Set it up so the same kind of thing is on top on both sides. Then cross-multiply.
Find the amount
A recipe for 4 people needs 300 g of rice. How much rice is needed for 10 people?
One person needs 300 ÷ 4 = 75 g, so 10 people need 75 × 10 = 750 g. As a proportion: 3004 = x10, and cross-multiplying gives 4x = 3,000, so x = 750. B doubles for no reason. C sets the proportion upside down — 4300 = x10 gives 0.13, and D forgets to divide by the 4.
| Word | Compares | Example |
|---|---|---|
| Ratio | the same kind of thing | 12 boys to 18 girls = 2 : 3 |
| Rate | different kinds | ₱480 for 6 kg |
| Unit rate | per one of something | ₱80 per kg |
12 : 18
divide both by 6
= 2 : 3
lowest terms
A ratio has no units when both sides measure the same thing — 2 : 3 is just 2 : 3. A rate keeps its units, because ₱80 per kg means nothing without them.
Divide the price by the quantity and the cheaper one is obvious.
| Pack | Price | Per litre |
|---|---|---|
| 1.5 L | ₱54.00 | ₱36.00 |
| 2 L | ₱68.00 | ₱34.00 |
| 500 mL | ₱19.00 | ₱38.00 |
The 2 L bottle wins. Note the units had to match first — 500 mL is 0.5 L, and 19 ÷ 0.5 = 38, not 19 ÷ 500.
Keep the same quantity on top on both sides.
3004 = x10
grams on top both sides
4x = 3,000
cross-multiply
x = 750 g
divide by 4
Writing grams over people on the left and people over grams on the right gives a confident, wrong answer. Decide what goes on top, then keep it there.
scale 1 : 50,000
1 cm on the map = 50,000 cm real
map distance 7 cm
how far in real life?
7 × 50,000 = 350,000 cm
still in centimetres
= 3.5 km
÷ 100,000
Answering "350,000" without converting is the trap here. A scale gives the same unit on both sides, so the conversion is a separate, final step.
Whatever number you are given, match it to its number of parts.
Two brothers' savings are in the ratio 4 : 9. The older has ₱300 more than the younger. How much does each have?
9 − 4 = 5 parts
the difference, in parts
one part = 300 ÷ 5 = ₱60
5 parts are the ₱300
4 × 60 = ₱240 and 9 × 60 = ₱540
check: 540 − 240 = 300 ✓
Dividing ₱300 by the 13 total parts would treat the difference as if it were the total.
An inverse proportion: 8 farmers can harvest a rice field in 6 days. How long would 12 farmers take, working at the same rate?
8 × 6 = 48 farmer-days
the size of the whole job
48 ÷ 12 = 4 days
more farmers share the same job
Writing 86 = 12x gives x = 9 days, so more farmers would take longer. When one quantity goes up as the other goes down, the product stays fixed: 8 × 6 = 12 × x, so x = 4.
Still "find one part"; these are the less obvious starting points.
Money is shared in the ratio 2 : 3 : 5 and the smallest share is ₱180. What was the total?
2 parts = ₱180, so one part = ₱90
start from the share you know
total = 10 parts = ₱900
2 + 3 + 5 = 10
The total is the unknown this time, so it comes last instead of first.
Simplify the ratio 12 : 23.
(12 × 6) : (23 × 6)
multiply both sides by the LCD, 6
= 3 : 4
whole numbers, lowest terms
Multiplying both sides by the same number keeps the ratio the same, just as dividing does.
Write 45 minutes to 2 hours as a ratio in lowest terms.
45 : 120
2 hours = 120 minutes
= 3 : 8
divide both by 15
Writing 45 : 2 compares minutes with hours; convert to one unit before simplifying.
Add the parts, find one part, then multiply.
₱2,400 shared 3 : 5
between two people
3 + 5 = 8 parts
the total number of shares
one part = 2,400 ÷ 8 = ₱300
the key step
₱900 and ₱1,500
3 × 300 and 5 × 300
Check they add back to ₱2,400 ✓ — that catches an arithmetic slip instantly.
Ratio items are mostly sharing problems, a missing term in a proportion, a map scale, or a best-buy comparison, with an occasional "more workers, fewer days". The fastest route is to find the value of one part, or the unit rate, and build from it; the 10-second check is that the shares add back to the total and that the answer moves in the right direction.
Share the amount
₱3,500 is shared between two students in the ratio 2 : 5. How much does the one with the larger share get?
There are 2 + 5 = 7 parts, so one part is 3,500 ÷ 7 = ₱500. The larger share is 5 × 500 = ₱2,500, and the smaller is ₱1,000. They add to ₱3,500 ✓ A is the smaller share, and C halves the money, ignoring the ratio entirely.
Hint: add the two numbers of the ratio first. That total is how many equal parts the money is being split into.
