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For the algebraic rule, start at Sections 1–3. For the original denominator restriction, go to Sections 5–7. If the problem comes from a real situation, check Sections 4 and 10–12 before forming your equation. Use the practice clinic to separate valid and invalid applications.
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Cross-multiplication works when you have a genuine equality between two fractions with nonzero denominators. It turns a/b = c/d into ad = bc by multiplying both sides by bd. It does not turn any four numbers into a valid proportion, does not permit division by zero, and cannot rescue a relationship that was never proportional in the first place.
The practical habit is straightforward: justify the two ratios, match numerator and denominator meanings, check restrictions, multiply complete expressions, and substitute the result back. For 3/(x + 2) = 2/5, the permitted solution is x = 5.5. Writing just crossed arrows without the denominator restriction misses part of the mathematical reasoning.
This G2 Mathematics learning guide builds the concept from numerical fractions into algebra, gives diagnostic cases and includes clearly identified extensions. G2, G1 and G3 are subject levels under Full Subject-Based Banding, not interchangeable syllabus labels. Refer to your school’s sequence and SEAB’s official 2027 SEC Mathematics syllabus for assessable content.
- Quick read
- 1. A cross product checks an equality, not a resemblance
- 2. Derive the rule by clearing nonzero denominators
- 3. The numerator and denominator are whole expressions
- 4. A proportion compares the same relationship
- 5. Full worked solution: an unknown denominator
- 6. Verify in the original fractions, not only the crossed equation
- 7. A zero denominator makes the original expression undefined
- 8. Equivalent fractions use one multiplicative factor
- 9. Solving an unknown numerator can be direct
- 10. Units and ratio direction must agree
- 11. Cross products alone do not establish proportionality in a dataset
- 12. A fixed fee can break simple direct proportion
- 13. Different orderings can be legitimate when consistent
- 14. Handle negative fractions without losing sign
- 15. A zero numerator requires care but can be valid
- 16. An identity can produce many allowed values
- 17. An impossible equation means there is no solution
- 18. Decimal proportions still follow the same logic
- 19. Nested fractions must first be read unambiguously
- 20. Do not confuse an inequality with a fraction equality
- 21. Use substitution as a diagnostic, not a proof of a model
- 22. Locate the first unsupported algebraic step
- 23. Keep a useful answer format and precision
- 24. Learn the conditions before memorising the shortcut
- 25. Connect to the mathematics ecosystem and official levels
- 26. Choose practice by error type, not by sheer volume
- 18 worked practice cases
- Frequently asked questions
Valid rule: if a/b = c/d and b and d are nonzero, then ad = bc. You may derive this by multiplying both sides by bd. When b or d contains x, write the excluded values. When a story involves rates, check that matching ratios and a genuine constant-rate relationship are present before applying the rule.
Key warning: addition of fractions, a fixed starting fee, mismatched units and a zero denominator are not situations that can be fixed by drawing diagonal arrows. A correctly solved algebraic equation can still be an incorrect model of an applied question. Verify the starting relationship as well as the final answer.
Cross-multiplication is a short way of rewriting an equality between two fractions. It does not mean that the numbers in every rectangle-shaped arrangement can be multiplied diagonally to produce a legitimate equation. The starting statement must have the form a/b = c/d, and the denominators must not be zero. Without that equality and those conditions, the shortcut has no justified target.
Worked checkpoint. For 2/3 = 8/12, the two products are 2 × 12 = 24 and 3 × 8 = 24, so the equality is true. For 2/3 = 8/11, the corresponding products are 22 and 24, so the fractions are unequal. The procedure checks equality; it does not manufacture it.
Check your reasoning. Say ‘the two ratios are asserted equal’ before crossing the products. If a problem merely lists two fractions with no equals sign, do not invent an equation.
Start with a/b = c/d, where b ≠ 0 and d ≠ 0. Multiply both sides by the common nonzero factor bd. The left side becomes ad and the right side becomes bc. Therefore ad = bc. Every part of the rule follows from the ordinary principle that multiplying both sides of an equation by the same nonzero expression preserves equality.
Worked checkpoint. Take 3/5 = 9/15. Multiply both sides by 75: the products simplify to 45 = 45. Using the compact rule directly gives 3 × 15 = 5 × 9. Neither method relies on the visual appearance of crossing lines; both are algebraic expressions of the same equality.
