$17 \frac{6}{7}-\frac{4}{6}$
Answer (2)
Convert the mixed number to an improper fraction: 17 7 6 = 7 125 .
Find a common denominator: 7 125 = 42 750 and 6 4 = 42 28 .
Subtract the fractions: 42 750 − 42 28 = 42 722 .
Simplify and convert to a mixed number: 42 722 = 21 361 = 17 21 4 .
Explanation
Problem Analysis We are asked to subtract 6 4 from the mixed number 17 7 6 . To do this, we first convert the mixed number to an improper fraction. Then, we find a common denominator for the two fractions and perform the subtraction. Finally, we simplify the result and convert it back to a mixed number.
Convert Mixed Number to Improper Fraction First, convert the mixed number 17 7 6 to an improper fraction. To do this, we multiply the whole number part (17) by the denominator (7) and add the numerator (6). This gives us the numerator of the improper fraction, and the denominator remains the same. So, we have: 17 7 6 = 7 17 × 7 + 6 = 7 119 + 6 = 7 125
Find Common Denominator Next, we need to subtract 6 4 from 7 125 . To do this, we need to find a common denominator for the two fractions. The least common multiple of 7 and 6 is 42. So, we will rewrite both fractions with a denominator of 42. 7 125 = 7 × 6 125 × 6 = 42 750 6 4 = 6 × 7 4 × 7 = 42 28
Subtract Fractions Now we can subtract the two fractions: 42 750 − 42 28 = 42 750 − 28 = 42 722
Simplify Fraction Now, we simplify the fraction 42 722 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 42 722 = 42 ÷ 2 722 ÷ 2 = 21 361
Convert to Mixed Number Finally, we convert the improper fraction 21 361 back to a mixed number. To do this, we divide 361 by 21. The quotient is the whole number part of the mixed number, and the remainder is the numerator of the fractional part. The denominator remains the same. 361 ÷ 21 = 17 with a remainder of 4 So, we have: 21 361 = 17 21 4
Final Answer Therefore, 17 7 6 − 6 4 = 17 21 4 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 17 7 6 cups of flour and you only want to make a portion that requires subtracting 6 4 cups, you need to perform the subtraction we just did. This ensures you get the correct amount of flour for your recipe, maintaining the right proportions and taste.
To solve 17 7 6 − 6 4 , first convert the mixed number to an improper fraction, find a common denominator, subtract the fractions, simplify, and convert back to a mixed number. The final answer is 17 21 4 .
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