(b) To find whether this sum is correct, add these fractions in the usual way: (c) What is the difference between and ? 6. Explain what is meant by a fraction in lowest terms? 7. How can you change a fraction to its lowest terms? Six may be written as the product of 2 and 3. Two and 3 are called the factors of 6, because they are the two numbers which when multiplied together "make" 6. Factor is a Latin word which means a maker. 8. Eight may be written as 4 x 2. These are factors of 8. But 4 may be divided again into 2 × 2. A factor, such as 2, 3, 5, 7, 11, which cannot be divided again except by itself or 1, is a prime factor. 10. Show why you can cancel two equal prime factors from the numerator and denominator of a fraction to change it to lowest terms. 11. Always put two tests to the result of your problem, if it contains a fraction: (a) Has every improper fraction been changed to a whole number or to a mixed number? (b) Is every proper fraction in its lowest terms? 1. (a) If we multiply two 10's together, we get 100, the second power of 10. (b) If we multiply three 10's together, we get 1000, the third power of 10. (c) Every fraction whose denominator is 10, 100, 1000, or some other power of 10 is a decimal fraction. (d) Decimal comes from a Latin word decem that means ten. (e) Usually decimal fractions are written without denominators. Instead, a dot or decimal point shows what the (f) How does the number of decimal places compare with the number of zeros in the denominator Begin at 100, 99, 98, 97, 96, . . . 91 and count backward by 3's, 4's, 5's, . . . 9's. Spend ten minutes each day for at least two weeks counting backward. Keep a record of the number of counters you can use in the ten minutes.* Drill on the following subtractions until you can read the results in one minute and a half, or less. * Pupils are to count backward first by 3's, then by 4's, and so on. These numbers are the counters. The first day a pupil may count only by 3's, 4's, and 5's. Gradually he may increase the number of counters he uses in 10 minutes. II. Practice Exercises Solve these examples in subtraction. Time yourself each day for a week. Make a graph of your record. Does it slope in the right direction? 5. (a) From 19,324 Minuend (meaning to be lessened) Subtract 8,697 Subtrahend (meaning to be taken away) 10,627 Difference (b) For convenience, we give special names to the three numbers in a subtraction problem. (c) Why is minuend a good name for the number from which another one is to be taken? (d) Why is subtrahend a good name for the number (e) What is the name of the result in subtraction? (g) Subtract the difference from the minuend. What (h) In what two ways may you check your work in subtraction? Which method is the easier? III. Time Tests Subtract and check the following problems. Time yourself. If it takes you longer than two minutes, make up similar problems for practice until you can work them |