Check your reasoning. Try deriving the rule without drawing arrows. When you can explain why denominators disappear, you will remember the nonzero condition rather than treating it as a decorative note.
A fraction bar groups its entire numerator and denominator. When a bracket appears, it is the whole bracket that participates in the cross product. Forgetting that grouping often drops a term, changes a sign or creates a wrong equation. This is the same structural issue encountered when students cancel a term out of a sum rather than factorising the complete expression.
Worked checkpoint. For 2/(x + 4) = 3/7, the correct equation is 2 × 7 = 3(x + 4), giving 14 = 3x + 12 and x = 2/3. The equation 14 = 3x + 4 would come from losing the bracket and is not equivalent to the original.
Check your reasoning. Draw one box around each complete numerator and denominator before multiplying. Carry those boxes into the new equation, then expand and simplify carefully.
In an applied question a proportion claims that two ratios express an equivalent relationship. It may arise from equal rates, similar shapes or other multiplicative comparisons, but the equality must be justified by the context. Cross-multiplication solves an equation once that equality is established. It does not independently prove that the real situation is proportional.
Worked checkpoint. If a recipe consistently uses three cups of flour for two portions, six portions require nine cups under the stated scaling rule. The proportion 3/2 = x/6 leads to 2x = 18 and x = 9. If the recipe has a fixed ingredient amount independent of portions, that simple proportion may no longer model the situation.
Check your reasoning. Before writing two fractions equal, state what the matching numerator and denominator quantities mean. If the relationship is additive rather than multiplicative, use another model.
Solve 3/(x + 2) = 2/5. First record the original restriction: x + 2 ≠ 0, so x ≠ −2. The two fractions are equal by the given equation, and their denominators are nonzero for permitted x. Multiply by 5(x + 2), or use the justified cross-product rule.
Worked checkpoint. The resulting equation is 3 × 5 = 2(x + 2). Expanding gives 15 = 2x + 4, so 11 = 2x and x = 11/2 = 5.5. This value obeys x ≠ −2. Check in the original equation: 3/7.5 = 0.4 and 2/5 = 0.4, so the solution works.
Check your reasoning. Show the restriction, the bracketed equation, the algebra and the substitution. The calculator check is useful, but the algebra explains why the answer was obtained.
| Stage | Working |
|---|---|
| Starting equation | 3/(x + 2) = 2/5 |
| Restriction | x ≠ −2 |
| Clear denominators | 15 = 2(x + 2) |
| Expand | 15 = 2x + 4 |
| Isolate unknown | x = 11/2 |
| Verify | 3/7.5 = 2/5 |
When a candidate solution has been found, substitute it into the original expressions. The check catches copying mistakes and excluded values. It also distinguishes finding a number that satisfies a transformed equation from finding a number permitted by the original question. A valid solution must do both.
Worked checkpoint. Solve 4/(x − 1) = 2/3. Cross-multiply: 12 = 2(x − 1), so x − 1 = 6 and x = 7. In the original fractions, 4/(7 − 1) = 4/6 = 2/3. The denominator is nonzero and the equality holds. This provides two independent reasons to accept the value.
Check your reasoning. Write the checked left-hand side and right-hand side explicitly. Merely re-copying the number x = 7 does not show that the starting fractions were tested.
No algebraic manipulation can make division by zero valid. If a denominator contains the unknown, identify every forbidden value before or during the solution. A later factor cancellation may hide the denominator but does not remove the exclusion from the original problem. The equality is a statement only on the domain where both sides exist.
Worked checkpoint. In (x − 3)/(x − 3) = 1, the algebraic left side equals one for every x except x = 3. At x = 3, it becomes 0/0, which is undefined rather than one. Multiplying across and simplifying to x − 3 = x − 3 is an identity but does not restore the excluded value.
Check your reasoning. Always keep the domain restriction alongside the working. A plausible-looking equality of polynomials is not enough to authorise a forbidden denominator.
Fractions can be equivalent because numerator and denominator are multiplied or divided by the same nonzero factor. This is multiplicative structure, not the result of adding the same number to both entries. Comparing simple examples helps learners see why cross products test equivalence rather than define arbitrary numerical similarity.
Worked checkpoint. The fractions 4/6 and 10/15 are equivalent: each reduces to 2/3, and 4 × 15 = 6 × 10 = 60. By contrast, 4/6 and 6/8 are not equivalent even though two was added to both entries. Their cross products are 32 and 36.
