Division Shortcuts

Division is often considered the hardest of the four basic operations to do mentally. However, in the UCAT, divisions tend to involve convenient numbers — you are dividing by 2, 4, 5, 8, 10, 20, 25, or 50 far more often than by 7 or 13. This lesson teaches shortcuts for the common divisors and strategies for handling the rest.

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Dividing by 5: ×2 then ÷10

This is the reverse of the ×5 shortcut. Since ÷5 = ×2 ÷10:

Calculation	×2	÷10	Answer
350 ÷ 5	700	70	70
225 ÷ 5	450	45	45
1,480 ÷ 5	2,960	296	296

---

Dividing by 25: ×4 then ÷100

Since ÷25 = ×4 ÷100:

Calculation	×4	÷100	Answer
500 ÷ 25	2,000	20	20
375 ÷ 25	1,500	15	15
1,750 ÷ 25	7,000	70	70

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Dividing by 50: ×2 then ÷100

Since ÷50 = ×2 ÷100:

Calculation	×2	÷100	Answer
850 ÷ 50	1,700	17	17
2,300 ÷ 50	4,600	46	46
4,750 ÷ 50	9,500	95	95

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Dividing by 4 and 8: Repeated Halving

Dividing by 4 is the same as halving twice. Dividing by 8 is halving three times.

Dividing by 4

Calculation	Half	Half again	Answer
340 ÷ 4	170	85	85
1,200 ÷ 4	600	300	300
520 ÷ 4	260	130	130

Dividing by 8

Calculation	Half	Half	Half	Answer
480 ÷ 8	240	120	60	60
2,400 ÷ 8	1,200	600	300	300
560 ÷ 8	280	140	70	70

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Recognising Common Fractions

Many QR divisions produce answers that correspond to well-known fractions. Recognising these instantly saves time:

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333...	33.3%
2/3	0.667...	66.7%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/6	0.167...	16.7%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/10	0.1	10%

How This Helps in QR

If a question asks "What fraction of total sales does Product A represent?" and you calculate 240 ÷ 960, you can simplify:

• 240/960 = 24/96 = 1/4 = 0.25 = 25%

Recognising that 240 is one quarter of 960 takes 2 seconds. Dividing 240 by 960 on the calculator takes 6–8 seconds.

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Simplifying Before Dividing

Before reaching for the calculator, check whether you can simplify the division by cancelling common factors.

Cancel Common Factors of 10

If both numbers end in zero(s), remove equal numbers of zeros:

Original	Simplified	Answer
4,500 ÷ 150	450 ÷ 15 → 90 ÷ 3	30
12,000 ÷ 400	120 ÷ 4	30
800 ÷ 200	8 ÷ 2	4

Cancel Common Factors of 2

If both numbers are even, halve both: