5.03. The largest hundredths number below 5.03 is one hundredth less: 5.02.
□=5.03−0.01=5.02\square = 5.03 - 0.01 = 5.02
Since it can't equal 5.03, step down one hundredth to the biggest allowed value.
Answer: 5.02

Review

Test 5.02: 5.02 + 3.25 = 8.27, which is less than 8.28 - true. Test 5.03: 5.03 + 3.25 = 8.28, not less than 8.28 - false. So 5.02 is indeed the greatest value that works.

Guess and Check near the boundary: try 5.03 (fails, equals), then 5.02 (works), confirming 5.02 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 9.82 - 1.54 and 8.28 - 3.25.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 5.03.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 2 answer: 2.13

Find the greatest number with two decimal places that can go in the □\square.

□+2.73<8.88−4.01\square + 2.73 < 8.88 - 4.01

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 2.73 stays less than 8.88 - 4.01.

Givens
  • The inequality is box + 2.73 < 8.88 - 4.01.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 8.88 - 4.01 = 4.87. So the inequality becomes box + 2.73 < 4.87.
8.88−4.01=4.878.88 - 4.01 = 4.87
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 2.73 from both sides to undo the addition: box < 4.87 - 2.73 = 2.14.
□<4.87−2.73=2.14\square < 4.87 - 2.73 = 2.14
Undo the +2.73 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 2.14. The largest hundredths number below 2.14 is one hundredth less: 2.13.
□=2.14−0.01=2.13\square = 2.14 - 0.01 = 2.13
Since it can't equal 2.14, step down one hundredth to the biggest allowed value.
Answer: 2.13

Review

Test 2.13: 2.13 + 2.73 = 4.86, which is less than 4.87 - true. Test 2.14: 2.14 + 2.73 = 4.87, not less than 4.87 - false. So 2.13 is indeed the greatest value that works.

Guess and Check near the boundary: try 2.14 (fails, equals), then 2.13 (works), confirming 2.13 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 8.88 - 4.01 and 4.87 - 2.73.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 2.14.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 3 answer: 3.62

Find the greatest number with two decimal places that can go in the □\square.

□+1.99<7.20−1.58\square + 1.99 < 7.20 - 1.58

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 1.99 stays less than 7.20 - 1.58.

Givens
  • The inequality is box + 1.99 < 7.20 - 1.58.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 7.20 - 1.58 = 5.62. So the inequality becomes box + 1.99 < 5.62.
7.20−1.58=5.627.20 - 1.58 = 5.62
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 1.99 from both sides to undo the addition: box < 5.62 - 1.99 = 3.63.
□<5.62−1.99=3.63\square < 5.62 - 1.99 = 3.63
Undo the +1.99 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.63. The largest hundredths number below 3.63 is one hundredth less: 3.62.
□=3.63−0.01=3.62\square = 3.63 - 0.01 = 3.62
Since it can't equal 3.63, step down one hundredth to the biggest allowed value.
Answer: 3.62

Review

Test 3.62: 3.62 + 1.99 = 5.61, which is less than 5.62 - true. Test 3.63: 3.63 + 1.99 = 5.62, not less than 5.62 - false. So 3.62 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.63 (fails, equals), then 3.62 (works), confirming 3.62 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 7.20 - 1.58 and 5.62 - 1.99.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.63.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 4 answer: 4.08

Find the greatest number with two decimal places that can go in the □\square.

□+2.08<7.60−1.43\square + 2.08 < 7.60 - 1.43

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 2.08 stays less than 7.60 - 1.43.

Givens
  • The inequality is box + 2.08 < 7.60 - 1.43.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 7.60 - 1.43 = 6.17. So the inequality becomes box + 2.08 < 6.17.
7.60−1.43=6.177.60 - 1.43 = 6.17
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 2.08 from both sides to undo the addition: box < 6.17 - 2.08 = 4.09.
□<6.17−2.08=4.09\square < 6.17 - 2.08 = 4.09
Undo the +2.08 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 4.09. The largest hundredths number below 4.09 is one hundredth less: 4.08.
□=4.09−0.01=4.08\square = 4.09 - 0.01 = 4.08
Since it can't equal 4.09, step down one hundredth to the biggest allowed value.
Answer: 4.08

Review

Test 4.08: 4.08 + 2.08 = 6.16, which is less than 6.17 - true. Test 4.09: 4.09 + 2.08 = 6.17, not less than 6.17 - false. So 4.08 is indeed the greatest value that works.

