Questions and Answers #80 Fractions

Questions and Answers Sheet 80 Fractions Question #1 What is the lowest form of the fraction 12 ? 18 Answer: Given fraction is 12 . 18 Six is the element that 12 and 18 have in common the most. Applying the greatest common factor, change the denominator and numerator.  12 = 6  2 and18 = 6  3  12 6  2 = 18 6  3 2 3 So the lowest form of 12 2 = . 18 3 Question #2 Solve the fraction. y = ((1 + X ) n − 1)  ( x(1 + x n )) Answer: set your problem to 0 0= (1 + x) n − 1 x( x + 1n ) then remove brackets: 0 = 1n + x n − 1/ x 2 + x n x n will cancell out, and 1 to any power is still 1. 0 = 0 / x2 since your fraction is now 0=0, your equation is undefined ( x 2 )0 = 0 / x 2 ( x 2 ) 0=0 Question #3 How is 1225 represented as a decimal? A) 4.8 B) 48 C) 0.048 D) 0.48 Answer: C is the correct option Given fraction is 1225. Decimate the denominator as multiples of 10, which in this case is 100.. ⇒ 12 × 425 × 4 ⇒ 48100 By counting the amount of zeros in the denominator, move the decimal point to the left now.. ∴ The decimal form of 1225=0.48 Question #4 Given H ( p ) = 9p , evaluate. p +8 H(1)? Given H ( p ) = 7p , evaluate. p+2 H(t)? Answer: H (1) = 9(1) 9 = =1 (1 + 8) 9 34) H (t ) = (7t ) (t + 2) Question #5 5x 4x − . x −7 x −5 Write in lowest terms. Answer: 5 x / [ x − 7] − 4 x / [ x − 5] = [5 x( x − 5) − 4 x( x − 7)] / [( x − 5)( x − 7)] = [5 x 2 − 25 x − 4 x 2 + 28 x] / [( x − 5)( x − 7)] = [ x 2 + 3x] / [( x − 5)( x − 7)] Question #6 How do you write 2 1 as an improper fraction. 4 Answer: 1 For converting mixed fraction into improper 4 fraction The numerator of the improper fraction = denominator Ч the whole number + the numerator of 1 4Ч 2 + 1 9 = Hence, the improper fraction of the mixed fraction Therefore, the improper fraction is 2 = 4 4 4 19 given mixed fraction 2 . 44 Find the improper fraction: Given mixed fraction is 2 Question #7 What is the result of converting 150% to a fraction? Answer: Given, we need to convert 150% to a fraction. If we want to convert a percent to a fraction, we need to divide it by 100. 150% = 150/100 = 15/10 = 3/2 Question #8 If x>2; then x2 − x − 6 x2 − 4 Answer: factor the denominator and numerator x2 − x − 6 x2 − 4 ( x − 3)( x + 2) the (x+2)'s halt leaving ( x + 2)( x − 2) ( x − 3) ( x − 2) Question #9 Find the rational fraction in lowest terms represented by the periodic decimal. show work 0.4444 Answer: Let x = 0.4444...x = 0.410 x = 0.4 1010 x = 4.410 x − 0.4 = 4.4 − 0.410 x − x = 49 x = 4x = 4 9 Question #10 What's 2/3 of 17 as a fraction. Answer: We can express 17 as the fraction mixed number 11 and 2 17 34 . Multiplying that by , you get which is equivalent to the 3 1 3 1 . 3 Question #11 2 66 % as a fraction is 3 A) 2 3 B) 1 4 C) 1 6 D) 1 3 . Answer: The ideal decision is A 2 3 2 200 200 1 2 66 % = %=  = 3 3 3 100 3 Question #12 Why is zero a whole number? Answer: Whole number: The whole numbers are real numbers that do not have fractions, decimals, and negative numbers There is no fraction or decimal equivalent to zero. It is neither positive nor negative. Zero adheres to the rule of whole numbers. It is the sum of any number and its opposite number. Example, 1 + ( −1) = 0; 4 + ( −4 ) = 0 Question #13 What is 1 of 40? 5 Answer: To get a fraction of a number, we will simply multiply this fraction by the number. In the given we want to find 1 of 40. 