Mini Mathematics
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Add and subtract decimals

Align equal place values and exchange units when adding and subtracting decimals.

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Align places, not the ends of the written numbers

For 4.7 + 2.68, write 4.7 as 4.70. Then add equal units: 4.70 + 2.68 = 7.38. Lining up the final digits without the dots would mix tenths with hundredths.

For 5-2.36, write 5.00. Exchange ones into tenths and tenths into hundredths as needed: 5.00-2.36 = 2.64. Check 2.36 + 2.64 = 5.00.

Match the operation to the amount wanted

A 3 ℓ jug contains 1.75 ℓ of water. Another 0.85 ℓ is added, then 0.60 ℓ is poured out. Estimate the final amount, then calculate it exactly. Does the exact amount exceed 2 ℓ?

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Adding about 0.9 ℓ and removing about 0.6 ℓ suggests a small increase from 1.75 ℓ, so about 2 ℓ is reasonable. An estimate this close to 2 ℓ cannot settle whether the exact amount exceeds it.

Calculate 1.75 + 0.85 = 2.60 ℓ, then 2.60-0.60 = 2.00 ℓ. The exact amount equals 2 ℓ. Every term measures litres of water, and even the largest amount, 2.60 ℓ, fits in the 3 ℓ jug.

A missing part

A total is 8.2 and one part is 3.47. Find the other part and check by addition.

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8.20-3.47 = 4.73. Check 3.47 + 4.73 = 8.20. Writing 8.2 as 8.20 preserves its value and aligns hundredths with hundredths.

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