Express the following rational number as the sum of an integer and a rational number: (1) 17/5
The Correct Answer and Explanation is:
To express the rational number 175\frac{17}{5}517 as the sum of an integer and a rational number, we begin by performing division.
Step 1: Divide 17 by 5
We ask: How many times does 5 go into 17?
5×3=155 \times 3 = 155×3=15
So, 5 goes into 17 three times, with a remainder of 2.
Thus,175=3+25\frac{17}{5} = 3 + \frac{2}{5}517=3+52
Final Answer:
175=3+25\frac{17}{5} = 3 + \frac{2}{5}517=3+52
Explanation:
Any rational number written in the form of a fraction ab\frac{a}{b}ba, where aaa and bbb are integers and b≠0b \neq 0b=0, can also be written as a mixed number or as the sum of a whole number and a proper fraction. This method makes it easier to interpret the value and location of the number on the number line.
In the case of 175\frac{17}{5}517, we are dividing 17 into groups of 5. Since 5 fits into 17 three full times (because 5×3=155 \times 3 = 155×3=15), we take the result 3 as the integer part. After accounting for those 15 units, we are left with 17−15=217 – 15 = 217−15=2 units. This remainder 2 is then written as a fraction of the original denominator: 25\frac{2}{5}52. So the complete expression becomes:175=3+25\frac{17}{5} = 3 + \frac{2}{5}517=3+52
This method is often used in real-world contexts where it’s easier to understand or compare quantities in terms of whole units and leftover parts. For example, if a recipe calls for 175\frac{17}{5}517 cups of flour, it might be clearer to measure out 3 full cups and then an additional 25\frac{2}{5}52 cup.
Thus, expressing 175\frac{17}{5}517 as 3+253 + \frac{2}{5}3+52 helps to visualize and work with the number more effectively.
