Question

subtract. simplify, if possible.
$4\frac{2}{7} - 1\frac{9}{14}$
? $\frac{\\ }{\\ }$
enter the whole number.

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{2}{7}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(4\frac{2}{7}\), we have \(a = 4\), \(b = 2\), \(c = 7\). Then \(4\frac{2}{7}=\frac{4\times7 + 2}{7}=\frac{28 + 2}{7}=\frac{30}{7}\).

Next, convert \(1\frac{9}{14}\) to an improper fraction. Here, \(a = 1\), \(b = 9\), \(c = 14\). So \(1\frac{9}{14}=\frac{1\times14+9}{14}=\frac{14 + 9}{14}=\frac{23}{14}\).

Step2: Find a common denominator

The denominators are 7 and 14. The least common denominator of 7 and 14 is 14. So we need to convert \(\frac{30}{7}\) to a fraction with denominator 14. Multiply the numerator and denominator of \(\frac{30}{7}\) by 2: \(\frac{30\times2}{7\times2}=\frac{60}{14}\).

Step3: Subtract the fractions

Now we have \(\frac{60}{14}-\frac{23}{14}\). When subtracting fractions with the same denominator, we subtract the numerators: \(\frac{60 - 23}{14}=\frac{37}{14}\).

Step4: Convert back to a mixed number

Now convert \(\frac{37}{14}\) back to a mixed number. Divide 37 by 14: \(14\times2 = 28\), \(37-28 = 9\). So \(\frac{37}{14}=2\frac{9}{14}\)? Wait, no, wait. Wait, original mixed numbers: \(4\frac{2}{7}-1\frac{9}{14}\). Wait, maybe I made a mistake in step 1. Wait, \(4\frac{2}{7}\) is \(4 + \frac{2}{7}\), and \(1\frac{9}{14}\) is \(1+\frac{9}{14}\). Maybe another approach: subtract the whole numbers and the fractions separately, but we need a common denominator for the fractions.

Let's try again. \(4\frac{2}{7}=4+\frac{2}{7}\), \(1\frac{9}{14}=1+\frac{9}{14}\). So \(4\frac{2}{7}-1\frac{9}{14}=(4 - 1)+(\frac{2}{7}-\frac{9}{14})\). Now, \(4 - 1 = 3\). Now, \(\frac{2}{7}-\frac{9}{14}\). Convert \(\frac{2}{7}\) to \(\frac{4}{14}\), so \(\frac{4}{14}-\frac{9}{14}=\frac{4 - 9}{14}=\frac{-5}{14}\). Oh, so we have a negative fraction, which means we need to borrow 1 from the whole number 3. So 3 becomes 2, and we add \(\frac{14}{14}\) to \(\frac{-5}{14}\): \(2+(\frac{14}{14}+\frac{-5}{14})=2+\frac{9}{14}=2\frac{9}{14}\)? Wait, no, that can't be. Wait, original problem: \(4\frac{2}{7}-1\frac{9}{14}\). Let's do it correctly.

Wait, \(4\frac{2}{7}=\frac{4\times7 + 2}{7}=\frac{30}{7}=\frac{60}{14}\), \(1\frac{9}{14}=\frac{23}{14}\). Then \(\frac{60}{14}-\frac{23}{14}=\frac{37}{14}\). Now, \(\frac{37}{14}\) as a mixed number: 142=28, 37-28=9, so \(2\frac{9}{14}\)? Wait, but 4 - 1 is 3, but the fraction part gave a negative, so we have to borrow. So 4 becomes 3, and \(\frac{2}{7}\) becomes \(\frac{2}{7}+\frac{14}{14}=\frac{4}{14}+\frac{14}{14}=\frac{18}{14}\)? Wait, no, borrowing 1 from the whole number (which is 4) means 4 becomes 3, and we add \(\frac{14}{14}\) to the fraction \(\frac{2}{7}\). So \(\frac{2}{7}=\frac{4}{14}\), so \(\frac{4}{14}+\frac{14}{14}=\frac{18}{14}\). Then subtract the fraction: \(\frac{18}{14}-\frac{9}{14}=\frac{9}{14}\). Then subtract the whole numbers: 3 - 1 = 2. So total is \(2\frac{9}{14}\)? Wait, but \(\frac{37}{14}=2\frac{9}{14}\) (since 142=28, 37-28=9). So the whole number is 2, and the fraction is \(\frac{9}{14}\). Wait, but let's check the calculation again.

Wait, \(4\frac{2}{7}\) is 4.2857..., \(1\frac{9}{14}\) is 1.6428..., subtracting them: 4.2857 - 1.6428 = 2.6428..., which is \(2\frac{9}{14}\) (since 9/14≈0.6428). So the whole number is 2, and the fraction is 9/14.

Answer:

2\(\frac{9}{14}\) (so the whole number is 2, and the fraction is \(\frac{9}{14}\))