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This educational resource covers fundamental mathematical principles including the Commutative, Associative, and Distributive Laws. It explains how the order and grouping of numbers do not affect the results in addition and multiplication. Additionally, it demonstrates how to perform mathematical operations by prioritizing brackets and the order of operations. The material includes examples of divisibility and patterns, enhancing students' problem-solving skills. Ideal for learners seeking to solidify their understanding of basic math concepts.
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Mathematics Chapter One
Commutative law • 5+3=? • The order of adding any 2 numbers does not affect the result. • This is the same for multiplication and division Answer: 5+3=3+5
Associative Law • 2+3+5=? • The order of grouping numbers together in addition does not affect the answer. • This is the same for multiplication only. Answer: 2+3+5=(2+3)+5
Distributive Law • 4x(5x9)=? • (4x5)+(4x9)=? • For any 3 whole numbers A, B, C we have Ax(B+C)=AxB+AxC. Answer: 4x(5x9)=180 Answer: (4x5)+(4x9)=56
Performing Maths Operations • Simplify any expression within brackets first. • Simplify any brackets within brackets first when needed. • Do multiplications and divisions first before doing adding and subtracting
Mathematics Chapter 2
Some Questions • Is 50836 divisible by 2? • Test 660 for divisibility by 2,3,4,5,10 and 11. • What is the square root of 4? Answer: 50836/2=25418 Answer: 660/2=330 660/3=220 660/4=165 660/5=132 660/10=66 660/11=60 Answer: square root is 2
Mathematics Chapter 3
Some Questions • State a rule for 3, 8, 13, 18 and write the next three terms. • Consider the pattern2=1x26=2x312=3x4.110=kx(k+1) • Write the 8th line of the pattern • The value of k. Answer: the rule is N+5. 23 28 33 Answer: 72=8x9 Answer: k=10
Continued • Fill the box with the appropriate number and state the rule used • 1, 3, ?, 27, 81. Answer: it is Nx3 = 9.