Learn Number and Algebra (Part 1) the Singapore Way

Learn to solve number and algebra problems using deduction and reverse engineering to identify unknowns, compute HCF and LCM from prime factors, and compare exponents to deduce P, Q, R.

Practice expressing a number as a prime factorization by dividing by primes, using a consistent system. 540 equals two squared times three cubed times five.

Walk through prime factorization by dividing 1400 by successive primes, revealing 2^3 × 5^2 × 7, and apply the same method to subsequent questions.

Learn how to factor 560 by prime division: divide by 2 until even, test 3, then use 5 and 7 as prime factors.

Practice prime factorization of 1512 by repeated division with a calculator, obtain the prime factors, express them in prime vectorized form, and verify the answer.

Express six over five as a prime factorization in index notation, showing the final form without intermediate steps, and check your answer for correctness.

Practice question demonstrates factoring 630 using prime factors, dividing by 2 and by 3 to reveal 2 × 3^2 × 5 × 7.

Explore prime factorization to generate pairs of factors greater than one hundred by mixing and matching prime components, using examples like 24 and 90 to illustrate factor combinations.

Determine the smallest integer n such that 150 multiplied by n is a perfect square by balancing prime factors 2, 3, and 5, showing that n equals 6.

Develop prime factorization skills using index notation to break numbers into primes and verify with a calculator, then apply these rules to find cube roots by adjusting exponents.

learn to perform prime factorization step by step for numbers like 7408, using division by primes, identifying factors, and applying cube roots to simplify exponents.

Practice question 8 leads you through prime factorization and the logic of making 4500K a perfect cube, finding the smallest positive integer K to achieve cube exponents.

Practice question 9 guides you to express numbers by prime factors, compute the greatest common divisor of 3400 and 720, and find the smallest k making 720k a multiple.

Analyze the prime factorization of 3780, then determine the minimal k (3 × 5 × 7) to make the product a perfect square.

Learn prime factorization and index notation to express numbers like 2744 as products of primes; apply cube roots and find the smallest K that makes the product a perfect square.

This lecture applies prime factorization to practice question 12, showing how to factor numbers, identify a perfect square, and determine the highest common factor.

Explore prime factorization by expressing 780 as a product of primes, verify factors with a calculator, and determine the smallest integer to make a number a perfect cube or multiple.

Learn prime factorization to determine hcf and lcm, divide by two toward a perfect square, and identify the smallest positive value for a given set.

Determine the maximum number of cubes that fit in a box by using the cube root of two for the cube side, then divide and multiply across dimensions.

Explore the application of the HCF and LCM for 792 and 990 using prime factorization, and confirm the HCF as 198.

Explore integers as whole numbers that can be positive, negative, or zero. Zero is neither positive nor negative, and integers include positive and negative values.

Identify and categorize numbers in a list by type, including positive numbers, zero, negative numbers, positive integers, and negative integers, using examples like five, six, and negative three.

Rational numbers expressible as p over q include fractions and many decimals, while irrational numbers cannot be expressed as a fraction; pi is irrational, and 22/7 is an approximation.

Identify numeric types - rational, irrational, and integers - using the p/q rule; note sqrt(5) and pi as irrational and recognize recurring decimals and -3 as a whole number.

Understand the number line: the right side holds smaller values and the left side larger ones, with negative numbers left of zero and positive numbers to the right.

Visualize numbers on a number line, identify negative values like negative half and negative five, place four over seven, and relate decimals such as 5.9 to six.

Demonstrate subtraction involving negative numbers using a number line, combining negatives and positives, and simplifying expressions like minus minus to find results.

Explore the multiplication of negative numbers through worked examples, applying the rule that negative times negative is positive and one negative yields a negative, with bracketed steps to avoid mistakes.

Explore division of negative numbers by treating division as multiplication by reciprocals and applying sign rules, with examples showing negative divided by positive and negative by negative yielding positive.

Explore how to simplify combined operations of negative numbers using brackets, order of operations, and signs, with worked examples on squaring, roots, division, and careful bracketed steps.

Practice question on manipulating negative numbers and simplifying expressions by rearranging terms, using brackets, and evaluating operations like division, multiplication, and addition to reach a result such as nine.

Practice question 3 applies negative numbers to temperature changes, showing a positive 50-degree rise and a negative 10-degree drop to reinforce interpreting positive and negative changes.

Explore the manipulation of negative numbers and order of operations by solving a bracketed expression, applying exponents, multiplication, and simplification steps.

Evaluate the multiplication of two fractions and show your working, since calculators are not allowed. Convert the result to a mixed fraction and present it clearly to show proficiency.

Evaluate a fraction expression by simplifying brackets, converting to common denominators, and combining terms into a single fraction, as shown in practice question 7.

Explore evaluating expressions without a calculator by applying order of operations, simplifying negative numbers, squares, and fractions through step-by-step bracket and multiplication rules.

Revisit the rounding off concept by identifying the target place, checking whether the digit is above or below five, and rounding to the nearest ten or hundred with examples.

Learn rule one of significant figures: all non-zero digits are significant, while zeros may be insignificant, and how these digits carry value in data and standard form.

Apply rule two: zeros between two non-zero digits are significant, while trailing zeros may be uncertain depending on rounding data.

Master rule 3 of significant figures by identifying leading zeros as not significant and zeros between nonzero digits as significant, to reflect measurement precision.

Explore rule four of significant figures in decimals: zeros after a non-zero digit are significant. Distinguish zeros between non-zero digits and decimal zeros as significant.

Explore how trailing zeros in whole numbers may be significant based on rounding to the nearest ten or hundred in rule 5 for significant figures.

Estimate computations using significant figures and rounding to the nearest whole number, then assess reasonableness with real-life scales illustrated by height and distance examples.

Learn to estimate a shopping total by multiplying item quantities by their prices, converting units, and rounding to rough values without a calculator.

Explore zero indices and exponent cancellation, showing that zero indices lead to one for nonzero bases. Note that certain exponent laws do not apply when indices are zero or negative.

Explore how to simplify expressions with negative indices by using reciprocals and squared terms, walking through worked examples and practical steps.

Explore rational indices and the power of a fraction, applying exponent laws to deduce roots and fractional exponents with positive rational numbers.

Explore how to find the unknown index in equations by aligning both sides to a common base, and apply prime factorization when the base is unclear.

Master the laws of indices by applying the product rule to same bases, adding exponents, and using the quotient rule to subtract exponents, with practice on varied bases.

Apply the first law of indices to simplify expressions by adding exponents for like bases, multiply coefficients, and ensure bases match before combining terms.

Apply law 2 of indices to simplify expressions, use fraction form and cancellation to handle division, and practice evaluating index-based expressions.

Apply the laws of indices to simplify expressions, as shown in worked example 4, using laws 1–4 to rewrite and combine terms step by step.

Apply the law of indices to simplify expressions, manipulating exponents on top and bottom, and practice with multiple examples to build proficiency.

Master the applications of laws of indices, including zero and negative indices, through worked examples that show converting to positive indices and simplifying complex expressions.