This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back Phatsimo — missed you this week. Here are the solutions to your questions: 1. Express the following decimals as proper fractions. Give your answers in lowest terms. a) 0.41 Step 1: Write the decimal as a fraction with a denominator of 100 (since there are two decimal places). 0.41 = (41)/(100) Step 2: Simplify the fraction. Since 41 is a prime number and 100 is not divisible by 41, the fraction is already in its lowest terms. (41)/(100) b) 0.6 Step 1: Write the decimal as a fraction with a denominator of 10 (since there is one decimal place). 0.6 = (6)/(10) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. (6 ÷ 2)/(10 ÷ 2) = (3)/(5) (3)/(5) c) 0.36 Step 1: Write the decimal as a fraction with a denominator of 100. 0.36 = (36)/(100) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. (36 ÷ 4)/(100 ÷ 4) = (9)/(25) (9)/(25) d) 0.72 Step 1: Write the decimal as a fraction with a denominator of 100. 0.72 = (72)/(100) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. (72 ÷ 4)/(100 ÷ 4) = (18)/(25) (18)/(25) e) 0.125 Step 1: Write the decimal as a fraction with a denominator of 1000 (since there are three decimal places). 0.125 = (125)/(1000) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 125. (125 ÷ 125)/(1000 ÷ 125) = (1)/(8) (1)/(8) 2. Convert the following to improper fractions. a) 8.4 Step 1: Express the decimal as a mixed number. 8.4 = 8 (4)/(10) Step 2: Simplify the fractional part. 8 (4 ÷ 2)/(10 ÷ 2) = 8 (2)/(5) Step 3: Convert the mixed number to an improper fraction. Multiply the whole number by the denominator and add the numerator. ((8 × 5) + 2)/(5) = (40 + 2)/(5) = (42)/(5) (42)/(5) b) 2.64 Step 1: Express the decimal as a mixed number. 2.64 = 2 (64)/(100) Step 2: Simplify the fractional part. 2 (64 ÷ 4)/(100 ÷ 4) = 2 (16)/(25) Step 3: Convert the mixed number to an improper fraction. ((2 × 25) + 16)/(25) = (50 + 16)/(25) = (66)/(25) (66)/(25) c) 7.24 Step 1: Express the decimal as a mixed number. 7.24 = 7 (24)/(100) Step 2: Simplify the fractional part. 7 (24 ÷ 4)/(100 ÷ 4) = 7 (6)/(25) Step 3: Convert the mixed number to an improper fraction. ((7 × 25) + 6)/(25) = (175 + 6)/(25) = (181)/(25) (181)/(25) d) 6.25 Step 1: Express the decimal as a mixed number. 6.25 = 6 (25)/(100) Step 2: Simplify the fractional part. 6 (25 ÷ 25)/(100 ÷ 25) = 6 (1)/(4) Step 3: Convert the mixed number to an improper fraction. ((6 × 4) + 1)/(4) = (24 + 1)/(4) = (25)/(4) (25)/(4) e) 3.125 Step 1: Express the decimal as a mixed number. 3.125 = 3 (125)/(1000) Step 2: Simplify the fractional part. 3 (125 ÷ 125)/(1000 ÷ 125) = 3 (1)/(8) Step 3: Convert the mixed number to an improper fraction. ((3 × 8) + 1)/(8) = (24 + 1)/(8) = (25)/(8) (25)/(8) 3. Express the following decimals as mixed numbers. a) 3.248 Step 1: Separate the whole number and the decimal part. 3.248 = 3 + 0.248 Step 2: Convert the decimal part to a fraction. 0.248 = (248)/(1000) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 8. (248 ÷ 8)/(1000 ÷ 8) = (31)/(125) Step 4: Combine the whole number and the simplified fraction to form a mixed number. 3 (31)/(125) b) 6.45 Step 1: Separate the whole number and the decimal part. 6.45 = 6 + 0.45 Step 2: Convert the decimal part to a fraction. 0.45 = (45)/(100) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (45 ÷ 5)/(100 ÷ 5) = (9)/(20) Step 4: Combine the whole number and the simplified fraction. 6 (9)/(20) c) 9.05 Step 1: Separate the whole number and the decimal part. 9.05 = 9 + 0.05 Step 2: Convert the decimal part to a fraction. 0.05 = (5)/(100) Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5. (5 ÷ 5)/(100 ÷ 5) = (1)/(20) Step 4: Combine the whole number and the simplified fraction. 9 (1)/(20) d) $