1
Match the unit to the rate before multiplying.
The rate is per hour, so every time in the problem has to become hours.
8:30 to 5:00 = 8 h 30 min
the shift
8 h 30 − 45 min = 7 h 45 min
the break is unpaid
7 h 45 min = 7.75 h
45 ÷ 60 = 0.75
7.75 × 75 = ₱581.25
answer C
| Choice | Who picks it |
|---|
| A. ₱558.75 | wrote 7 h 45 min as 7.45 hours |
|---|
| B. ₱675.00 | counted 9 hours — 8:30 to 5:30 |
|---|
| C. ₱581.25 | read the whole question |
|---|
| D. ₱637.50 | forgot to subtract the break |
|---|
Every wrong choice here is a reading error, not a calculation error. That is
typical, and it is why re-reading beats re-calculating.
2
7 h 45 min is not 7.45 hours.
Minutes are sixtieths. Only 60-based fractions convert cleanly.
| Minutes | As a decimal hour |
|---|
| 15 min | 0.25 h |
|---|
| 20 min | 0.333… h |
|---|
| 30 min | 0.5 h |
|---|
| 45 min | 0.75 h — never 0.45 |
|---|
| 50 min | 0.833… h |
|---|
When the minutes are awkward, work in minutes throughout and convert the rate
instead: ₱75 per hour is ₱1.25 per minute, and 465 minutes × 1.25 gives the same
₱581.25.
Speeds convert the same way: change km to m and hours to seconds or minutes.
90 km/h = 90,000 m in 3,600 s = 25 m/s
1 h = 3,600 s
in 12 s: 25 × 12 = 300 m
distance = speed × time, units matched
per minute: 90,000 ÷ 60 = 1,500 m
1 h = 60 min
3
Squared units do not scale the way you expect.
area
1 m² = 10 000 cm²
100 × 100
a garden 3 m by 250 cm
two different units
250 cm = 2.5 m
convert first
The same trap in volume
1 m³ is 1 000 000 cm³, and 1 litre is 1000 cm³. Convert the lengths first and
the awkward numbers never appear.
4
The words that change the arithmetic.
how many more
at least
at most
not
increased to
off
| Phrase | Means | Not |
|---|
| how many more A than B | A − B, the gap | the value of A |
|---|
| at least 3 | 3 or more, ≥ 3 | more than 3 |
|---|
| at most 3 | 3 or fewer, ≤ 3 | fewer than 3 |
|---|
| increased by 20% | × 1.20 | the new total is 20 |
|---|
| increased to 20 | the new value is 20 | add 20 |
|---|
| increased to 130% of its value | new = 1.3 × old, a 30% increase | a 130% increase |
|---|
| 20% off | you pay 80% | you pay 20% |
|---|
| the probability it is not red | 1 − P(red) | P(red) |
|---|
“At least one” is the flag for the complement: work out the probability of
none and subtract from 1.
“How many more than the average” — a gap to a third number. Carla has 12 more stickers than Dina, and together they have 60.
Dina = (60 − 12) ÷ 2 = 24, Carla = 24 + 12 = 36
take the gap off the total, then halve
average = 60 ÷ 2 = 30
the new reference point
36 − 30 = 6 more than the average
half the gap — not 12, and not 36
5
Check the unit of the answer, not just the number.
The choices are often printed in a unit you did not work in.
you found
2.5 m
correct length
choices read
25, 250, 2500
all in cm
answer
250 cm
convert before choosing ✓
Rounding is part of the question
“To the nearest peso” and “to two decimal places” are instructions. So is “how
many buses are needed” — 6.2 buses means 7, because you cannot send a fifth of a
bus. Round up whenever the leftover still needs a whole thing.
6
Variations: decimal hours back to minutes, across midnight, and rounding down.
The conversion the other way: write 3.4 hours in hours and minutes.
0.4 h × 60 = 24 min
only the decimal part converts
3.4 h = 3 h 24 min
not 3 h 40 min
What is different: the digits after the point are tenths of an hour, not minutes. Multiply them by 60.
Across midnight: how long is it from 10:40 p.m. to 6:15 a.m.?
10:40 p.m. → 12:00 midnight = 1 h 20 min
up to the change of day
12:00 midnight → 6:15 a.m. = 6 h 15 min
then on to the end
total = 7 h 35 min
add the two pieces
What is different: subtracting the clock readings (10:40 − 6:15 = 4 h 25 min) measures the wrong gap. Split at midnight instead.
Rounding down, not up: how many ₱45 notebooks can ₱500 buy?
500 ÷ 45 = 11.1…
not a whole number
11 notebooks, ₱5 change
11 × 45 = 495
What is different: buses round up because every student needs a seat; notebooks round down because a 12th one cannot be paid for. Ask which way the leftover pushes.
7
“At least one” and “or fraction thereof”.
Two phrases that change the method, not just the arithmetic.
A box holds 4 faulty and 6 good bulbs. Two are taken without replacement. What is the probability that at least one is faulty?
opposite of “at least one faulty” = “both good”
one case instead of three
P(both good) = (610)(59) = 3090 = 13
one fewer good bulb for the second draw
P(at least one faulty) = 1 − 13 = 23
subtract from 1
Parking costs ₱40 for the first 3 hours and ₱10 for each additional hour or fraction of an hour. What do 5 hours 20 minutes cost?
extra time: 5 h 20 min − 3 h = 2 h 20 min
past the flat part
charged as 3 extra hours
the 20 minutes count as a whole hour
40 + 3 × 10 = ₱70
flat rate plus extras
The planted choices
13 answers “both good”, the opposite question. For the parking, ₱60 charges only
the 2 whole extra hours, and charging all 5⅓ hours at ₱10 ignores the flat first part.
“Or fraction thereof” always rounds the extra time up.
On the exam
Wording items look easy and are built to catch a careless read: time in hours and
minutes, mixed units, “at least”, “increased to”, buses or boxes that round up. Circle
the unit of the rate and the last phrase of the question first; most wrong choices are
correct arithmetic on a misread.
✓
The thirty-second habit.
Four passes over every word problem, each one taking a few seconds.
1
underline what is asked
before any working
2
circle every unit
make them match
3
solve
the easy part
4
re-read the question
does your number answer it?
Remember the flow
What is asked · Which unit · Then calculate
The last re-read is worth more marks than the first calculation.
