PER CENTS

The fraction, a hundredth, is so important that we have another name for it, a per cent. This means by the hundred. 5 per cent is 15 10 per cent is 10%. 33 per cent is thirty-three and one third hundredths. Just as

we have as the sign for cent and $ as the sign for dollar or 100, so also we have a sign for hundredths or per cents. This sign for hundredths is %, called per cent.

6% of $1 is 16 of 100%, or 6¢

50% of $1 is 50 of 100%, or 50¢

100

Per cents are especially used in dealing with money; for when one lends money to another, the lender usually asks the borrower not only to give him back after a time all his money, but also to pay him so many per cent for the use of the money. This payment is called interest. Also we pay the governments of our town or city and of our State every year so many per cent of the money value of our property. This payment is called a tax. It supports the police and schools and takes care of the streets or roads.

AREAS

We find the areas of rectangles in square measure by multiplying the lengths of the adjoining sides.

1. If the sides of this rectangle were 2 inches and 3 inches, its area would be 2 in. x 3 in. = 6 square inches = 6 sq. in.

2. If a mirror is 3 ft. × 41 ft. in size, its area is 13 sq. ft.

We find the areas of right-angled triangles by multiplying together the lengths of the sides which make the right angle and dividing their product by two.

The dotted lines show the rectangle which the multiplication of the lengths of the

two sides gives

us.

3. Find the area of these triangles, A and B.

Find the areas of these triangles:

4. 2 miles by 61⁄2 miles. 5. 3 yds. by 9 yds.

CIRCUMFERENCES

A circle may be drawn on the blackboard by making a loose knot in a string and setting the knot around the crayon. Then if one holds the free end of the string against the blackboard with one finger of the left hand, and stretches it tight, a circle of any desired diameter may be made. The finger marks the center. With a pin, a pencil, and a piece of cardboard with holes in it for the pin and pencil, circles may be drawn on paper. Circles may also be drawn with dividers or compasses.

The diameter of a circle is twice its radius. A radius is any straight line from the center to the circumference. The string makes the length of the radius of the circle drawn on the blackboard.

The circumference of any circle equals almost exactly three and a seventh times the diameter. We can prove this by drawing circles and comparing their diameters and circumferences.

1. Find the circumference of a circle 2 in. in diameter.

2 in. × 3 = 62 in.

2. Find the circumference of a circle 4 yd. in diameter. 4 yd. × 3 = 124 yd.

3. Draw circles of various diameters and find their circumferences.

In these questions we always need to know how to multiply a whole number and a fraction.

60.

80

75

70

SCHOOL PER CENTS

1. John had 87% in his arithmetic, 60% in reading, 80% in manual work, 75% in drawing, 70% in music, 60% in spelling, and 90% in Nature study. What was his average, if each study counted the same?

87% 7)522

744%

2. But what was his per cent if arithmetic counted 3 points, reading and manual work 2 points each, and the other exercises 1 point each?

4. In a class of 36 boys and girls 33% were girls. How many girls were there? How many boys? 50% were not absent in October. How many came every day? 25% were tardy once each during the entire school year. How many were tardy?

5. In another class of 45 boys and girls 33% were girls. How many boys were there? How many girls? 80% were not absent in October. How many came every day? 9 were tardy once during the year. What per cent of 45 was that? What is the ratio of 9 to 45? is what per

cent of 100 ?

3. Find the averages of various reports.

A

RATIOS AND FRACTIONS

B

C

D

1. What is the ratio of A to B? of B to A? of A to C? of B to C?

2. Why is the ratio of B to C and of C to B3 ?

3. What is the ratio of A to D? of D to A? of B to D? of D to B?

4. Why is the ratio of C to D and of D to C ?

E

F

B

5. What is the ratio of B to E? of E to B? of B to F? of F to B?

6. What fraction of E is C? D? of F is C? is D?

10. Fold paper to show fractions and ratios like these.

11. Make drawings of larger sizes, showing similar ratios and fractions.