By Percival Frost Joseph Wolstenholme

This Elibron Classics booklet is a facsimile reprint of a 1863 variation by means of Macmillan and Co., Cambridge - London.

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**Additional resources for A Treatise on Solid Geometry**

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A. 3 1 + 5 2 b. 1 3 , 5 10 c. 1 S U M MARY In this section, real numbers were deﬁned as the set of all rational and irrational numbers. Decimals are approximated by either truncating or rounding. ■ ■ Truncating: Eliminate all values after a particular digit. Rounding: Look to the right of a particular digit. If the number is 5 or greater, increase the digit by 1; otherwise, leave it as is and eliminate all digits to the right. The order in which we perform operations is 1. parentheses (grouping); work from inside outward.

7. EXAMPLE 10 Using Properties of Negatives and the Distributive Property Eliminate the parentheses Ϫ(2x Ϫ 3y). C O M M O N M I S TA K E A common mistake is applying a negative only to the ﬁrst term. ★ CORRECT Ϫ(2x Ϫ 3y) ϭ Ϫ(2x) Ϫ (Ϫ3y) ϭ Ϫ2x ϩ 3y ■ Answer: a. Ϫ2x Ϫ 10y b. Ϫ3 ϩ 2b ■ YO U R T U R N INCORRECT Error: Ϫ2x Ϫ 3y The negative (Ϫ) was not distributed through the second term. Eliminate the parentheses. a. Ϫ2(x ϩ 5y) b. Ϫ(3 Ϫ 2b) What is the product of any real number and zero? The answer is zero.

C O M M O N M I S TA K E A common mistake is applying a negative only to the ﬁrst term. ★ CORRECT Ϫ(2x Ϫ 3y) ϭ Ϫ(2x) Ϫ (Ϫ3y) ϭ Ϫ2x ϩ 3y ■ Answer: a. Ϫ2x Ϫ 10y b. Ϫ3 ϩ 2b ■ YO U R T U R N INCORRECT Error: Ϫ2x Ϫ 3y The negative (Ϫ) was not distributed through the second term. Eliminate the parentheses. a. Ϫ2(x ϩ 5y) b. Ϫ(3 Ϫ 2b) What is the product of any real number and zero? The answer is zero. 3). 1 Real Numbers P R O P E RTI E S OF ZERO D ESCRIPTION MATH (LET a A real number multiplied by zero is zero.