Practice · Find the extreme decimal satisfying an inequality · Sensim Math

Variant 1 easy

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

$\square + 1.46 < 6.05 - 2.19$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 1.46 < 6.05 - 2.19.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 6.05 - 2.19 = 3.86. So the inequality becomes

\square

+ 1.46 < 3.86.

6.05 - 2.19 = 3.86

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 1.46 from both sides to undo the addition:

\square

< 3.86 - 1.46 = 2.40.

\square < 3.86 - 1.46 = 2.40

Undo the +1.46 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 2.40

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 2.40. The largest hundredths number below 2.40 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 2 easy

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

$\square + 1.99 < 7.20 - 1.58$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 1.99 < 7.20 - 1.58.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 7.20 - 1.58 = 5.62. So the inequality becomes

\square

+ 1.99 < 5.62.

7.20 - 1.58 = 5.62

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 1.99 from both sides to undo the addition:

\square

< 5.62 - 1.99 = 3.63.

\square < 5.62 - 1.99 = 3.63

Undo the +1.99 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.63

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.63. The largest hundredths number below 3.63 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 3 easy

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

$\square + 2.08 < 7.60 - 1.43$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 2.08 < 7.60 - 1.43.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 7.60 - 1.43 = 6.17. So the inequality becomes

\square

+ 2.08 < 6.17.

7.60 - 1.43 = 6.17

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 2.08 from both sides to undo the addition:

\square

< 6.17 - 2.08 = 4.09.

\square < 6.17 - 2.08 = 4.09

Undo the +2.08 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 4.09

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 4.09. The largest hundredths number below 4.09 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 4 medium

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

$\square + 2.73 < 8.88 - 4.01$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 2.73 < 8.88 - 4.01.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 8.88 - 4.01 = 4.87. So the inequality becomes

\square

+ 2.73 < 4.87.

8.88 - 4.01 = 4.87

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 2.73 from both sides to undo the addition:

\square

< 4.87 - 2.73 = 2.14.

\square < 4.87 - 2.73 = 2.14

Undo the +2.73 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 2.14

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 2.14. The largest hundredths number below 2.14 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 5 medium

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

$\square + 3.87 < 9.50 - 2.26$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 3.87 < 9.50 - 2.26.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 9.50 - 2.26 = 7.24. So the inequality becomes

\square

+ 3.87 < 7.24.

9.50 - 2.26 = 7.24

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 3.87 from both sides to undo the addition:

\square

< 7.24 - 3.87 = 3.37.

\square < 7.24 - 3.87 = 3.37

Undo the +3.87 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.37

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.37. The largest hundredths number below 3.37 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 6 medium

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

$\square + 3.25 < 9.82 - 1.54$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 3.25 < 9.82 - 1.54.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 9.82 - 1.54 = 8.28. So the inequality becomes

\square

+ 3.25 < 8.28.

9.82 - 1.54 = 8.28

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 3.25 from both sides to undo the addition:

\square

< 8.28 - 3.25 = 5.03.

\square < 8.28 - 3.25 = 5.03

Undo the +3.25 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 5.03

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 5.03. The largest hundredths number below 5.03 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 7 medium

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

$\square + 4.17 < 10.45 - 2.71$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 4.17 < 10.45 - 2.71.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 10.45 - 2.71 = 7.74. So the inequality becomes

\square

+ 4.17 < 7.74.

10.45 - 2.71 = 7.74

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 4.17 from both sides to undo the addition:

\square

< 7.74 - 4.17 = 3.57.

\square < 7.74 - 4.17 = 3.57

Undo the +4.17 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.57

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.57. The largest hundredths number below 3.57 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 8 hard

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

$\square + 4.62 < 11.00 - 2.75$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 4.62 < 11.00 - 2.75.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 11.00 - 2.75 = 8.25. So the inequality becomes

\square

+ 4.62 < 8.25.

11.00 - 2.75 = 8.25

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 4.62 from both sides to undo the addition:

\square

< 8.25 - 4.62 = 3.63.

\square < 8.25 - 4.62 = 3.63

Undo the +4.62 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.63

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.63. The largest hundredths number below 3.63 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 9 hard

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

$\square + 5.19 < 12.34 - 3.88$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 5.19 < 12.34 - 3.88.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 12.34 - 3.88 = 8.46. So the inequality becomes

\square

+ 5.19 < 8.46.

12.34 - 3.88 = 8.46

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 5.19 from both sides to undo the addition:

\square

< 8.46 - 5.19 = 3.27.

\square < 8.46 - 5.19 = 3.27

Undo the +5.19 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.27

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.27. The largest hundredths number below 3.27 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Variant 10 hard

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

$\square + 5.34 < 13.00 - 4.66$

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The inequality is $\square$ + 5.34 < 13.00 - 4.66.
The $\square$ must be a number with exactly two decimal places (a hundredths number).

Unknowns

The greatest two-decimal-place number that fits in the $\square$ .

Constraints

The filled value must keep the inequality strictly true (less than, not equal).
The answer must have exactly two decimal places.

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Simplify the right side

#11 Work Backwards 5.NBT.B.7

Compute the right-hand subtraction: 13.00 - 4.66 = 8.34. So the inequality becomes

\square

+ 5.34 < 8.34.

13.00 - 4.66 = 8.34

Turn the right side into one clean number before solving.

2Isolate the $\square$

#11 Work Backwards 5.NBT.B.7

Subtract 5.34 from both sides to undo the addition:

\square

< 8.34 - 5.34 = 3.00.

\square < 8.34 - 5.34 = 3.00

Undo the +5.34 by subtracting it, leaving the

\square

alone.

3Pick the greatest two-decimal number below 3.00

#6 Guess and Check 4.NF.C.7

The

\square

must be strictly less than 3.00. The largest hundredths number below 3.00 is one hundredth less: 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

4 · Reviewdoes it hold up?

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.

Another way: 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.

Standardsmin 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.

💡Takeaway. Clean up each side, undo the addition to free the

\square

, then step down one hundredth for the biggest 'less-than' answer!

Find the extreme decimal satisfying an inequality · 10 practice problems

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