Check your reasoning. Ask what operation converts the first numerator and denominator into the second pair. A common multiplicative scale supports equivalence; a common addition usually does not.
Cross-multiplication is not always the simplest method. If a scale factor is obvious, use it; if not, the cross-product rule gives a dependable equation. Either way, maintain corresponding positions. A ratio of children to adults is not the same ratio as adults to children, even though the same numbers appear.
Worked checkpoint. For x/5 = 6/10, observe that 5 becomes 10 by multiplying by two, so x becomes 6 by the same scale and x = 3. The cross-product method agrees: 10x = 5 × 6 = 30, so x = 3.
Check your reasoning. After solving, reduce the fractions to check: 3/5 = 6/10. You should be able to explain either the shared factor or the preserved equality.
A genuine proportion may compare prices per item, length per time or people in matching categories. The numerator-to-denominator meaning must be consistent. Cross-multiplication of mismatched ratios can deliver a mathematically correct solution to the wrong real-world equation. Convert incompatible units and choose one ratio orientation.
Worked checkpoint. Suppose three notebooks cost twelve dollars and five notebooks of the same kind cost x dollars. Use 12/3 = x/5 or 3/12 = 5/x, keeping the orientation matched. The first gives 3x = 60 and x = 20. A fraction of dollars per notebook cannot be equated directly to notebooks per dollar.
Check your reasoning. Label the numerator and denominator of each fraction before crossing products. Include units in the final answer so a reversed ratio becomes visible.
SECTION 13 OF 30
11. Cross products alone do not establish proportionality in a dataset
Equal ratios between two observed pairs are evidence of a pattern but may not justify assuming a rule across every possible input. In school modelling, the problem may explicitly declare direct proportion, in which case the equality is warranted. Outside that assumption, further data or a known relationship is needed. Do not promote a convenient fraction into a universal law.
Worked checkpoint. Two tickets cost ten dollars and four cost twenty dollars in a simple example. These observations have the same rate, but a real ticket seller might also offer discounts or surcharges for other quantities. Mathematics can solve the declared constant-rate model without claiming that a business follows it in every possible case.
Check your reasoning. Separate ‘the given model says the ratio is constant’ from ‘two samples happen to give the same ratio’. The distinction protects reasoning in science, economics and daily purchases.
Some quantities include a starting charge plus a variable part. The total is then y = mx + c rather than y = mx. When c is nonzero, doubling the number of units does not normally double the total. A cross-multiplication set up as total1/units1 = total2/units2 would be invalid even if the subsequent algebra is executed perfectly.
Worked checkpoint. A service charges four dollars plus three dollars per hour in a fictional pricing model. One hour costs seven dollars and two hours cost ten dollars. The ratios 7/1 and 10/2 are seven and five, not equal. Use total = 4 + 3 × hours; do not force those totals into a direct proportion.
Check your reasoning. Look for words such as ‘initial’, ‘booking’, ‘basic charge’ and ‘plus’. They can signal an additive component that prevents a simple ratio model.
You can express equivalent proportions in different orientations, but you must change both ratios consistently. Inverting both nonzero fractions preserves equality. Switching only one fraction generally does not. A good ratio table labels quantities so that corresponding components can be paired without memorised diagonals.
Worked checkpoint. If the ratio of blue to red counters is 2/3 in one group and 8/12 in another, 2/3 = 8/12 is valid. The inverted statement 3/2 = 12/8 is also valid. The mismatched statement 2/3 = 12/8 is false. Cross products immediately expose the inconsistent orientation.
Check your reasoning. Write both fractions with matching category labels above and below. The same ordering across both sides is more important than which ordering you choose.
Negative signs belong to the value of a numerator, denominator or whole fraction. They cannot be dropped merely because products are drawn diagonally. When denominators are known nonzero, clearing them in an equality preserves the sign algebraically. A final sign check by substitution often catches a mistaken expansion or simplification.
Worked checkpoint. For −2/3 = x/12, cross products give −2 × 12 = 3x, hence −24 = 3x and x = −8. Substitute: −8/12 = −2/3. The negative sign stays with the fraction throughout the calculation.
Check your reasoning. Place a bracket around each negative number in a product, such as (−2) × 12. If your answer turns positive despite a negative ratio and positive denominator, investigate.
