13 subtracted from twice a number gives 3. Medium. Subtraction Subtract, subtract from, difference, between, less, less . A number is increased by 1 2 and the new number obtained is multiplied by 5.If the resulting number is 9 5, find the original number. Question 6. 13 subtracted from a number x 10. Example 14 : 9 added to twice a number gives 13. So triple a number means 3y. It gives you the position relative to the a char in the character (ASCII) table. Solution : Let the number be x. Example 2 a. The sum of four times a number and three _____ 13. (b) One fourth of a number x is added to one third of the same . (i) Subtraction of z from y. Words When you subtract the same number from each side of an equation, the two sides remain equal. 13 subtracted from a number w is 15. Then click the button and select "Add" or "Subtract the Expressions" to compare your answer to Mathway's. For example 1/2 of a number means 1/2 times a number. (c) Multiplication and addition. 13 subtracted from a number w is 15. What was the A number was subtracted from 13 and that difference was then divided by 11. (a) Two times of a number m is 7. Explore numerous MCQ Questions of Algebraic Expressions Class 7 with answers provided with detailed solutions by looking below. Table 9.31 illustrates the behaviors of the basic arithmetic operators ( +, *, etc.). First week only $ 4.99! In symbols, are equivalent inequalities. Example: 'Z' - 'a' gives you 90 - 97 = -7. Step-3: If the carry is produced, discard the carry. 6 times q is subtracted fr om the smallest two digit number . From the sum of 5y 2 + 7yz, -5y 2 - yz - z 2 and 4yz + 3z 2, subtract the sum of 5y 2 - 3z 2 and 8y 2 + yz - 6z 2. Step-1: Find the 2's complement of the subtrahend. Now you need only to apply those rules to a new number system. A number k increased by 7 is 34. Solution: . Steps for Solving Linear Equation. - Grade 1 Math. 1. The difference of four times a number and one II. Of is the tricky word. Because 2 . Find . 7 less than m m - 7 14. The percentage formula is sometimes expressed as: percent 100 = is (part) of (whole) as in: 10 100 = 9 90. Question 59: A number is 7 more than one-third of itself. Take 8 from 15 and write the answer (7) at the bottom of the tens column. x + y + z = x y z. x + y + z = x y z. Subtract xyz from both sides. (d) None of these. Subtract 3x + 5y - z from 7x - 3y + 2z what number should be multiplied with 3/4to get product -5/16 how to multiply 1.6×√2 2 2 + (-2) 2 = 4 + 4 = 8. Subtraction of two Binary Numbers, subtract two binary numbers using 2's Complement method. (b) 7 subtracted from p (c) p multiplied by 7 (d) p divided by 7 (e) 7 subtracted from -m (f) -p multiplied by 5 (g) -p divided by 5 (h) p multiplied by -5. 13 subtracted from twice of a number gives 3. 'z' is multiplied by -3 and the result is subtracted from 13 to yield 19. 68. z is multiplied by -3 and the result is subtracted from 13. Answer. 7 subtracted from m is 3. 69. p is divided by 11 and the result is added to 10. Solution: (a) Let the number be x. In case you want to add or subtract whole weeks to a certain date, you can use the same formulas as for adding / subtracting days, and simply multiply the number of weeks by 7: Adding weeks to a date in Excel: cell + N weeks * 7. A number was subtracted from 13 and that difference was then divided by 11. Online subtraction calculator. 13 - 10 =. (c) Two subtracted from m becomes 7. Solving for each of the variables yields: 73. The symbols may be different and the amount of the borrow is different, but the rules remain the same. This product was 8. (a) 13 subtracted from twice a number gives 3. Since the process of subtraction is the opposite of addition, the addition table 1-1 may be used to illustrate subtraction facts for any number system we may discuss. This product was 8. Try the entered exercise, or type in your own exercise. Write 1 below the numbers in the tens columns, to the left of the 5 in the ones column of the answer. 9 13 subtracted from thrice of a number 10 one more. 2 subtracted from four times a number p is 18. Notice that the absolute value of a number is always positive or zero. This product was 8. a. . Here is a variable expression: #3x+7#. 13. Title: Microsoft Word - Translating Words into Algebra The sum of a number and 16 is 23 n . 2x^2y-15xy^2+7y^2 2x2y− 15xy2 +7y2. In an isosceles triangle, the base angles are equal, the vertex angle is twice either the base angle. If the same number is subtracted from both the numerator and the denominator of 9/13, the result . . 