Question

1. to find the difference of $7 - 3\frac{5}{12}$, how do you rename the 7? 11. higher order thinking is it necessar rename $4\frac{1}{4}$ to subtract $\frac{3}{4}$? explain.

Explanation:

Question 10

Step1: Understand mixed number subtraction

When subtracting a mixed number from a whole number, we need to rewrite the whole number as a mixed number with the same denominator as the fraction part of the mixed number we are subtracting. The denominator here is 12.

Step2: Rename the whole number

We can write 7 as a mixed number. Since \( 7 = 6 + 1 \), and \( 1=\frac{12}{12} \), we can rename 7 as \( 6\frac{12}{12} \). This way, we have a fraction part with the same denominator (12) as the fraction \( 3\frac{5}{12} \), allowing us to subtract the mixed numbers.

To determine if we need to rename \( 4\frac{1}{4} \) to subtract \( \frac{3}{4} \), we look at the fraction parts. The fraction part of \( 4\frac{1}{4} \) is \( \frac{1}{4} \), and we are subtracting \( \frac{3}{4} \). Since \( \frac{1}{4}<\frac{3}{4} \), we can't subtract the fractions directly. So we need to rename \( 4\frac{1}{4} \). We take 1 from the whole number part (4) and add it to the fraction part. \( 1=\frac{4}{4} \), so \( 4\frac{1}{4}=3 + 1+\frac{1}{4}=3+\frac{4}{4}+\frac{1}{4}=3\frac{5}{4} \). Now we can subtract: \( 3\frac{5}{4}-\frac{3}{4}=3\frac{2}{4}=3\frac{1}{2} \). If we didn't rename, \( \frac{1}{4}-\frac{3}{4} \) would give a negative fraction, which is not how we typically perform subtraction of positive numbers in this context, so renaming is necessary.

Answer:

To rename 7 for \( 7 - 3\frac{5}{12} \), we write 7 as \( 6\frac{12}{12} \) (by expressing 7 as \( 6 + 1 \) and then writing 1 as \( \frac{12}{12} \), so \( 6+\frac{12}{12}=6\frac{12}{12} \)).

Question 11