Therefore the quotient of 1825 divided by 4 is 456-1/4, or 456 and 1 remainder. SHORT DIVISION: INDUCTIVE EXPLANATION Dividing Large Numbers 1. Tom, Dick, Will, and Fred put in 2 cents each to buy an eight-cent bag of marbles. There are 128 marbles in it. How many should each boy have, if they divide the marbles equally among the four boys? ----- 4 |128 _Think "12 = three 4s." Write the 3 over the 2 in the tens column._ _Think "8 = two 4s." Write the 2 over the 8 in the ones column._ _32 is right, because 4 × 32 = 128._ 2. Mary, Nell, and Alice are going to buy a book as a present for their Sunday-school teacher. The present costs 69 cents. How much should each girl pay, if they divide the cost equally among the three girls? ---- 3|69 _Think "6 = .... 3s." Write the 2 over the 6 in the tens column._ _Think "9 = .... 3s." Write the 3 over the 9 in the ones column._ _23 is right, for 3 × 23 = 69._ 3. Divide the cost of a 96-cent present equally among three girls. How much should each girl pay? ------ 3|96 4. Divide the cost of an 84-cent present equally among 4 girls. How much should each girl pay? 5. Learn this: (Read ÷ as "_divided by_.") 12 + 4 = 16. 16 is the sum. 12 - 4 = 8. 8 is the difference or remainder. 12 × 4 = 48. 48 is the product. 12 ÷ 4 = 3. 3 is the quotient. 6. Find the quotients. Check your answers by multiplying. ---- ---- ---- ----- ----- ----- 3|99 2|86 5|155 6|246 4|168 3|219 [Uneven division is taught by the same general plan, extended.] LONG DIVISION: DEDUCTIVE EXPLANATION To Divide by Long Division 1. Let it be required to divide 34531 by 15. _Operation_ Divided Divisor 15)34531(2302-1/15 Quotient 30 -- 45 45 -- 31 30 -- 1 Remainder For convenience we write the divisor at the left and the quotient at the right of the dividend, and begin to divide as in Short Division. 15 is contained in 3 ten-thousands 0 ten-thousands times; therefore, there will be 0 ten-thousands in the quotient. Take 34 thousands; 15 is contained in 34 thousands 2 thousands times; we write the 2 thousands in the quotient. 15 × 2 thousands = 30 thousands, which, subtracted from 34 thousands, leaves 4 thousands = 40 hundreds. Adding the 5 hundreds, we have 45 hundreds. 15 in 45 hundreds 3 hundreds times; we write the 3 hundreds in the quotient. 15 × 3 hundreds = 45 hundreds, which subtracted from 45 hundreds, leaves nothing. Adding the 3 tens, we have 3 tens. 15 in 3 tens 0 tens times; we write 0 tens in the quotient. Adding to the three tens, which equal 30 units, the 1 unit, we have 31 units.