existence and uniqueness of binary representation
... then cr = 1. Therefore, n ≥ 2r (the equality is achieved when all the other coefficients ci are 0s.) Now, consider the number Σqi=1 2i . This number is greater than the number in the second representation (here, we set all di ’s to 1). Now, n ≤ Σqi=1 2i < 2r ≤ n, where the middle unequality comes f ...
... then cr = 1. Therefore, n ≥ 2r (the equality is achieved when all the other coefficients ci are 0s.) Now, consider the number Σqi=1 2i . This number is greater than the number in the second representation (here, we set all di ’s to 1). Now, n ≤ Σqi=1 2i < 2r ≤ n, where the middle unequality comes f ...
RATES AND UNIT RATES 7.1.1 – 7.1.3
... with the decimal points in a vertical column. Write in zeros so that all decimal parts of the number have the same number of digits. Add or subtract as with whole numbers. Place the decimal point in the answer aligned with those above. MULTIPLYING DECIMALS: Multiply as with whole numbers. In the pro ...
... with the decimal points in a vertical column. Write in zeros so that all decimal parts of the number have the same number of digits. Add or subtract as with whole numbers. Place the decimal point in the answer aligned with those above. MULTIPLYING DECIMALS: Multiply as with whole numbers. In the pro ...
Grade 6 Math Circles Prime Time Solutions
... 8. What is the smallest number that you must multiply 48 by so that the product is divisible by 45? 15 9. The eight digit number 1234678 is divisible by 11. What is the digit ? 9 10. What is the smallest prime number greater than 200? 211 11. The four digit number 43 is divisible by 3, 4 and 5. ...
... 8. What is the smallest number that you must multiply 48 by so that the product is divisible by 45? 15 9. The eight digit number 1234678 is divisible by 11. What is the digit ? 9 10. What is the smallest prime number greater than 200? 211 11. The four digit number 43 is divisible by 3, 4 and 5. ...
Adding mixed numbers with unlike denominators ppt
... To Add Mixed Fractions With Unlike Denominators This number is also called the least common denominator. ...
... To Add Mixed Fractions With Unlike Denominators This number is also called the least common denominator. ...
1 Study Guide #4: Quadratic Functions and Complex Numbers
... (3) Prepare to add the needed value to create the perfect square trinomial. Be sure to balance the equation. The boxes may help you remember to balance. x2 + 8x + _____ = 4 + _____ (4) To find the needed value for the perfect square trinomial, take half of the coefficient of the middle term, square ...
... (3) Prepare to add the needed value to create the perfect square trinomial. Be sure to balance the equation. The boxes may help you remember to balance. x2 + 8x + _____ = 4 + _____ (4) To find the needed value for the perfect square trinomial, take half of the coefficient of the middle term, square ...
Dividing Signed Numbers
... The natural numbers to the right of zero are called positive integers. The opposites of the natural numbers to the left of zero on the number line are called negative integers. Zero is neither positive nor negative. Therefore, the integers to the left of zero are opposites of the integers to the rig ...
... The natural numbers to the right of zero are called positive integers. The opposites of the natural numbers to the left of zero on the number line are called negative integers. Zero is neither positive nor negative. Therefore, the integers to the left of zero are opposites of the integers to the rig ...