Questions and Answers #92 Fractions

Questions and Answers Sheet 92 Fractions Question #1 Daphne takes 510 of a colored sheet to make a gift card. If that sheet is further divided into 100 parts, how many parts should she take so that the fraction remains the same? A)5/10 B)5/1000 C)50 D)5 Answer: The right answer is C 50 Fraction of the parts of the sheet Daphne colored =5/10 Total parts of the further divided sheet =100 Earlier Daphne colored 5 out of 10 parts. So, we need to determine how many of the 100 parts she would color. Such that the new fraction is equivalent to 5/10. ⇒5/10=?/100 ⇒5/10=5×10/10×10=50/100 50/100 means Daphne must color 50 parts out of the total parts of the sheet. Thus, answer D is the right answer. Question #2 A pizza is cut into 6 equal slices. I eat half of one slice. What fraction of the pizza do I eat? A)5/15 B)1/12 C)2 D)1/6 Answer: The correct choice is D 1/12 Six slices of the pizza are taken. Fraction of each slice of pizza = 1/6 Half of one slice = 1/2 of 1/6 = 1/12 Therefore, fraction of the pizza I eat = 1/12 Question #3 Write each fraction in the simplest form: Answer: 26 39 To find the simplest form of 26 . After dividing the denominator and numerator by 13 , we have 39 26 2 = 13 = 39 3 13 Hence, the simplest form of 26 2 is . 39 3 Question #4 ing divisibility tests, determine if given number is divisible by 64335 Answer: If a whole integer satisfies the two requirements listed below, it is said to be divisible by 6. It should be possible to divide the provided entire number by two. If the digit in the number's units position (0, 2, 4, 6, or 8) is even, then the number is divisible by two. The provided entire number must divide evenly by three. A number is precisely divisible by three if the sum of all its digits is also precisely divisible by three. The number given is 4335. Given that the number ends at 5, Consequently, the supplied number, 4335, cannot be divided by 2. The sum of the given number's digits, which equals 15, is divisible by three. The number 4335 is divisible by 3 but not by 2, so not divisible by 6. Question #5 What is 2503 ? Answer: A dividend is a number that is being divided, while a divisor is a number by which a dividend is split. 250 is the dividend and 3 is the divisor. When we divide 250 by 3. 250 = 83.33333333 3 The required answer after division is 83.33333... Question #6 19.25 25 evaluate Answer: 19.25  25 = 0.77 Question #7 What is the opposite and reciprocal of 1 ? 3 Answer: Step 1 1 . The term opposite represents the additive inverse of a number. The sum of the 3 1 1 number and its additive inverse is 0. The number which gives 0 on adding with is the negative of , 3 3 1 1 1 that is the number − . Hence, the opposite of is − . 3 3 3 Identify the opposite of Step 2 1 . The term reciprocal represents the multiplicative inverse of a number. The 3 1 sum of the number and its multiplicative inverse is 1. The number that gives 1 on multiplication with is 3 1 1 1 3 1 1 divided by . Discover the value of 1 divided by : = 1  = 3 . Hence, the reciprocal of the 1 3 3 1 1 3 3 1 number 3 . 3 Identify the reciprocal of Question #8 How many km did Yochanan cover by walking and how many did he cover by travelling on the bus? Answer: 5 km walking, 30 km on the bus. Let w represent the distance traveled on foot, and b represent the distance traveled by bus. The total distance is 35 km. w + b = 35 The total time is 1.5 hours. Each leg has time equal to distance/speed. 