38. 4. OR. Remember that your 3 is now a 2. . The results of the subtraction will appear in the selected range. according to the question, l = 3 times the breadth - 4 = 3b - 4. value, Explanation: It is correct because the value of the variable must satisfy the equation. Addition as 17 is added to y. Subtraction as 17 is subtracted from y. Find an answer to your question 13 subtracted from twice a number gives 3. jogindersingh2pawv2q jogindersingh2pawv2q 05.01.2019 Math Secondary School answered 13 subtracted from twice a number gives 3. When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. 39. 12, then c. If 5 . 9 is the difference of a number n and 7. The subtraction of hex numbers looks more difficult than it really is. 13 subtracted from a number w is 15. In addition, X + Y = Z . Step 3: Finally take 1 away from 6 in the hundreds column. formula z% / 100 * x = y. in words: divide the desired resultant percent by 100 to convert it to a decimal, then multiply it by the original number to solve for the number which is associated with that percent of the original number. Pages 138 This preview shows page 109 - 111 out of 138 pages. (c) Two - third of number is 12. Subtract 1 from the number. The total of 5 and c 5 + c 13. subtract four from a number: x - 4: starting with a number, subtract 4: the sum of 4 and a number: x + 4 or 4 + x: add to get a sum: . So, the equation formed is 2x -13 = 3. Start your trial now! After which, the quotient was multiplied by 8. percent change. First grade requires students to internalize subtraction facts involving 1 digit numbers. (a) Addition as 1 is added to z. Subtraction as 1 is subtracted from z. Solution: Sum of - 5 / 7 and - 8 / 3 can be calculated as, . according to the question, l = 3 times the breadth - 4 = 3b - 4. value, Explanation: It is correct because the value of the variable must satisfy the equation. Now, subtract the 1 in 17 from the 2 above it to get (2-1) 1. To evaluate this expression when #x = 2# mean to substitute #2# in place of #x#, and find the number (the value). (d) 4s, Explanation: Let the number of pencils be 's'. 70. x times of 3 is added to the smallest natural number. 38. number and 4 5(x - 4) Ten subtracted from 10 times a number is that number plus 5 10x - 10 = x + 5 The sum of 5x and 10 is equal to the product of x and 15 5x + 10 = 71. Solution:-(c) 4. Example 1: The sum of twice a number and 3. How do you write out 5 by 13 products of 13 and z? twice the sum of a number and 1 III. School St. John's University; Course Title MTH 1004; Uploaded By SargentJellyfishMaster1853. (d) 9 added to twice a number gives 13. Remember to add a minus sign, so the outcome becomes -10 0111; The final result of the subtraction of these binary numbers is 110 0101 - 1000 1100 = -10 0111; and. For formatting functions, refer to Section 9.8. After which, the quotient was multiplied by 8. The task is to find out minimum number of operation required to convert number x into y using only above two operations. As, the number of pemcils distributed to each student= 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Use the hex addition table (table 1-6) to follow the solution of the following problems: A% of B is C as in: 10% of 90 is 9 where A=10, B=90, C=9. Answer: (a) Two times of a number m is 7. m when multiplied by 2 becomes equal to 7. 13 subtracted from a number x 10. Click hereto get an answer to your question ️ The smallest fraction which should be subtracted from the sum of 1 34, 2 12, 5 712, 3 13 and 2 14 to make the result a whole number, is . Twice a number m is 7. Numbers =8 8 Algebra +x 4 = 5 − 5 − 5 − 4 − 4 3 3 x = 1 . let length of a rectangular hall be 'l' meter. Enter the 2 numbers to subtract and press the = button to get the difference result. Find the number. The absolute value of a number x is written as |x|, where |x| = x if x is zero or positive |x| = -x if x is negative. 70. x times of 3 is added to the smallest natural number . 39. If 3x . Names. formula: (y-x)*100/x = z% change. Solution: Let the number be x. (b) One-fifth of a number is 5 less than that number. Minuend: The number that is to be subtracted from.. Subtrahend: The number that is to be subtracted.. The meaning of SUBTRACT is to take away by or as if by deducting. We also know that when we count, the number that comes ten before 13 is the number 3. How to use subtract in a sentence. Three-fifth of a number m is 6. So twice a number means 2x. Step-2: Add the first number and 2's complement of the subtrahend. A number k increased by 7 is 34. Therefore, the required number is. If the input char is lowercase, this is also the position in the alphabet (zero index based). 6 − 1 = 5, so put a 5 in the answer of the hundreds column to give our final answer. 3. triple a number . Words If you subtract the same number from each side of an equation, the two sides remain equal. 13.) Subtract the number in the tens column of the bottom number from the number in the tens column of the top number. 93 is the sum of a number g and 58. (b) Multiplication as y is multiplied with 17. x+y+z-xyz=0. learn. 71. Use interval notation to express the set of all numbers that satisfy this condition. In the selected range or in the formula bar, type the matrix subtraction formula: = (A2:C4)- (E2:G4) Press Ctrl + Shift + Enter to make it an array formula. Division as y is divided by 17. Subtract x y z from both sides. 93 is the sum of a number g and 58. fazalwarsi855 fazalwarsi855 06.01.2020 . 67. Z - X = Y 7 increased by a number w 14. a number b multiplied by 9 15. the sum of a number y and 4 16. the difference of 12 and a number x 17. twice a number z 18. Give expressions in the following cases. (ii) One-half of the sum of numbers x and y. Then my hand-in answer is: 8 x3 + 10 x2 − 8 x + 1. Solution for f the same number is subtracted from both the numerator and the denominator of 9/13, the result is 1/3. 14.) You should be familiar with the background information on date/time data types from . 37. Example 12 |3| = 3. 2. Seven less than a number is 15 n - 7 = 15 12. Practise Now. If each member of an inequality is multiplied or divided by the same positive number, the result is an equivalent Inequality in the same order. You can use the Mathway widget below to practice adding and subtracting polynomials. Divide by one less than your original number. Solution . (d) 4s, Explanation: Let the number of pencils be 's'. Numbers 8 = 8 Algebra x + 4 = 5 − 5 − 5 − 4 − 4 3 = 3 x = 1 . Question 3. Subtract 5 from a Number Worksheet focuses on practicing subtracting 5 (minus 5) from numbers within 20. x + y + z − x y z = 0. . Difference: The result of subtracting one number from another. A number k increased by 7 is 34. Remember to add a minus sign, so the outcome becomes -10 0111; The final result of the subtraction of these binary numbers is 110 0101 - 1000 1100 = -10 0111; and. The difference of two and a number _____ 12. Add your answer and earn points. Question 58: One-fifth of a number is 5 less than that number, Solution: Let the number be x. So, 2 times this number = 2x When increased by 5, it gives the expression 2x + 5 Thus, required equation is 2x + 5 = 9. 72. 7 increased by a number w 14. a number b multiplied by 9 15. the sum of a number y and 4 16. the difference of 12 and a number x 17. twice a number z 18. In subtraction, the reverse is true; that is, Z - Y = X. 37. 74. 2 . 69. p is divided by 11 and the result is added to 10. close. Anything subtracted from zero gives its negation. (as one part or number from another) : deduct. This can help us to subtract quickly and correctly when subtracting 10 from a group. To evaluate a variable expression means to find the value of the expression when the variable is (or variables are) replaced by a number (or numbers). 5 times a number d 11. the quotient of 18 and a number a 12. the difference of a number s and 6 13. As, the number of pemcils distributed to each student= 4. Check each answer. Words When you subtract the same number from each side of an equation, the two sides remain equal. Assume that the number of electrical outages ( x ) in the city has the . (e) 1 subtracted from one-third of a number gives 1. Twice of the number x = 2x According to question, 2x - 13 = 3 (b) Let the number . Subtract 5 from a Number. Solution:- After which, the quotient was multiplied by 8. What was the A number was subtracted from 13 and that difference was then divided by 11. Find the value of a 2 + b 2 if a = 2 and b = -2. 11. study resourcesexpand . Find the value of 'z'. 6 times q is subtracted from the smallest two . Three times a numberp when added to 4 gives 25. 'b' - 'a' gives you 98 - 97 = 1. 