Some common fractions may be very easily changed to decimals. We know that a quarter of a dollar of money is Cents mean hundredths of a dollar. twenty-five cents. DECIMALS AND COMMON FRACTIONS Every common fraction may be expressed in an equivalent decimal fraction, and every decimal may be expressed as a common fraction. 14 = 50 per cent of anything, since of 100 is 50; and in percentage we think of everything as having 100 equal parts. } = 121% } = 20% 1% = 10% 1 = 25% 50% may be written in decimals: 50.5; 25% = .25; 121% = .125, since 12% = .12, and of .01 1⁄2 of .010, = 20% .20 .2. 10%.10.1. Since all these things we know from percentage, we can now say We studied all these facts when we learned the aliquot parts of 100. We are now expressing just the same facts, but in a different way. There are a good many decimal fractions which are easy to change to common fractions. .1.2, because..25=4. .333+= nearly sinceof 100 = 333. .4, since .666+. .75 = 3. . .5=1. 1. Write the common fractions which equal .2; .333; .25; .50; .75; .1; and .375. 2. Mary had of a dollar, and spent 20 cents for a box. of strawberries and 30 cents for half a quart of fine ice Can you find the answer to this question by using decimals? Do so, if you think you can. cream. RATIOS The scale arms in the first picture are supported at the center. A weight upon one of the pans is ex actly counterbalanced by a weight upon the other. One pound of the weight balances one pound of sugar. Four ounces balance four ounces. But the scale arms in the second picture are supported at one third of the distance from the right. SCALES FOR WEIGHING. A=2B. The ratio of A to B is 2. A 1-pound weight in A counterbalances 2 pounds of sugar. The principle of the scale for weighing is ratio. The even balance or scale as seen above shows the principle of the equation, both of whose terms are always equal. Things equal to the same things are equal to each other. 1. If 3 apples cost 10 and 2 oranges cost the same as 3 apples, how much do the 2 oranges cost? 2. If John and Charles earn together $1 a day, and Thomas earns as much as both John and Charles, how much does Thomas earn? 3 A would equal 3 B or 3 C. Equal multiples of equal things are equal. 3. If Mary and Sally are each 6 yr. old, when Mary is 12 years old, how old will Sally be, if she lives? 4. If one book costs $1, how much will ten $1 books cost? Equal parts of equal things equal each other. 5. If John earns 50 a day for ten hours of work, how much will he earn in one fifth of a day? RATIO AND PROPORTION of a thing equals of a thing equals is a ratio. of the same thing.. It is the ratio of 1 to 2. is a ratio. It is the ratio of 2 to 4. These ratios are equal, since } = } = •⚫ to So we can say, The ratio of 1 to 2 equals the ratio of 2 to 4. Expressed briefly, we say, 1 is to 2 as 2 is to 4. We can write this: 1:2=2:4. This last form, 1:2 2:4, is a proportion. = 4. Draw squares to show these ratios and proportions. USEFULNESS OF PROPORTION If we have the ratio of 2 to 4 and the number 6, and wish to know what number is to 6 as 2 is to 4, we can find it by proportion. is to as what is to 2:42:6 We find it very helpful in arithmetic to have another This sign is x, the unknown quantity. sign for ?. 2:4 x 6. Find x. x = 1 of 6. 2:43:6. Proportion helps 2 = 1 of 4. tities. But of 6 = 3. x=3. us find unknown quan |