Zero divided by a nonzero denominator equals zero. That is different from a zero denominator, which makes the fraction undefined. Cross-multiplication can be used with a zero numerator as long as every denominator is allowed. A zero cross product can then convey a valid condition on the other numerator.
Worked checkpoint. Consider x/7 = 0/5. The equation gives 5x = 0, so x = 0. Both fractions are defined and equal zero. By contrast, x/0 = 0/5 has no valid meaning and cannot be solved by setting 5x = 0.
Check your reasoning. Check whether the zero is on top or bottom of the fraction bar. The same digit in those two positions has completely different consequences.
After cross-multiplication, the resulting equation may simplify to a statement that is true for every value in the permitted domain. In that case the answer is a set of allowed values, not a unique number. Domain exclusions still matter even when the algebra on both sides becomes identical.
Worked checkpoint. For 2/(x + 1) = 4/(2x + 2), the right denominator is twice the left. Cross-multiplication gives 2(2x + 2) = 4(x + 1), so 4x + 4 = 4x + 4. Every real x except −1 satisfies the original equality.
Check your reasoning. Report both the identity and x ≠ −1. Saying ‘all real numbers’ without the exclusion would be incomplete.
An algebraic equation may reduce to a contradiction after a valid transformation. This means no permitted number satisfies the original equality. Do not force an answer from the numerical symbols or assume every proportional statement has a solution simply because the exercise contains an x.
Worked checkpoint. For 1/(x + 2) = 1/(x − 2), require x ≠ −2 and x ≠ 2. Multiplying across gives x − 2 = x + 2. Subtract x: −2 = 2, which is false. There is no solution. The fractions have different denominators for every permissible x, so they cannot be equal.
Check your reasoning. Recognise a contradiction promptly. If the variables cancel and the remaining constants disagree, the equation is inconsistent.
Fractions and decimals describe numbers, not different algebraic rules. You can solve a proportion involving decimals by converting to convenient fractions, multiplying through by powers of ten or cross-multiplying carefully. Estimating the result first reduces the chance of shifting a decimal point incorrectly.
Worked checkpoint. Solve 0.6/1.5 = x/5. Since 0.6/1.5 = 0.4, x/5 = 0.4 and x = 2. Cross multiplication agrees: 1.5x = 0.6 × 5 = 3, giving x = 2. The result makes sense because two is forty percent of five.
Check your reasoning. Use exact decimal arithmetic where possible and write the scaling relation. A screen result alone does not show whether units and ratio direction were chosen correctly.
A compact printed expression can hide which terms belong together. When a fraction contains a fraction in its numerator or denominator, place brackets or rewrite it as an ordinary division expression before using a proportion rule. Students often create a wrong cross product by interpreting the wrong fraction bar.
Worked checkpoint. For (1/2)/3, the quantity is one half divided by three, which equals 1/6. For 1/(2/3), the quantity is one divided by two thirds, which equals 3/2. They are not the same expression. The grouping determines every later transformation.
Check your reasoning. Copy the original expression with visible parentheses before simplifying. Cross-multiplication is never a substitute for parsing the expression correctly.
For fractions with known positive denominators, comparison through cross products can be valid, but inequalities need special care when a denominator’s sign is unknown. Multiplying an inequality by a negative number reverses its direction. This extension is worth recognising even when a student’s current focus is equation solving.
Worked checkpoint. Compare 3/4 and 5/7. Both denominators are positive. Cross products are 3 × 7 = 21 and 5 × 4 = 20, so 3/4 > 5/7. If a variable denominator could be negative, that reasoning would need a sign analysis before an inequality is multiplied through.
Check your reasoning. Keep equality problems and inequality problems distinct. The cross-product equation ad = bc is not automatically an inequality direction rule for all possible denominators.
Substituting a proposed value into a given equality can verify that value satisfies the equality. It does not prove that the original equation was the right model for the real situation. Those are separate judgments: mathematical validity within a model and suitability of the model for the context.
Worked checkpoint. A student writes a proportion for a taxi journey that actually includes a fixed starting fare. The algebra may produce a number that fits the student-created ratio, but it does not establish the actual cost. Checking the original statement of the problem is necessary before checking the algebra.
Check your reasoning. Ask two questions in order: does the proportion belong in this story, and does the solved number satisfy that proportion? A reliable solution needs both answers to be yes.
When a cross-multiplication question goes wrong, there are several plausible causes: an invalid starting ratio, reversed units, zero denominator, missing brackets, a sign error or an incorrect equation solution. These causes require different corrections. Repeating the diagonal-arrow mnemonic rarely repairs the missing mathematical reasoning.