5 This can be computed as follows: 1 1 of 40 =  40 5 5 = 40  1 40 = =8 5 5 Question #14 Solve: 8−5 1 4 Answer: Convert all the numbers to a fraction with common denominator of 4 8 4 32 = 4 4 Therefore, 32 1 32 21 11 −5 = − = 4 4 4 4 4 Question #15 Prove that 1 1 1 1 2 + + + .... +  n n +1 n + 2 2n 3 Prove that for (a) And n 1 1 1 1 2 + + + .... +  n n +1 n + 2 2n 3 (b) 1 1 1 1 1 2  + + ..... + + ....  2 3n + 1 3n + 2 5n 5n + 1 3 my attempt : 1 1 1 1 1 1 1 1 n +1 1 + + + .... +  + + + .... + =  n n +1 n + 2 2n 2n 2n 2n 2n 2n 2 Where i am missing and how to processed second question Answer: By C-S 1 1 1 (1 + 1 + ... + 1) 2 ( n + 1) 2 2( n + 1) 2 + + ... +  = =  n n +1 2n n + (n + 1) + ... + (2n) (n + 1)(2n + n) 3n 3 2 1 1 1 1 (1 + 1 + ... + 1) 2 + + ..... +  = 3n + 1 3n + 2 5n 5n + 1 (3n + 1) + (3n + 2) + ... + (5n + 1) (2n + 1) 2 2n + 1 1 = =  . (2n + 1)(2(3n + 1) + 2n) 4n + 1 2 2 1 1 1 1 + + ..... +  3n + 1 3n + 2 5n 5n + 1 for all For 5 n +1  3n 1 5n + 1 2 dx = ln  x 3n 3 n2 n = 1 we see that 1 1 1 2 + +  is true. 4 5 6 3 Question #16 -2x + 2y + 5 = 0 how do you graph a fraction as the y intercept? Answer: y -intercept is the point where a function when plotted in X-Y plane crosses or touches Y- axis any point on Y axis is of form (0,y) where y can be any real number from ( − . ) for given function -2x + 2y + 5 = 0 y intercept can be found out by keeping x = 0 i.e 2y+5= 0 5 i.e y = (− ) is y-intercept 2 Question #17 Convert 0.35 to a fraction in lowest terms Answer: Step 1 Convert the decimal to decimal fraction - Any decimal can be converted to a decimal fraction by x removing the decimal and writing 10 in the denominator, where x represents the number of digits after decimal - 0.35 = 35 35 = 2 10 100 Step 2 Reduce the fraction to the lowest term - HCF of 35&100 − 35 = 5  7100 = 2  2  5  5 HCF = 5 . Divide both the numerator and denominator by HCF - Therefore, 0.35 in fractional form is 35 35  5 7 = = . 100 100  5 25 7 . 25 Question #18 Which of these is the simplest form of the fraction 1) 5 25 2) 25 125 3) 1 5 4) 50 250 25 ? 125 Answer: The correct option is 3) 1 5 When the numerator and denominator of a fraction cannot be further reduced by dividing them both by the same integer, that fraction is said to be in its simplest form. After that, divide the numerator and denominator of 25 25 5 = by 5, we get 125 25 125 But this may be made even more straightforward. Because the denominator and numerator are both divisible by five, Dividing both numerator and denominator of So, 5 1 5 = by 5 again, we get 25 5 25 1 25 is the simplest form of the fraction as it cannot be reduced further. 125 5 Question #19 What is the reciprocal of −2 ? 3 Answer: −2 . The reciprocal of a fraction is obtained by interchanging the numerator 3 −2 1 −3 and denominator numbers. The reciprocal of . Hence, the required reciprocal of the given = 3 −2 2 3 −3 fraction is . 2 Determine the reciprocal of Question #20 In the decimal form, fraction 25 = 3.125 . 8 Answer: To convert a fraction to a decimal number, follow these steps: (i) we first convert it into an equivalent fraction with denominator 10 or 100 or 1000 or any number of form 1 followed by zeros. (ii) write its numerator and mark decimal point after one place or two place or three places from right towards left if the denominator is 10 or 100 or 1000 respectively. If the denominator has 1 followed by n zeros, then put the decimal after n places from the right to the left. 8 × 125 = 10000 So, we will multiply and divide the fraction 258 by 1000. 25  125 3125 = = 3.125 Note: If the numerator is short of digits, insert zeroes 8  125 1000 at the left of the numerator and then put the decimal point.