Guess and Check near the boundary: try 4.09 (fails, equals), then 4.08 (works), confirming 4.08 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 7.60 - 1.43 and 6.17 - 2.08.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 4.09.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 5 answer: 2.99

Find the greatest number with two decimal places that can go in the □\square.

□+5.34<13.00−4.66\square + 5.34 < 13.00 - 4.66

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 5.34 stays less than 13.00 - 4.66.

Givens
  • The inequality is box + 5.34 < 13.00 - 4.66.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 13.00 - 4.66 = 8.34. So the inequality becomes box + 5.34 < 8.34.
13.00−4.66=8.3413.00 - 4.66 = 8.34
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 5.34 from both sides to undo the addition: box < 8.34 - 5.34 = 3.00.
□<8.34−5.34=3.00\square < 8.34 - 5.34 = 3.00
Undo the +5.34 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.00. The largest hundredths number below 3.00 is one hundredth less: 2.99.
□=3.00−0.01=2.99\square = 3.00 - 0.01 = 2.99
Since it can't equal 3.00, step down one hundredth to the biggest allowed value.
Answer: 2.99

Review

Test 2.99: 2.99 + 5.34 = 8.33, which is less than 8.34 - true. Test 3.00: 3.00 + 5.34 = 8.34, not less than 8.34 - false. So 2.99 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.00 (fails, equals), then 2.99 (works), confirming 2.99 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 13.00 - 4.66 and 8.34 - 5.34.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.00.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 6 answer: 3.56

Find the greatest number with two decimal places that can go in the □\square.

□+4.17<10.45−2.71\square + 4.17 < 10.45 - 2.71

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 4.17 stays less than 10.45 - 2.71.

Givens
  • The inequality is box + 4.17 < 10.45 - 2.71.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 10.45 - 2.71 = 7.74. So the inequality becomes box + 4.17 < 7.74.
10.45−2.71=7.7410.45 - 2.71 = 7.74
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 4.17 from both sides to undo the addition: box < 7.74 - 4.17 = 3.57.
□<7.74−4.17=3.57\square < 7.74 - 4.17 = 3.57
Undo the +4.17 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.57. The largest hundredths number below 3.57 is one hundredth less: 3.56.
□=3.57−0.01=3.56\square = 3.57 - 0.01 = 3.56
Since it can't equal 3.57, step down one hundredth to the biggest allowed value.
Answer: 3.56

Review

Test 3.56: 3.56 + 4.17 = 7.73, which is less than 7.74 - true. Test 3.57: 3.57 + 4.17 = 7.74, not less than 7.74 - false. So 3.56 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.57 (fails, equals), then 3.56 (works), confirming 3.56 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 10.45 - 2.71 and 7.74 - 4.17.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.57.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 7 answer: 2.39

Find the greatest number with two decimal places that can go in the □\square.

□+1.46<6.05−2.19\square + 1.46 < 6.05 - 2.19

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 1.46 stays less than 6.05 - 2.19.

Givens
  • The inequality is box + 1.46 < 6.05 - 2.19.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 6.05 - 2.19 = 3.86. So the inequality becomes box + 1.46 < 3.86.
6.05−2.19=3.866.05 - 2.19 = 3.86
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 1.46 from both sides to undo the addition: box < 3.86 - 1.46 = 2.40.
□<3.86−1.46=2.40\square < 3.86 - 1.46 = 2.40
Undo the +1.46 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 2.40. The largest hundredths number below 2.40 is one hundredth less: 2.39.
□=2.40−0.01=2.39\square = 2.40 - 0.01 = 2.39
Since it can't equal 2.40, step down one hundredth to the biggest allowed value.
Answer: 2.39

Review

Test 2.39: 2.39 + 1.46 = 3.85, which is less than 3.86 - true. Test 2.40: 2.40 + 1.46 = 3.86, not less than 3.86 - false. So 2.39 is indeed the greatest value that works.

Guess and Check near the boundary: try 2.40 (fails, equals), then 2.39 (works), confirming 2.39 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 6.05 - 2.19 and 3.86 - 1.46.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 2.40.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 8 answer: 3.26

Find the greatest number with two decimal places that can go in the □\square.

□+5.19<12.34−3.88\square + 5.19 < 12.34 - 3.88

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 5.19 stays less than 12.34 - 3.88.

Givens
  • The inequality is box + 5.19 < 12.34 - 3.88.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 12.34 - 3.88 = 8.46. So the inequality becomes box + 5.19 < 8.46.
12.34−3.88=8.4612.34 - 3.88 = 8.46
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 5.19 from both sides to undo the addition: box < 8.46 - 5.19 = 3.27.
□<8.46−5.19=3.27\square < 8.46 - 5.19 = 3.27
Undo the +5.19 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.27. The largest hundredths number below 3.27 is one hundredth less: 3.26.
□=3.27−0.01=3.26\square = 3.27 - 0.01 = 3.26
Since it can't equal 3.27, step down one hundredth to the biggest allowed value.
Answer: 3.26

Review

Test 3.26: 3.26 + 5.19 = 8.45, which is less than 8.46 - true. Test 3.27: 3.27 + 5.19 = 8.46, not less than 8.46 - false. So 3.26 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.27 (fails, equals), then 3.26 (works), confirming 3.26 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 12.34 - 3.88 and 8.46 - 5.19.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.27.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 9 answer: 3.36

Find the greatest number with two decimal places that can go in the □\square.

□+3.87<9.50−2.26\square + 3.87 < 9.50 - 2.26

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 3.87 stays less than 9.50 - 2.26.

Givens
  • The inequality is box + 3.87 < 9.50 - 2.26.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 9.50 - 2.26 = 7.24. So the inequality becomes box + 3.87 < 7.24.
9.50−2.26=7.249.50 - 2.26 = 7.24
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 3.87 from both sides to undo the addition: box < 7.24 - 3.87 = 3.37.
□<7.24−3.87=3.37\square < 7.24 - 3.87 = 3.37
Undo the +3.87 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.37. The largest hundredths number below 3.37 is one hundredth less: 3.36.
□=3.37−0.01=3.36\square = 3.37 - 0.01 = 3.36
Since it can't equal 3.37, step down one hundredth to the biggest allowed value.
Answer: 3.36

Review

Test 3.36: 3.36 + 3.87 = 7.23, which is less than 7.24 - true. Test 3.37: 3.37 + 3.87 = 7.24, not less than 7.24 - false. So 3.36 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.37 (fails, equals), then 3.36 (works), confirming 3.36 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 9.50 - 2.26 and 7.24 - 3.87.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.37.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!
Variant 10 answer: 3.62

Find the greatest number with two decimal places that can go in the □\square.

□+4.62<11.00−2.75\square + 4.62 < 11.00 - 2.75

Show solution

Understand

Find the greatest number with two decimal places that can fill the box so that box + 4.62 stays less than 11.00 - 2.75.

Givens
  • The inequality is box + 4.62 < 11.00 - 2.75.
  • The box must be a number with exactly two decimal places (a hundredths number).
Unknowns
  • The greatest two-decimal-place number that fits in the box.
Constraints
  • The filled value must keep the inequality strictly true (less than, not equal).
  • The answer must have exactly two decimal places.

Plan

#11 Work Backwards · also uses: #6 Guess and Check

First simplify the right side to a single number, then work backwards to isolate the box. The box must be less than some value, so the greatest two-decimal number is the largest hundredths value strictly below it.

Execute

#11 Work Backwards 5.NBT.B.7
Compute the right-hand subtraction: 11.00 - 2.75 = 8.25. So the inequality becomes box + 4.62 < 8.25.
11.00−2.75=8.2511.00 - 2.75 = 8.25
Turn the right side into one clean number before solving.
#11 Work Backwards 5.NBT.B.7
Subtract 4.62 from both sides to undo the addition: box < 8.25 - 4.62 = 3.63.
□<8.25−4.62=3.63\square < 8.25 - 4.62 = 3.63
Undo the +4.62 by subtracting it, leaving the box alone.
#6 Guess and Check 4.NF.C.7
The box must be strictly less than 3.63. The largest hundredths number below 3.63 is one hundredth less: 3.62.
□=3.63−0.01=3.62\square = 3.63 - 0.01 = 3.62
Since it can't equal 3.63, step down one hundredth to the biggest allowed value.
Answer: 3.62

Review

Test 3.62: 3.62 + 4.62 = 8.24, which is less than 8.25 - true. Test 3.63: 3.63 + 4.62 = 8.25, not less than 8.25 - false. So 3.62 is indeed the greatest value that works.

Guess and Check near the boundary: try 3.63 (fails, equals), then 3.62 (works), confirming 3.62 is the largest two-decimal number that keeps the inequality true.

Standards · min grade 5

  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Computing 11.00 - 2.75 and 8.25 - 4.62.
  • 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size — Choosing the greatest hundredths value strictly below 3.63.
💡 Clean up each side, undo the addition to free the box, then step down one hundredth for the biggest 'less-than' answer!