There is no calculator. That is not a hardship the exam invented to be difficult - it is what makes this section testable at all - but it does mean the method you were taught at school is the wrong tool. Long division is correct and it is too slow.
Learn about a dozen fraction-decimal-percent equivalences by sight, so the common ones need no working at all. Everything else on this page is what to do with the handful that are not on the list.
The table that does most of the work
These come up far more often than chance would suggest, because they are the fractions that produce clean decimals - which is exactly why an item writer reaches for them.
Worth knowing without thinking
Fraction
Decimal
Percent
1/2
0.5
50%
1/3
0.333…
33 1/3%
2/3
0.666…
66 2/3%
1/4
0.25
25%
3/4
0.75
75%
1/5
0.2
20%
2/5
0.4
40%
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%
The eighths are the ones people leave out and the ones that turn up most. They are easier than they look: 1/8 is 0.125, and every other eighth is a multiple of it. Three eighths is three of them, 0.375. Five eighths is five, 0.625.
Straight off the table, no working
Express 0.875 as a percent.
A20%
B75%
C50%
D87.5%
7/8 = 0.875 = 87.5%. A fraction becomes a decimal by dividing the top by the bottom, and a decimal becomes a percent by moving the point two places right. These few values are worth knowing by sight; they turn up inside percentage and word problems where working them out costs time you need elsewhere.
AThis is the value of a different fraction in the same form.
BThis is the value of a different fraction in the same form.
CThis is the value of a different fraction in the same form.
The two moves for everything not on the table
Fraction to decimal: make the bottom a power of ten. If the denominator divides into 10, 100 or 1000, multiply top and bottom to get there and read it off. 7/20 → multiply both by 5 → 35/100 → 0.35. That is one step, where long division is four.
Decimal to fraction: say it out loud. 0.35 is “thirty-five hundredths”, which is 35/100, which reduces to 7/20. The saying-it-aloud step is not a mnemonic - it is where the denominator comes from.
Both directions in one step each. Long division is the fallback for denominators that will not reach a power of ten - sevenths, ninths - and those are rare on this paper.
On the table, but worth seeing as an item
Express 1/4 as a decimal.
A0.3
B0.875
C0.625
D0.25
1/4 = 0.25 = 25%. A fraction becomes a decimal by dividing the top by the bottom, and a decimal becomes a percent by moving the point two places right. These few values are worth knowing by sight; they turn up inside percentage and word problems where working them out costs time you need elsewhere.
AThis is the value of a different fraction in the same form.
BThis is the value of a different fraction in the same form.
CThis is the value of a different fraction in the same form.
Adding: the lowest common denominator is usually smaller than you think
Multiplying the two denominators together always works and often gives you a larger number to reduce afterwards. For 3/4 and 5/6 the product is 24; the lowest common denominator is 12. Look for the smaller one first - it takes a second and saves the reduction.
Addition · watch what makes B wrong
What is 3/4 + 5/6, in lowest terms?
A19/12
B38/24
C13/8
D4/5
Put both over 24: 18/24 + 20/24 = 38/24, which reduces to 19/12. The question asks for lowest terms, so an unreduced answer is only most of the way there.
BThis is not the value of the expression in lowest terms.
CThis is not the value of the expression in lowest terms.
DThis adds the tops and the bottoms separately. Denominators are not added; they have to be made the same first.
Option B is worth sitting with. It is the same number as the answer, written unreduced. The question says “in lowest terms”, and that phrase is doing real work: an answer that is arithmetically right and not reduced is marked wrong. Reduce before you look at the options, every time.
Multiplying: cancel before you multiply
Multiplying fractions is the easy operation - top times top, bottom times bottom - and the place it goes wrong is the size of the numbers. Cancel common factors across the diagonal first and the multiplication becomes trivial.
Multiplication · cancel first
What is 3/6 x 6/8, in lowest terms?
A19/48
B2/3
C3/8
D18/48
Multiply across: 3 x 6 over 6 x 8 = 18/48, which reduces to 3/8. The question asks for lowest terms, so an unreduced answer is only most of the way there.
AThis is not the value of the expression in lowest terms.
BThis is not the value of the expression in lowest terms.
DThis is not the value of the expression in lowest terms.
For 3/6 × 6/8: the sixes cancel outright, leaving 3/8. Doing it the other way gives 18/48 and a reduction to perform under time pressure - and 18/48 is on the option list, because stopping there is the predictable outcome.
Two habits that save more time than any trick
Estimate before you compute. 3/4 + 5/6 is a bit under 1 plus a bit under 1, so the answer is somewhere near 1.6. That single thought eliminates two options before any arithmetic, and it catches the misplaced decimal point that is otherwise invisible.
Convert the question, not the options. When an item mixes fractions, decimals and percents, put everything into whichever form is easiest for the numbers in front of you - usually decimals for comparing, fractions for multiplying - rather than converting four options one at a time.
Practising it
This is the most improvable format on the numerical section, because the whole of it is recognition and recognition responds to volume. Fractions and decimals practice generates fresh conversions and operations indefinitely, so the table above stops being something you look up and becomes something you know.