Worked checkpoint. Suppose 3/(x + 5) = 2/7 is followed by 21 = 2x + 5. The student crossed products appropriately but failed to multiply the entire bracket by two. Repair that step: 21 = 2(x + 5) = 2x + 10, giving x = 11/2. The corrected denominator is nonzero.
Check your reasoning. Look for the earliest line that no longer follows from the preceding line. Repair that line before calculating further.
Some ratios produce an exact fraction, some a terminating decimal, and some a value that depends on measurement precision. Do not round intermediate calculations unnecessarily. If a question asks for an exact algebraic value, a fraction may communicate the result better than a rounded decimal. For a measurement, state the unit and the required precision.
Worked checkpoint. An answer x = 11/2 is exact. Writing 5.5 is also exact for this particular value. Writing 5.49 after a careless approximation is not equivalent. In contrast, a measurement such as 2.667 metres may be an approximation whose displayed decimals should follow the question’s instructions.
Check your reasoning. Check final form separately from the algebra. A mathematically correct value can be marked or interpreted poorly if the required accuracy or unit is omitted.
The useful habit is to name the equality, mark the denominator restrictions, multiply complete expressions and then verify the result. A shortcut works best when the learner already knows why it works and when not to use it. This is a bridge from arithmetic fractions to equations and broader algebraic reasoning.
Worked checkpoint. For a quick diagnostic, solve 5/(x − 2) = 3/4. Require x ≠ 2. Then 20 = 3(x − 2), so 20 = 3x − 6 and x = 26/3. Substituting gives 5/(20/3) = 3/4, as required. The denominator restriction is satisfied.
Check your reasoning. Practise the explanation ‘multiply both sides by the common nonzero denominator’. It is more transferable than arrows without justification.
Fraction equality, proportional reasoning, algebraic equations and rational expressions are connected ideas, but they are not identical demands at every school level. Treat this as an explanatory learning guide, not a promise that every extension is examined under G2 in the same way. The current school syllabus and teacher’s guidance remain the controlling sources.
Worked checkpoint. Continue through the How Mathematics Works hub and the Clementi Mathematics reference. SEAB publishes an official 2027 G2 Mathematics K210 syllabus listing, which is the appropriate place to check examination requirements.
Check your reasoning. Use the G1 explanation of remainders when numerical units are unstable, and use the G3 quadratic interpretation guides when graph meanings are confused. Repair the precise obstacle instead of rushing ahead.
If the source ratio is unjustified, practise translating contextual relationships. If the denominator could be zero, add a domain-check habit. If the algebra drops a bracket, focus on distributive expansion. If the answer fails substitution, revisit arithmetic and sign control. A small set of mixed examples can reveal more than a large set of identical ones.
Worked checkpoint. Build a ten-minute exercise with a true proportion, a false proportion, a fixed-fee problem, an unknown denominator, a zero numerator and an identity. For each, write whether cross-multiplication is legal and why, then calculate if appropriate. Review the first unsupported step in any unsuccessful attempt.
Check your reasoning. The goal is not to use cross-multiplication more often. It is to use it only when the equation actually warrants it and to know what the resulting solution means.
SECTION 29 OF 30
Practice clinic: valid proportions, invalid models and worked answers
Cover each answer first. Before calculating, say whether the two ratios have been legitimately equated and whether their denominators can become zero. Check the unit or variable restriction and decide whether the outcome is one value, many permitted values or no solution. The aim is to judge validity before applying a procedure.
Case 1. Is 2/3 equal to 8/12?
Answer and working: Yes. Both cross products equal 24.
Why this works or fails: The rule is checking an equality of two fully defined fractions.
Case 2. Is 2/3 equal to 8/11?
Answer and working: No. The cross products 22 and 24 differ.
Why this works or fails: Numbers can look close to an equivalent scale without satisfying the exact proportion.
Case 3. Solve 2/3 = x/12.
Answer and working: 3x = 24, so x = 8.
Why this works or fails: Check 8/12 = 2/3 after simplifying.
Case 4. Solve 3/(x + 1) = 1/4.
Answer and working: 12 = x + 1, so x = 11; the forbidden value is −1.
Why this works or fails: Substituting gives 3/12 = 1/4.
Case 5. Solve x/(x − 2) = 3/5.
