Sensim Math · Depth 한국어

4-2 · Decimal Addition and Subtraction

Find the extreme decimal satisfying an inequality

5.NBT.B.74.NF.C.7 · take · grade 5

Archetype: Compare Fractions and Decimals by Structure · step in a 7-type progression

▶ Practice — 10 problems

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!