Understand the problem: Understand the problem. We need to subtract the fraction 4(1)/(4) from the fraction 6(6)/(7).Convert to improper fractions: Convert the mixed numbers to improper fractions. 6(6)/(7) can be converted to an improper fraction by multiplying the whole number 6 by the denominator 7 and adding the numerator 6, then placing the result over the original denominator. 6(6)/(7) = (6*7 + 6)/7 = (42 + 6)/7 = 48/7 Similarly, for 4(1)/(4), multiply the whole number 4 by the denominator 4 and add the numerator 1, then place the result over the original denominator. 4(1)/(4) = (4*4 + 1)/4 = (16 + 1)/4 = 17/4Find common denominator: Subtract the second fraction from the first. Now we have two improper fractions: 48/7 and 17/4. To subtract them, we need a common denominator. The least common multiple (LCM) of 7 and 4 is 28.Convert to common denominator: Convert both fractions to have the common denominator of 28. For 48/7, we multiply both the numerator and the denominator by 4 to get the equivalent fraction with a denominator of 28. 48/7 * (4/4) = (48*4)/(7*4) = 192/28 For 17/4, we multiply both the numerator and the denominator by 7 to get the equivalent fraction with a denominator of 28. 17/4 * (7/7) = (17*7)/(4*7) = 119/28Subtract with common denominator: Subtract the fractions with the common denominator. Now we subtract 119/28 from 192/28. 192/28 - 119/28 = (192 - 119)/28 = 73/28Simplify result: Simplify the result, if possible. 73/28 cannot be simplified further as 73 is a prime number and does not share any common factors with 28.

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$6 \frac{6}{7}-4 \frac{1}{4}=$

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Algebra 1

Multiplication with rational exponents

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6 \frac{6}{7}-4 \frac{1}{4}=

Understand the problem: Understand the problem. $\newline$ We need to subtract the fraction $4\frac{1}{4}$ from the fraction $6\frac{6}{7}$ .
Convert to improper fractions: Convert the mixed numbers to improper fractions. $\newline$ $6\frac{6}{7}$ can be converted to an improper fraction by multiplying the whole number $6$ by the denominator $7$ and adding the numerator $6$ , then placing the result over the original denominator. $\newline$ $6\frac{6}{7} = \frac{6\times7 + 6}{7} = \frac{42 + 6}{7} = \frac{48}{7}$ $\newline$ Similarly, for $4\frac{1}{4}$ , multiply the whole number $4$ by the denominator $4$ and add the numerator $1$ , then place the result over the original denominator. $\newline$ $4\frac{1}{4} = \frac{4\times4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4}$
Find common denominator: Subtract the second fraction from the first. $\newline$ Now we have two improper fractions: $\frac{48}{7}$ and $\frac{17}{4}$ . To subtract them, we need a common denominator. The least common multiple (LCM) of $7$ and $4$ is $28$ .
Convert to common denominator: Convert both fractions to have the common denominator of $28$ . For $\frac{48}{7}$ , we multiply both the numerator and the denominator by $4$ to get the equivalent fraction with a denominator of $28$ . $\frac{48}{7} \times \frac{4}{4} = \frac{48\times4}{7\times4} = \frac{192}{28}$ For $\frac{17}{4}$ , we multiply both the numerator and the denominator by $7$ to get the equivalent fraction with a denominator of $28$ . $\frac{17}{4} \times \frac{7}{7} = \frac{17\times7}{4\times7} = \frac{119}{28}$
Subtract with common denominator: Subtract the fractions with the common denominator. $\newline$ Now we subtract $\frac{119}{28}$ from $\frac{192}{28}$ . $\newline$ $\frac{192}{28} - \frac{119}{28} = \frac{192 - 119}{28} = \frac{73}{28}$
Simplify result: Simplify the result, if possible. $\frac{73}{28}$ cannot be simplified further as $73$ is a prime number and does not share any common factors with $28$ .