Answer and working: 5x = 3x − 6, giving x = −3; exclude x = 2.
Why this works or fails: Check −3/−5 = 3/5.
Case 6. Solve 4/6 = (x + 1)/9.
Answer and working: 36 = 6(x + 1), so x + 1 = 6 and x = 5.
Why this works or fails: The fraction on the right is 6/9, equivalent to 4/6.
Case 7. Can 2/(x − 3) = 0 have a solution?
Answer and working: No, with x ≠ 3 the numerator stays two, so the fraction cannot be zero.
Why this works or fails: The equation 2 × 1 = 0 × (x − 3) would produce 2 = 0.
Case 8. When is 0/(x + 2) = 0/5 true?
Answer and working: For every x except x = −2.
Why this works or fails: Zero numerators are allowed, but zero denominators are never allowed.
Case 9. Solve x/4 = 0/7.
Answer and working: x = 0.
Why this works or fails: The fractions are defined because the denominators four and seven are nonzero.
Case 10. Is 7/8 = 21/24 true?
Answer and working: Yes. Both fractions simplify to seven eighths.
Why this works or fails: A factor of three scales both numerator and denominator.
Case 11. Is −1/2 = −3/6 true?
Answer and working: Yes. Cross products are −6 and −6.
Why this works or fails: The negative signs remain part of the numerical expressions.
Case 12. Solve 1/(x + 2) = 1/(x − 2).
Answer and working: There is no solution; crossing gives x − 2 = x + 2, a contradiction.
Why this works or fails: The original denominators also exclude x = −2 and x = 2.
Case 13. Solve 2/(x + 1) = 4/(2x + 2).
Answer and working: It is true for every real x except −1.
Why this works or fails: The two fractions are equivalent wherever their original denominators exist.
Case 14. Three identical pens cost $12. What do five cost at the same unit price?
Answer and working: The proportion 12/3 = x/5 gives x = $20.
Why this works or fails: The constant price-per-pen assumption makes the proportion valid.
Case 15. A service charges $4 plus $3 per hour. Can cost/hour be held constant?
Answer and working: No. One hour costs $7 but two cost $10, giving ratios seven and five.
Why this works or fails: An additive fixed fee breaks the direct-proportion shortcut.
Case 16. Compare 3/4 and 5/7.
Answer and working: Three quarters is larger, since 21 > 20 with positive denominators.
Why this works or fails: The inequality comparison needs positive denominator assumptions.
Case 17. Solve 0.6/1.5 = x/5.
Answer and working: x = 2, because the left fraction equals 0.4.
Why this works or fails: Use a quick estimate and substitute into the equality.
Case 18. Solve 5/(x − 2) = 3/4.
Answer and working: x = 26/3, with the forbidden value x = 2 excluded.
Why this works or fails: The original fractions both equal three quarters.
A good practice routine mixes numerical equality tests, unknown numerators, unknown denominators, negative signs, zero numerators, constant-fee traps and identity cases. Repeating only easy equations can conceal misunderstandings. When a check fails, locate the earliest line that is unsupported: the ratio model, the domain, the cross product, the expansion or the final substitution.
Can I cross-multiply two fractions that are being added?
Not merely because they appear on the page. Addition requires a common denominator or another valid transformation. The cross-product equality rule applies to an actual equation between two fractions with nonzero denominators.
Why do I need to say the denominator is not zero?
Because a fraction with zero denominator is undefined. Multiplying both sides by a denominator is justified only when that denominator is nonzero; solving a transformed equation must not reintroduce excluded values.
What if cross-multiplication removes the unknown?
If you obtain a true identity, every value in the original domain may satisfy the equation. If you obtain a contradiction, there is no solution. Check the domain in either case.
Is cross-multiplication always the quickest way?
No. An obvious scale factor can be faster, particularly with simple numerical ratios. Cross-multiplication is helpful when solving an equation, but explaining the equality and verifying the answer matter more than the speed of the shortcut.
Does the G2 SEC syllabus mean every example here is examined?
No. This guide includes helpful extensions and diagnostic examples. SEAB’s K210 2027 syllabus and the student’s school programme define the actual assessment expectations.
Use the G1/G2/G3 Mathematics directory and the Clementi Mathematics teaching reference for linked learning. Official examination subject listings are published by SEAB for G1 K110, G2 K210 and G3 K310.
Continue the G1/G2/G3 Mathematics series
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