Question 1 To calculate: The solution of the equation 0.36 𝑢 + 2.55 = 0.41 𝑢 + 6.8 0.36u+2.55=0.41u+6.8 by clearing the decimals. Answer 1 Step 1 The equation is 0.36 𝑢 + 2.55 = 0.41 𝑢 + 6.8 0.36u+2.55=0.41u+6.8 Consider the equation, 0.36 𝑢 + 2.55 = 0.41 𝑢 + 6.8 0.36u+2.55=0.41u+6.8 In order to find the solution, follow the steps given below: Find the least common denominator of all the fractions. Multiply both sides of the equation by the least common denominator. Use the Distributive Property, which states that for any real numbers 𝑎 a, 𝑏 b, and 𝑐 c: 4 ( 𝑏 + 𝑐 ) = 𝑎 𝑏 + 𝑎 𝑐 4(b+c)=ab+ac Then simplify. Step 2 The equation can be written as, 36 100 𝑢 + 255 100 = 41 100 𝑢 + 680 100 100 36 u+ 100 255 = 100 41 u+ 100 680 The least common denominator is 100. So, 100 ( 0.36 𝑢 + 2.55 ) = 100 ( 0.41 𝑢 + 6.8 ) 100(0.36u+2.55)=100(0.41u+6.8) 36 𝑢 + 255 = 41 𝑢 + 680 36u+255=41u+680 36 𝑢 + 255 − 41 𝑢 = 41 𝑢 + 680 − 41 𝑢 − 255 36u+255−41u=41u+680−41u−255 − 5 𝑢 = 425 −5u=425 Solve further to get, 𝑢 = 425 − 5 u= −5 425 𝑢 = − 85 u=−85 Hence, 𝑢 = − 85 u=−85 is the solution of 0.36 𝑢 + 2.55 = 0.41 𝑢 + 6.8 0.36u+2.55=0.41u+6.8 Question 2 Express the given percent as a decimal. 37% Answer 1 37 % = ( 37 100 ) = ( 37 100 ) 37%=( 100 37 )=( 100 37 ) (We have two zeros in the denominator 100, so we put the decimal point after 2 digits of the number in the numerator from the right side.) Thus, 37 % = 0.37 37%=0.37 Question 3 Write the decimals in words. Write the money amounts in words for dollars and fractions for cents. Write the words in decimals. 0.4 Answer 1 According to the names that apply to digits of decimal numbers we have: 0.4 = Four tenths Question 4 Compare the decimals. 8.86 ... 8.65 Answer 1 We start by comparing the ones: 8 = 8 8=8 Next, we compare the tenths: 8 > 6 8>6 We conclude that 8.86 > 8.65 8.86>8.65. Question 5 Find three decimals that make the number sentence true. − 0.01 ≤ _ _ _ ≤ 0.01 −0.01≤___ ≤0.01 Answer 1 − 0.01 ≤ _ _ _ −0.01≤___ So we need to put the right number to make the sentence true. In this case, we just need to put numbers that are the same or bigger than − 0.01 −0.01. So the correct answer can be: − 0.01 , 0 , 0.01 −0.01,0,0.01.