REVIEW OF SUBTRACTION Subtraction is the process of finding the difference between two numbers or of taking one number from another. The minuend is the greater number; the subtrahend is the smaller number; and the difference or remainder is the answer. Drill thoroughly on these combinations in subtraction: 9 15 12 16 11 13 12 9 8 17 15 11 4 7 6 7 4 9 3 3 2 8 4 3 1. 12 13 10 11 10 15 14 18 13 17 13 15 8 16 11 13 12 10 16 14 5. A grocer sells butter for 18¢ and receives a half dollar. In making change he adds 2 cents to 18 cents, and then adds the pieces of money that will make 50 cents. What are they? 6. Make change from $1 for a purchase of 724; 856; 64¢. This is called the adding or the making change method of subtraction. 7. Solve by this method: 842 - 385. Think: What number added to 5 will make 12 ? 842 (7.) Write down 7; carry one. What number 385 added to 9 (8 + 1) will make 14? (5.) Write down 457 5; carry 1. What number added to 4 (3 + 1) will make 8? (4.) Write down 4. To test subtraction, add the remainder and the subtrahend. 9. 36005 – 19096 10. 90000 — 27938 11. 23000 – 17500 12. $4629.70 - $3675.84 13. $1475.558 - $539.47 14. $3000.73 – $2036.75 15. $9143.65 – $6183.69 16. $24000.47 - $ 6937.64 17. $2039.05 – $1729.89 18. $9400.37 – $2869.94 19. 630209 – 189768 REVIEW OF MULTIPLICATION Multiplication is the process of taking one number as many times as there are units in another. The multiplicand is the number multiplied; the multiplier is the number showing how many times the multiplicand is taken; and the product is the result of multiplication. 1. 6 + 6 + 6 + 6 = ? In what short way can you find the answer? Multiplication is a shortened form of addition. 2. 3 * $7 = $21. What number is multiplied ? By what number is it multiplied ? What is the name of the answer ? 3. Read : 5 x 4 ft. ; 6 x 3 doz. ; 9 x 2 yd. ; 8 x 74. When the multiplier is written before the multiplication sign, X, as in 4 x 8 bu., it is read “ times” as 4 times 8 bu. When the multiplier is written after the sign, it is read « multiplied by.” Thus, 4 ft. X 8 is read 4 ft. multiplied by 8. 4. Does 6 apples times 4 make sense ? The multiplier cannot name things ; as, feet, hours, etc., since it indicates the number of times the multiplicand is to be taken. An abstract number is a number used without reference to a particular thing; as, 5, 6, 50. A concrete number is a number used with reference to a particular thing; as, 5 trees, 6 dollars. The multiplier is always regarded as an abstract number since it shows how many times the multiplicand is taken. The product is always like the multiplicand. 5. Select the multipliers and the multiplicands : 6 x 9 doz. 3 x 9 qt. 8 hr. x 5. 6. Find the cost of 15 oranges at 3¢ each. 7. How many minutes are there in 4 hours ? in 8 hours ? 8. Multiply 323 bu. by 25. Multiplicand 323 bu. 323 bu. Multiplier 25 25 1st partial product 1615 bu. = 5 x 323 bu. 1615 2d partial product 6460 bu.= 20 x 323 bu. 646 Entire product 8075 bu. = 25 x 323 bu. 8075 bu. To test multiplication, use the multiplicand for a multiplier and perform the multiplication again ; or divide the product by the multiplier. 9. How much will 48 chairs cost at $1.25 each? $ 1.25 48 1000 Multiply as before, and mark off as many cents in the prod500 uct as you have in the multiplicand. $ 60.00 2. The multiplicand and the multiplier are called factors of the product. 3 is one factor of 12. What is the other factor? The product divided by one factor gives the other factor. 3. The product is 84 and one factor is 12. What is the other factor? 4. Find the unknown factors : product 96, one factor 8; product 144, one factor 12; product 284, one factor 4; product 1080, one factor 9; product 1274, one factor 7. An integer or an integral number is a whole number. A multiple of a number is one or more integral times the number. 5. 28 is a multiple of 4 and 7. 22 is a multiple of what numbers ? 36 is a multiple of what two numbers ? 6. Name all the multiples of 2 from 2 to 50. 7. Name all the multiples of 3 from 3 to 66. 8. Name two multiples of 4 and 6; of 8 and 10. 9. Tell which of the following are multiples of 3; of 5; of 9: 45 63 72 65 108 24 90 18 27 REVIEW OF DIVISION Division is the process of finding how many times one number contains another, or of separating a number into equal parts. The dividend is the number divided; the divisor is the number by which we divide ; and the quotient is the result of division. The remainder is the part of the dividend remaining when the division is not exact. 1. How many times is $ 10 contained in $120 ? Here both dividend and divisor are concrete numbers. Are they alike? The quotient, 12, is abstract because the $120 is measured or divided by $10; or $10 is contained 12 times in $120. 2. In the problem $120 - 10 = $12, or y of $120= $12, the divisor is abstract. Observe that the quotient is like the dividend, and that $120 is separated into 10 equal parts. This kind of division is called partition. |