𝑤 𝑏 + = 1.5 5 60 Multiply by 60 to clear the fractions. 12 w + b = 90 Subtract the first equation, 11w =90-35=55 w=5 b = 30 Check: 𝑤 5 + 𝑏 60 = 1 + .5 Question #9 Find a number, such that when it is divided by 37 gives a quotient of 28 and a remainder of 19. Answer: Here, Divisor = 37 Quotient = 28 Remainder = 19 The dividend will be the number. From the verification formula, Dividend = Divisor × Quotient + Remainder = 37  28 + 19 ⇒ Number = 1036 +19 = 1055 Question #10 Find: 37.8 1.4 . Answer: Compute the required value. The decimal numbers will first be changed to a fraction. That is 37.8 = and 1.4 = = 378 14 378 10 14  =  . [ Taking the reciprocal ] . So we can write that 37.8  1.4 = 10 10 10 14 10 378 = 27 . Hence, the value of 37.8 1.427 . 14 Question #11 Write 0.066 as fraction in lowest term. Answer: We know 0.066 = 0.066 1000 66 33 33 = = Answer: 1000 1000 1000 1000 Question #12 What is 1.6 repeating as a fraction? Answer: 𝑥 = 1.6 = ̅ 1.666666666 … 10𝑥 = 16.6. . (2) ̅ 9𝑥 = 15 ⇒ 𝑥 = 10𝑥 − 𝑥 = 16.6− ̅ 1.6 ⇒ 15 5 2 = =1 9 3 3 Question #13 Convert the decimal 0.6666 into a fraction Answer: 378 10 Let, F = 0.6666 By dividing both sides by 10, we arrive at  10F = 6.6666 On substracting two equations, we get:  9F = 6 6 F= 9 2 F= 3 Question #14 What is ( −30 )  ( −5) ? Answer: ( −30)  ( −5) Can be expressed as → Because, −30 30 = −5 5 −x x = −y y v = 6 Question #15 What number is 175% of 220? Answer: Find 175% of 220. Since 100% equals 220, 175% will be almost twice as much as 220. 175% xx 220 = 175/100 xx 220/1 =385 Question #16 Find: 2.48  4 . Answer: Compute 2.48  4 . Numerator and denominator will first be multiplied by 100. That is 2.48ч 4 = 2.48Ч 100 248 31 = = = 0.62 . Thus, the value of 2.48  4 is 0.62 . 4Ч 100 400 50 Question #17 Find the equivalent fraction of 3 having denominator 20. 5 Answer: 3 ( ) = 3  20 = 5  ( 5 20 12 ) = 12 . Hence, the equivalent fraction is . 20 Do the equivalent fraction calculation: The equivalent fraction is expressed as Cross multiplying ] 60 = 5  ( )( ) = 60 ( 5 Question #18 Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit. A) 235.47,7 B) 235.047,4 C) 235.47,4 D) 234.057,7 Answer: The right answer is B) 235.047,4 Converting the given fractions into decimals first: 4 100 = 0.04 7 = 0.007. 1000 Examine the amount 200 + 30 + 5 + 4 100 + 7 1000 200 + 30 + 5 + 0.04 + 0.007 = 235.047 235.047. Since 4 is located at position 2, following the decimal point, we have the hundredths digit to be 4. Question #19 Find four equivalent fractions of the given fraction: 6 12 Answer: Finding equivalent fractions: To get equivalent fractions of a fraction, multiply or divide the same number in the numerator and denominator. The given fraction is 6 . 12 Let us multiply 2 in both the numerator and denominator = 6  2 12 = 12  2 24 )[ Thus, 12 6 is an equivalent fraction of . 12 24 Similarly multiply 3, 4, 5 in both the numerator and denominator one by one to obtain fractions of 6 . 12 Multiplying with 3 = 6  3 18 = 12  3 36 Multiplying with 4 = 6  4 24 = 12  4 48 Multiplying with 5 = 6  5 30 = 12  5 60 Therefore, 3 more equivalent 12 18 24 30 6 are four equivalent fractions of . 24 36 48 60 12 Question #20 7 The mixed fraction representation of is... 3 Answer: To obtain the mixed fraction, divide the numerator by the denominator, then put the quotient next to the fraction with the residual in the numerator and the original denominator. 3 divided by 7 yields a quotient of 2 and a residual of 1. Answer is 2 1 3