7 copies of the sum of 8 fifths and 4
The correct answer and explanation is:
Let’s break down the problem step-by-step:
Problem:
“7 copies of the sum of 8 fifths and 4”
Step 1: Understand the phrase
- “8 fifths” means the fraction 85\frac{8}{5}.
- “Sum of 8 fifths and 4” means 85+4\frac{8}{5} + 4.
- “7 copies of” means multiply the sum by 7.
So, mathematically, the expression is:
7×(85+4)7 \times \left(\frac{8}{5} + 4\right)
Step 2: Calculate the sum inside the parentheses
Convert the whole number 4 to a fraction with denominator 5 to add easily:
4=4×55=2054 = \frac{4 \times 5}{5} = \frac{20}{5}
Now add: 85+205=8+205=285\frac{8}{5} + \frac{20}{5} = \frac{8 + 20}{5} = \frac{28}{5}
Step 3: Multiply by 7
Multiply 285\frac{28}{5} by 7: 7×285=7×285=19657 \times \frac{28}{5} = \frac{7 \times 28}{5} = \frac{196}{5}
Step 4: Simplify or convert to mixed number
Divide 196 by 5: 196÷5=39 remainder 1196 \div 5 = 39 \text{ remainder } 1
So, 1965=3915\frac{196}{5} = 39 \frac{1}{5}
Final answer:
7×(85+4)=1965=39157 \times \left(\frac{8}{5} + 4\right) = \frac{196}{5} = 39 \frac{1}{5}
Explanation (300 words):
This problem involves basic operations with fractions and whole numbers. First, it’s important to understand the phrase “7 copies of the sum of 8 fifths and 4.” “Copies” means multiplication. So, 7 copies mean multiplying by 7. The “sum of 8 fifths and 4” means adding the fraction 85\frac{8}{5} to the whole number 4.
Because fractions and whole numbers must have a common form to be added, the whole number 4 can be expressed as 205\frac{20}{5} (since 4=2054 = \frac{20}{5}). This allows for straightforward addition of fractions with a common denominator: 85+205=285\frac{8}{5} + \frac{20}{5} = \frac{28}{5}
Next, multiplying the sum 285\frac{28}{5} by 7 involves multiplying the numerator by 7 while keeping the denominator the same: 7×285=19657 \times \frac{28}{5} = \frac{196}{5}
Finally, this improper fraction 1965\frac{196}{5} can be converted to a mixed number by dividing the numerator by the denominator: 196÷5=39 remainder 1196 \div 5 = 39 \text{ remainder } 1
So, the mixed number is 391539 \frac{1}{5}. This mixed number shows that seven copies of the sum equal thirty-nine wholes and one-fifth more.
In conclusion, the answer is 1965\frac{196}{5} or 391539 \frac{1}{5}. Understanding how to convert between whole numbers and fractions and knowing basic fraction addition and multiplication are key to solving this type of problem.