Decimals on the abacus

Adding and taking away: the unit point is the decimal point

Choose a rod with a unit point as your ones rod. Everything to its right is tenths, hundredths and so on. Line both numbers up on that rod and calculate exactly as you would with whole numbers.

Multiplying: rule A

When the multiplier is a whole number, or has a whole part like 1.2, the answer's ones rod is to the right of the multiplicand's ones rod by the number of whole digits in the multiplier, plus one.

• One-digit multiplier: 2 rods right. (4 × 2 = 8)
• Two-digit multiplier: 3 rods right. (25 × 15 = 375)
• Mixed decimal with one whole digit, like 1.2: 2 rods right. (34 × 1.2 = 40.8)

Dividing: rule B

The mirror image: when the divisor is whole or has a whole part, the quotient's ones rod is to the left of the dividend's ones rod by the number of whole digits in the divisor, plus one.

• One-digit divisor: 2 rods left. (8 ÷ 2 = 4)
• Two-digit divisor: 3 rods left. (375 ÷ 15 = 25)
• Mixed decimal like 1.2: 2 rods left. (40.8 ÷ 1.2 = 34)

Multiplying by a pure decimal: rule C

When the multiplier has no whole part, look at where its first non-zero digit sits. In the tenths place, the answer's last digit forms one rod to the right of the multiplicand's last digit. Each place further right moves the answer one more rod to the left.

Dividing by a pure decimal: rule D

The mirror image of rule C. With the divisor's first non-zero digit in the tenths place, the quotient's last digit forms one rod to the left of the dividend's last digit, and each place further right moves it one more rod to the right.

• 12.8 ÷ 0.4 = 32 — one rod left.
• 1.28 ÷ 0.04 = 32 — same rod.
• 0.128 ÷ 0.004 = 32 — one rod right.

Check with an estimate

While the rules are still new, round both numbers to something easy and estimate the size of the answer first. 34 × 1.2 is roughly 30 × 1 = 30, so the answer must be about 40, not 4 or 400. Use the estimate to confirm where the point goes, and lean on the rules more as they become automatic.