32 3 × 2 = .... _Where do you write the 6?_ 3 3 × 3 = .... _Where do you write the 9?_ -- 4. Prove that 128, 64, and 96 are right by adding four 32s, two 32s, and three 32s. 32 32 32 32 32 32 32 32 32 -- -- -- Multiplication You #multiply# when you find the answers to questions like How many are 9 × 3? How many are 3 × 32? How many are 8 × 5? How many are 4 × 42? 1. Read these lines. Say the right numbers where the dots are: If you #add# 3 to 32, you have .... 35 is the #sum#. If you #subtract# 3 from 32, the result is .... 29 is the #difference# or #remainder#. If you #multiply# 3 by 32 or 32 by 3, you have .... 96 is the #product#. Find the products. Check your answers to the first line by adding. 2. 3. 4. 5. 6. 7. 8. 9. 41 33 42 44 53 43 34 24 3 2 4 2 3 2 2 2 -- -- -- -- -- -- -- -- 10. 11. 12. 13. 14. 15. 16. 43 52 32 23 41 51 14 3 3 3 3 2 4 2 -- -- -- -- -- -- -- 17. 213 _Write the 9 in the ones column._ 3 _Write the 3 in the tens column._ --- _Write the 6 in the hundreds column._ _Check your answer by adding._ Add 213 213 213 --- 18. 19. 20. 21. 22. 23. 24. 214 312 432 231 132 314 243 2 3 2 3 3 2 2 --- --- --- --- --- --- --- SHORT DIVISION: DEDUCTIVE EXPLANATION Divide 1825 by 4 Divisor 4 |1825 Dividend -------- 456-1/4 Quotient EXPLANATION.--For convenience we write the divisor at the left of the dividend, and the quotient below it, and begin at the left to divide. 4 is not contained in 1 thousand any thousand times, therefore the quotient contains no unit of any order higher than hundreds. Consequently we find how many times 4 is contained in the hundreds of the dividend. 1 thousand and 8 hundreds are 18 hundreds. 4 is contained in 18 hundreds 4 hundred times and 2 hundreds remaining. We write the 4 hundreds in the quotient. The 2 hundreds we consider as united with the 2 tens, making 22 tens. 4 is contained in 22 tens 5 tens times, and 2 tens remaining. We write the 5 tens in the quotient, and the remaining 2 tens we consider as united with the 5 units, making 25 units. 4 is contained in 25 units 6 units times and 1 unit remaining. We write the 6 units in the quotient and indicate the division of the remainder, 1 unit, by the divisor 4.