Modern Junior Mathematics

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 edition. Excerpt: ... of (c). S = x (2 x + 3) + 2 (2 x + 3) = 2x2 + 3x + 4x + 6 = 2x2 + 7x + 6 11. Find the perimeter of the rectangle given in example 10. 12. (a) Measure the line x and find the numerical num ber of square inches in the area. (b) Find the number of inches in the perimeter. (1) Solution of (a). I = 2x + 3 w = x + 2 f in. (f)2 = A sq. hi. 2 x2 + 7 a? + 6 2 (A) + 7(f) + 6 Subst. f for x 1 + + 6 1 + 5i + 6 12 sq. in. area of Note: Prove this area ia correct by multiplying the length in inches by the width in inches. (2) Solution of (b). In example 11 we By measurement, Therefore (.'.) = 4 + 10 = 14 inches. By measurement, x x2 = We found S = Note: The word therefore is used a great many times in mathematical problems. The symbol for it is three small dots put in the form of an equilateral triangle (..). 13. Find the areas and perimeters of rectangles whose dimensions follow. In each case, measure the given line and check the results. 14. (a) Draw two unmeasured lines, x and y centimeters long, and draw a rectangle of these lines. (b) Find area. S = l x w = 1X1/ = xy Just as 2 x means 2 times x, so #?/ means x times J/. The times sign is omitted between two factors when one or both of them are letters. In arithmetic 2x3 could not be written 23, for digits in arithmetical numbers have place value and the 2 means 2 tens or 20. (d) Measure x and y in centimeters; find the value of S and P and the ratio of the dimensions. 16. Find the areas and perimeters of rectangles having the following dimensions: 17. (a) In finding the product of two factors that have unlike letters, what do you do with the coefficients? (b) What do you do with the two letter factors? (c) How do you write the product of two like letter factors? (a)...