Translating a sentence into symbols is its own skill, separate from solving. Learn a handful of phrase patterns and the blank page fills.
This page sits within SPM Mathematics and follows on from checking a long word problem before writing equations.
Which phrases turn into which symbols?
| Words in the question | Symbols |
|---|---|
| “a number increased by 7” | x + 7 |
| “7 less than a number” | x − 7 |
| “twice a number” | 2x |
| “a number divided among 4” | x ÷ 4 |
| “the sum is 30” | (expression) = 30 |
| “is 3 times as much as” | first = 3 × second |
The pattern to watch is “less than”: the quantity after it comes first in the subtraction.
Worked example: from sentence to equation
An original problem: Aina is 4 years older than her brother Hadi. The sum of their ages is 30. Find Hadi’s age.
Step one, name the unknown: let Hadi’s age be h. Step two, express the other: Aina is h + 4. Step three, write the sum: h + (h + 4) = 30.
Step four, solve: 2h + 4 = 30, so 2h = 26, so h = 13. Step five, check: Aina is 17 and 13 + 17 = 30.
What mistake reverses the meaning?
A student reads “Hadi is 4 years younger than Aina” and writes h = 4 − a. The phrase “4 years younger than Aina” means Aina’s age minus 4, so h = a − 4.
A test with real numbers catches it: if Aina is 17, then h = 4 − 17 = −13, which is impossible for an age. A negative age is the signal that the order is reversed.
A short self-check
Try this: a pen costs RM2 more than a pencil. Three pens and two pencils cost RM16. Find the price of a pencil.
Answer
Let the pencil cost p, so a pen costs p + 2. Then 3(p + 2) + 2p = 16, so 3p + 6 + 2p = 16, so 5p = 10, so p = 2. A pencil costs RM2 and a pen RM4. Check: 3 × 4 + 2 × 2 = 12 + 4 = 16.
If you wrote 3p + 2(p + 2), you attached the extra RM2 to the wrong item. Sketching “pen = pencil + 2” beside the equation prevents it.
For more drills, use the algebra step repair trainer. If the wording itself is the barrier, the English and BM terminology bridge pairs the terms.
When might one-to-one tuition help?
If you stall even with the table, the problem may be reading speed or a language gap rather than algebra. A teacher can ask you to explain each sentence aloud and hear where the meaning changes.
You can begin with the one-hour trial class (from RM50), a real taught lesson, using word problems from your own workbook. The fee is agreed before the trial, and afterwards you decide whether the teacher is a good fit. More is on the SPM Mathematics tuition page.