Question

kiara has 6\frac{3}{8} inches of ribbon. she cuts off \frac{5}{8} inch. how much ribbon is left? write your answer as a mixed number.

Explanation:

Step1: Identify the operation

We need to subtract the length cut off from the original length. The original length is \( 6\frac{3}{8} \) inches and the length cut off is \( \frac{5}{8} \) inch. So the operation is \( 6\frac{3}{8}-\frac{5}{8} \).

Step2: Subtract the fractions

First, handle the fractional parts. The fractional part of the mixed number is \( \frac{3}{8} \), and we are subtracting \( \frac{5}{8} \). Since \( \frac{3}{8}<\frac{5}{8} \), we need to borrow 1 from the whole number part. \( 6\frac{3}{8} = 5 + 1+\frac{3}{8}=5+\frac{8}{8}+\frac{3}{8}=5\frac{11}{8} \).

Step3: Perform the subtraction

Now subtract the fractional parts: \( \frac{11}{8}-\frac{5}{8}=\frac{6}{8}=\frac{3}{4} \), and the whole number part remains 5. So the result is \( 5\frac{6}{8} \), which simplifies to \( 5\frac{3}{4} \) (by dividing numerator and denominator of the fraction by 2). Wait, no, wait. Wait, \( 6\frac{3}{8}-\frac{5}{8} \): let's do it again. \( 6\frac{3}{8} = \frac{6\times8 + 3}{8}=\frac{51}{8} \), and \( \frac{5}{8} \) is just \( \frac{5}{8} \). Then \( \frac{51}{8}-\frac{5}{8}=\frac{46}{8} \). Now convert \( \frac{46}{8} \) to a mixed number: \( 46\div8 = 5 \) with a remainder of 6, so \( \frac{46}{8}=5\frac{6}{8}=5\frac{3}{4} \)? Wait, no, \( 6\frac{3}{8}-\frac{5}{8} \): the whole number is 6, fraction is \( \frac{3}{8} \). Subtract \( \frac{5}{8} \) from \( \frac{3}{8} \), we can't do that, so we take 1 from 6, making it 5, and the fraction becomes \( \frac{3 + 8}{8}=\frac{11}{8} \). Then \( \frac{11}{8}-\frac{5}{8}=\frac{6}{8}=\frac{3}{4} \), and the whole number is 5, so \( 5\frac{6}{8} \) simplifies to \( 5\frac{3}{4} \)? Wait, no, \( \frac{6}{8} \) simplifies to \( \frac{3}{4} \), so \( 5\frac{6}{8}=5\frac{3}{4} \). Wait, but let's check: \( 5\frac{6}{8} \) is equal to \( 5\frac{3}{4} \) because \( 6\div2 = 3 \) and \( 8\div2 = 4 \). But wait, the original problem: Kiara has \( 6\frac{3}{8} \) inches, cuts off \( \frac{5}{8} \) inch. So \( 6\frac{3}{8}-\frac{5}{8} \). Let's compute the whole number and fraction separately. The whole number is 6, fraction is \( \frac{3}{8} \). Subtract \( \frac{5}{8} \) from \( \frac{3}{8} \), we get \( \frac{3 - 5}{8}=-\frac{2}{8} \), so we need to borrow 1 from the whole number, making the whole number 5, and the fraction becomes \( \frac{3 + 8}{8}=\frac{11}{8} \). Then \( \frac{11}{8}-\frac{5}{8}=\frac{6}{8}=\frac{3}{4} \), so the result is \( 5\frac{6}{8}=5\frac{3}{4} \)? Wait, no, \( 6\frac{3}{8}-\frac{5}{8}=5\frac{6}{8}=5\frac{3}{4} \). Wait, but let's check with improper fractions: \( 6\frac{3}{8}=\frac{51}{8} \), \( \frac{5}{8} \) is \( \frac{5}{8} \), \( \frac{51 - 5}{8}=\frac{46}{8}=5\frac{6}{8}=5\frac{3}{4} \). Yes, that's correct.

Wait, but maybe I made a mistake. Let's do it again. \( 6\frac{3}{8}-\frac{5}{8} \). The fractional parts: \( \frac{3}{8}-\frac{5}{8}=-\frac{2}{8} \). So we take 1 from the 6, so 6 becomes 5, and we add \( \frac{8}{8} \) to \( \frac{3}{8} \), getting \( \frac{11}{8} \). Then \( \frac{11}{8}-\frac{5}{8}=\frac{6}{8} \), so the whole number is 5, and the fraction is \( \frac{6}{8} \), which simplifies to \( \frac{3}{4} \). So the result is \( 5\frac{6}{8}=5\frac{3}{4} \). Wait, but \( 6\frac{3}{8}-\frac{5}{8}=5\frac{6}{8}=5\frac{3}{4} \). Yes, that's correct.

Answer:

\( 5\frac{6}{8} \) (or simplified \( 5\frac{3}{4} \)) Wait, no, the problem says to write as a mixed number. Wait, \( 6\frac{3}{8}-\frac{5}{8} \): let's do it step by step. Original length: \( 6\frac{3}{8} \) inches. Cut off: \( \frac{5}{8} \) inch. So subtract: \( 6\frac{3}{8}-\frac{5}{8} \). The fraction part: \( \frac{3}{8}-\frac{5}{8} \) is negative, so we borrow 1 from 6, making it 5, and the fraction becomes \( \frac{3 + 8}{8}=\frac{11}{8} \). Then \( \frac{11}{8}-\frac{5}{8}=\frac{6}{8} \), so the result is \( 5\frac{6}{8} \), which simplifies to \( 5\frac{3}{4} \). Wait, but \( 5\frac{6}{8} \) is also a mixed number, but we can simplify the fraction. So the answer is \( 5\frac{6}{8} \) (or \( 5\frac{3}{4} \)). But let's check the calculation again. \( 6\frac{3}{8} = \frac{51}{8} \), \( \frac{5}{8} \) is \( \frac{5}{8} \), \( \frac{51 - 5}{8}=\frac{46}{8} \). \( 46\div8 = 5 \) with a remainder of 6, so \( \frac{46}{8}=5\frac{6}{8}=5\frac{3}{4} \). So the correct answer is \( 5\frac{6}{8} \) (or simplified \( 5\frac{3}{4} \)). But the problem says "write your answer as a mixed number", so either is correct, but simplifying the fraction is better. So the answer is \( 5\frac{3}{4} \)? Wait, no, \( 5\frac{6}{8} \) simplifies to \( 5\frac{3}{4} \) because 6 and 8 are both divisible by 2. So the final answer is \( 5\frac{6}{8} \) (or \( 5\frac{3}{4} \)). But let's confirm with the subtraction: \( 6\frac{3}{8}-\frac{5}{8}=5\frac{6}{8}=5\frac{3}{4} \). Yes.