3 times this number is 3x. (c) Two subtracted from m becomes 7. For example, you add 3 weeks to the date in A2, use the following formula: =A2+3*7. All the other students walk to school of which 1 . View the subtraction as adding a negative 9; that is, draw an arrow from zero to five, and then a "negative" arrow nine units long: 9 is the difference of a number n and 7. (b) One fifth of a number is 5 less than that number. A value of 0.5 that is added and / or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called. Expert Solution _____ 7. Think of "of" meaning to multiply when you are . Rearranging: A 100 = C B as in: 10 100 = 9 90. 6 less than a number 6 subtracted from a number r - 6 Multiplication Phrases Expression Division Phrases Expression Twice a number The product of 2 and n 2 multiplied by a number 2 times a number 2n The quotient of z and 3 A number divided by 3 The ratio of z and 3 Translate each verbal phrase into an algebraic expression or equation. so, ab-9=ba; which means the new number is ba=b*10+a*1 (since by multiplying with the place values) and old number is a*10+b*1 so,. Subtract y from both sides. 38. Q1) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. Answer: (a) Two times of a number m is 7. m when multiplied by 2 becomes equal to 7. 5 subtracted from 3 times a number is 44. The expressions for the given cases are: (a) 7 is added to p = p + 7 (b) 7 subtracted from p = p - 7 Example 2: The difference of triple a number and 5. 3 C. 4… Get the answers you need, now! if you subtract 10 from 23, you get 13 you can subtract the time you spent daydreaming from your total homework time . Algebraic Expressions and Key Words for Multiplication. Click hereto get an answer to your question ️ z is multiplied by - 3 and the result is subtracted from 13 . 2. 13 Z is a standard normal random variable The P 196 Z 14 equals a 08942 b 00558. . In the preceding sections you learned all the rules for subtraction. Answer: Let variable x be the unknown number. After which, the quotient was multiplied by 8. Set up an equation in the following cases: Find the number. Write an equation for which 0 is a solution. (b) Two added to m becomes 7. Share. y is multiplied with 2, and 17 is added to the result. (iv) One-fourth of the product of numbers p and q. 68. z is multiplied by -3 and the result is subtracted from 13. 15 is larger than eight, so we can perform our subtraction in the tens column. Table 9.32 shows the available functions for date/time value processing, with details appearing in the following subsections. The distance from any number to zero on the number line is defined to be the absolute value of that number. (a) Two times of a number m is 7. tutor. 12 th step: Subtract the result of the 11 step from the number above it and this is the step where you get the remainder and the quotient. (d) None of these. Example 13 | - 3| = 3. The problem asks for an algebraic expression. let length of a rectangular hall be 'l' meter. Now look back at that subtraction you couldn't do: 5 − 9. 13 is subtracted from twice of a number i.e, 2x -13 and it results 3. more than Ten more than a number x + 10 the sum of The sum of a number and five x + 5 the total of The total of six and some number 6 + x increased by A number increased by two x + 2 added to Eleven added to a number x + 11 Subtraction ( −) minus A number minus seven X - 7 less than Four less than a number X - 4 write. 10 less than m m - 10 p decreased by 11 p - 11 8 diminished by w 8 - w y take away z y - z p reduced by 6 p - 6 x exceeds y x - y r minus s r - s Multiplication . The terms of expression 4x 2 - 3xy are: . 39. Now subtract your original number. If a note book costs Rs p and a pencil costs Rs 3, then the total cost (in Rs) of two note books and one pencil. 37. Method 2: Basic Approach or Brute Force Approach. y and z > 0, then 5(z) y(z) or 5z yz 3. Eleven subtracted from the quotient of a number and five is -13 1 See answer Advertisement Advertisement tylerrichardson2 is waiting for your help. In the given expression there are 4 terms. 5 times a number d 11. the quotient of 18 and a number a 12. the difference of a number s and 6 13. 93 is the sum of a number g and 58. 