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Understanding Repeating Decimals and Linear Relationships in Math

This comprehensive math prep guide explores the difference between the decimal notations 1.8 and 1.08, illustrating the significance of repeating digits. It also includes a section on linear relationships represented in equations, based on the time-velocity relationship showcased in a table. Additionally, the guide presents various mixed number problems, including fractional targets hit in shooting events, perimeter calculations of triangles and rectangles, shared cake portions, work completion fractions, and distance traveled in running races. An engaging joke offers a light-hearted break, emphasizing the fun in learning math.

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Understanding Repeating Decimals and Linear Relationships in Math

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  1. Flashback 9-19-12 ACT Prep: What is the difference between 1.8 and 1.08 ? (Note: A bar indicates a digit pattern that is repeated.) A. 0.71 B. 0.71 C. 0.719 D. 0.72 E. 0.72 • Which of the following equations represents the linear relationship between time, t, and velocity, v, shown in the table below? F. v = 32t G. v = 32t + 120 H. v = 120t J. v = 120t + 32 K. v = 120t + 120

  2. Joke of the day What do organic mathematicians throw into their fireplaces?

  3. Natural Logs.

  4. Mixed Numbers and Word Problems • i) Three friends Christ, Marx and Davey participated in gun shooting events. Each of them was given 10 chances. They hit the targets 3 times, 2 times and 4 times respectively out of 10 chances each. Find the total targets hit by them in fraction. • ii) An side of an equilateral triangle is 3/11 feet. Find the perimeter of a triangle.

  5. iii) The length and width of a rectangle is 3/2 cm and 1/2 cm respectively. Find the perimeter of a rectangle. • iv) Sam celebrates his birthday with two small cakes. 7 people attended the birthday party. What fraction of cake each one will receive excluding Sam?

  6. v) Nick and Robert have worked together and completed 3/4 of work in a day. Robert has done 2/5 of work. Find the work done by Nick. • vi) Mr. Briar, principal of Edward Public School, collects funds for School development. 2/3 of funds are collected from school students and 1/6 of funds are collected from school development charity and the rest are collected from Public. What fraction of funds collected from public?

  7. vii) Anne has 1 pizza, Eris ton has 1 3/4 of pizza and Julie has 1/7 of pizza. Find the total number of pizzas.  viii) To make a milk shake, 2 gallons of milk, 1/7 of gallons of essence and 3/4 of gallons of fruit juice were required. Find the total gallons of milk shake made out of it.

  8. ix) Harris has to travel 2 2/3 of a mile. He walked 1 1/3 of the distance and the remaining by car. Find the distance covered by car.

  9. Exit Slip •  Kate and Tony took part in running race. They covered a distance of 5/8 yards and 8/9 yards respectively. Find the distance between these athletes. 

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