Our School Pages



What is the value of (185 + 278 + 579) – (85 + 178 + 279) ?Evaluate -2 + 7 × 32 – 4+32What number multiplied by itself is equal to the product of 6 and 150?A cell takes half a day to divide, forming two cells. If a cell culture starts with one cell, how many cells will there be after nine days?Find the value of the sum:12 + 14 + 16 + 18 + … + 1100What whole number between 100 and 200 is both a perfect square and a multiple of 7?Evaluate the following expression: 52 - 42122 + 52. Express your answer as a reduced fraction.2n means that 2 is used as a factor n times. For example, 24 means 2 x 2 x 2 x 2 = 16. We say that 24 ends in 6 and that 24 has a units digit of 6. If 21997 is multiplied out, what is the units (ones) digit of the product?BONUS PROBLEMSMaria writes the same whole number in each box below and gets a true statement. Jon does the same as Maria and also gets a true statement. But Jon and Maria choose different numbers. What two numbers do they choose?12 + ( □ x □ ) - (7 x □ ) = 0If 518 x 220 is multiplied out, what is the leading digit of the product? (Note: the leading digit of a number is the digit in the leftmost position.)Express the difference 10112 – 1102 in base 2.What is 20117 expressed as a base nine number?SOLUTIONS:500To do this quickly in your head, note that each number in the first set is greater than its counterpart in the second set by an obvious amount:185 – 85 = 100278 – 178 = 100579 – 279 = 300Then 100 + 100 + 300 = 500Or, you could simply do the full arithmetic, evaluating the expressions inside the parentheses first:(185 + 278 + 579) – (85 + 178 + 279) =1042 – 542 = 50012Evaluate the expression in the following order:Please Excuse My Dear Aunt SallyParentheses Exponents Multiplication Division Addition Subtraction-2 + 7 × 32 – (4 + 3)2 = -2 + 7 × 32 – (7)2 = -2 + 7 × 9 – 49 = -2 + 63 – 49 =61 – 49 = 12306 x 150 = 900Since 9 = 3 x 3, then 900 = 30 x 30262,144The cells double in count every half a day for nine days, so there will be 18 doublings. So starting with a single cell, that’s:1 × 2 × 2 × 2 × 2 × ….. (total of 18 times)which is:1 × 218or just:218Using the [xy] or [^] function on your calculator, this is 262,144.50The value of 1 raised to any integral power is still 1. For example, 14 = 1 x 1 x 1 x 1 = 1. Since there are only even powers of 1, there are 50 addends of 1 to be summed. Therefore the sum is 50 x 1 = 50.196List the perfect squares between 100 and 200:112 = 121122 = 144132 = 169142 = 196 Of these, only 196 is a multiple of 7. The desired number is 196.31352 - 42 = 25 – 16 = 99 = 3122 + 52 = 144 + 25 = 169169 = 13So, the answer is 3/13.21997 ends in 2Look for a pattern.21 is 222 is 423 is 824 is 16, which ends in 625 ends in 226 ends in 427 ends in 828 ends in 629 ends in 2210 ends in 4211 ends in 8212 ends in 6213 ends in 2214 ends in 4215 ends in 8216 ends in 6The unit’s digit repeats in groups of four: 2, 4, 8, 6. So 24, 28, 212, 216, and every power of 2 whose exponent is a multiple of four has a units digit of 6. Therefore 21996 has a units digit of 6 and 21997 has a units digit of 2.The two numbers are 3 and 4Decide what values are possible and then substitute. To produce an end result of 0, 12 + ( □ x □ ) must be equal to (7 x □ ). Therefore ( □ x □ ) is less than (7 x □ ), and □ is less than 7. Thus □ represents the whole numbers 0, 1, 2, 3, 4, 5, or 6. Replace all three boxes with the same number until two different choices work. 4Noting that 220 can be written as 218 x 22, then 518 x 220 = 518 x 218 x 22. 518 x 218 is 1 followed by a string of 18 zeroes (1018), then the leading digit is 1 x 22 = 4. 101210112-1102____________1012Subtracting from right to left, in the ones, twos, fours and eights columns: 1 – 0 = 1; 1 – 1 = 0, and in base 2, 10 – 1 = 1 (1 eight – 1 four = 1 four).85120117 is (2 x 343) + (0 x 49) + (1 x 7) + 1 = 694 in base 10. Converting to base 9, 69410 = (8 x 81) + (5 x 9) + 1. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download