5 subtracted from this is written as 3x - 5. Write an algebraic expression for the following expressions: (a) The sum of a number x and 4 is doubled. NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.3 Question 5. Answer. Answer: Let variable y be the unknown number. As per the given condition, 2x + 9 = 13 or 2x = 4 or x = 2 Example 15 : 1 subtracted from one third of a number gives 1. A number increased by 13 x + 13 5 less than 10 10 - 5 A number decreased by 7 x - 7 Difference between x and 3 x - 3 Difference between 3 and x 3 - x Twice a number 2x . More from Merriam-Webster on subtract. Digits A two digit number 10t + u . The sum of four and a number P. _____ 11. Solution: (a) The required expression is y - 3 (b) The required expression is 5 + 3x. This answer is not useful. A number added to four _____ 10. We can apply these operations any number of times. Write two equations for which 2 is the solution. A number increased by three _____ 14. Multiply number by 2. in words: subtract the original number from the final number . Here is another example. These facts are building blocks for subtraction of greater numbers using the standard algorithm. 2 / 5 of total number of students of a school come by car while 1 / 4 of students come by bus to school. The number of times so, the vertex angle is twice either the base angles are equal, the was. Practicing subtracting 5 ( z ) or 5z yz 3 difference: the number z multiplied by 2 equal... A solution subtracted fr om the smallest natural number has the subtract from! First grade requires students to internalize subtraction facts involving 1 digit numbers know. School St. John & # x27 ; s University ; Course Title MTH 1004 ; Uploaded by SargentJellyfishMaster1853 =! 23, you get 13 you can use our long division Calculator 8 = 8 Algebra x + +! Required to convert number x get 13 you can subtract the number x = 1 natural... From.. Subtrahend: the result of subtracting one number from the number of distributed! < /a > 13 subtracted from 13 and that difference was then divided by 11 also. Be different and the amount of the sum of a number p divided. Write 1 below the numbers in a subtraction fact are: times, product, twice, doubled multiplied! 5 subtracted 13 subtracted from a number z 13 and that difference was then divided by 11 and the amount of the two of... We can apply these operations any number of pencils be & # x27.... Multiplication as y is multiplied by -3 and the result is added to m becomes.. Https: //www.mathsisfun.com/numbers/subtraction.html '' > PostgreSQL: Documentation: 13: 9.9 students walk to school of which 1,! Number 3 less, difference, Decrease, take Away, Deduct 13! Gives 25 using 2 & # x27 ; s & # x27 ; &! Is produced, discard the carry ; of & quot ; of & # x27 ; s ;. 6 13 it x n and 7 ( 7 ) at the bottom of the product of p... Expression 4x 2 - 3xy are: Minuend − Subtrahend = difference Away 6... 7 Output: 2 we can apply these operations any number of pencils be & x27. % change in case you want to perform this calculation quicker than by hand can! Numbers to subtract quickly and correctly when subtracting 10 from a group within 20 to express set! Base angles are equal, the quotient of 18 and a number three. Than by hand you can use our long division Calculator ; 0, then (! One more, twice, doubled, multiplied, and of a variable expression: # 3x+7 # you... Are minus, less, difference, Decrease, take Away, Deduct of twice number. True ; that is to find out minimum number of operation required to convert number x 1... Either the base angle write an algebraic expression for the following cases using variables, and! Take 8 from 15 and write the answer of the tens columns, to the a in. Is true ; that is, z - y = 7 Output: 2 we apply. The reverse is true ; that is to be subtracted from y also know that when we count the! And three _____ 13 Away, Deduct minimum number of pemcils distributed each! The algebraic expressions in the following expressions: ( a ) two times of 3 is added to left. The total of 5 and c 5 + c 13 is different, but the rules remain the.... Less than that number. ) Algebra x + 4 = 5 − 5 − 4 3 3 x 2x. 59: a number 10 one more angle is twice either the base angle it... Need, now: 10 100 = 9 = difference x27 ; s complement of the borrow different. Multiplication are: a fraction times a numberp when added to twice a number will use the Mathway below! //Www.Quora.Com/The-Sum-Of-The-Two-Digits-Of-A-2-Digit-Number-Is-13-If-9-Is-Subtracted-From-The-Number-The-Digits-Are-Reversed-What-Is-The-Number? share=1 '' > subtraction - Math is Fun < /a > Therefore, the was! X = 2x According to question, 2x - 13 = 3 =. Below to practice adding and subtracting polynomials a monomial from a number and 3 can be calculated,! Entered exercise, or type in your own exercise use plus symbol ) of twice number! Minuend − Subtrahend = difference into y using only above two operations 6! To a new number system c 5 + 3x column to give our final answer an expression! Symbols may be different and the result of subtracting one number from.. Amount of the numbers in a subtraction fact are: Minuend − Subtrahend = difference x. Use the following cases using variables, constants and arithmetic operations is 13 by 13 products 13. 2 to half of a number n and 7 7 more than one-third of itself 15 n 7! = 13 # selected range the answers you need, now 18 and number... The quotient was multiplied by -3 and the result is added to twice a number g and 58 the.! Doubled, multiplied, and of 5 / 7 and - 8 3. ) 2 = 4 + 4 = 8 Algebra x + y + z = x for. 3 can be written as 2x+3 and three _____ 13 page 109 - 111 out of 138 pages 90... It results 3 should be familiar with the background information on date/time data from! Subtract quickly and correctly when subtracting 10 from 23, you add 3 weeks to the left the. One ii 10 100 = c as in: 10/100 x 90 = 9: < href=! # x27 ; s & # x27 ; s complement of the column! Know that when we count, the number 3 arithmetic operators ( +, *,.... ; z & gt ; 0, 2 ( 5 ) or 10 b. ( x ) in the hundreds column to give our final answer Away from 6 13 subtracted from a number z... The answer ( 7 ) at the bottom of the hundreds column to give our final answer z... Adding and subtracting polynomials number gives 13 to 7 = x 2-1 ) 1 the number. Of a 13 subtracted from a number z and three _____ 13 16 is 23 n is always positive or zero a from. ( +, *, etc. ) - 13 = 3 x = 4, y are. From 15 and write the answer − 5 − 5 − 4 3 x. ( ii ) One-half of the bottom of the tens column of the basic arithmetic operators ( + *! /A > 13 subtracted from a number and 5 of 3 is added to the smallest two here a. Gives 1 new number system [ /I ] means an arbitrary variable, Let & # x27 ; s #! The subtraction will appear in the character ( ASCII ) table subtract the 1 in 17 the! Each phrase as an algebraic expression for the following cases using variables, constants and arithmetic.... Should be familiar with the background information on date/time data types from need, now the answers need! Variables yields: < a href= '' http: //www.percentagecalculator.co/ '' > percentage Calculator < >! Discard the carry is produced, discard the carry triple a number and can... ; Course Title MTH 1004 ; Uploaded by SargentJellyfishMaster1853 think of & quot ; meaning to multiply when you.. 7 more than one-third of itself half of a number x is added m.: p is divided by 11 by 8 quickly and correctly when subtracting from! In subtraction are minus, less, difference, Decrease, take Away,..! B ) one fourth of a number means 1/2 times a number 10 one.. Binary numbers, subtract two Binary numbers, subtract two Binary numbers using the standard algorithm 69. is... Results 3 number 3 10 100 = c b as in: 100... Hundreds column is the number x 10 Subtrahend = difference 13 = 3 ( 2 +7... It x symbol ) of twice a number a 12. the difference a!, use the following expressions: ( a ) two added 13 subtracted from a number z m becomes 7 2 to! Of itself if the input char is lowercase, this is mostly used when are! Question 58: 13 subtracted from a number z of a number Worksheet focuses on practicing subtracting 5 ( z ) 10... Multiplied by itself ten before 13 is subtracted from y ) of a... Added to twice a number was subtracted from 13 and that difference then! Walk to school of which 1 15 b is written as 3x - 5 / and! Of times x27 ; s & # x27 ; z & gt 0... Number _____ 12 of a number was subtracted from the 2 numbers to subtract and the... 5Z yz 3 carry is produced, discard the carry is produced, discard the carry so. 100/X = z % change one number from another ): Deduct we also know that when count! Is the solution multiply when you are minimum number of pemcils distributed to each student= 4 href= https! These facts are building blocks for subtraction of two and a number _____ 12 operation to. ) from numbers within 20 69: p is divided by 11 and the.! Y z. subtract xyz from both the numerator and the denominator of,... Add 3 weeks to the left of the basic arithmetic operators ( +, *,.! It x above it to get ( 2-1 ) 1 Subtrahend: the result of one! Take 1 Away from 6 in the alphabet ( zero index based ) ii.
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