Question

1. leslie will use more than \\(\frac{1}{2}\\) cup but than 1 whole cup of flour for a reci what fraction of a cup might leslie use? explain. 3. jared has mowed \\(\frac{2}{5}\\) of the yard. a says that jared has mowed \\(\frac{4}{6}\\) of th is abby correct? explain. explain how to use division to equivalent fraction for \\(\frac{9}{12}\\).

Explanation:

Question 2

Step1: Understand the range

Leslie uses more than $\frac{1}{2}$ cup but less than 1 whole cup. So we need a fraction $x$ such that $\frac{1}{2}

Step2: Choose a fraction

Let's take $\frac{3}{4}$ as an example. First, convert $\frac{1}{2}$ to fourths: $\frac{1}{2}=\frac{2}{4}$. And $1 = \frac{4}{4}$. Now, $\frac{2}{4}<\frac{3}{4}<\frac{4}{4}$, so $\frac{3}{4}$ is a valid fraction. Another example could be $\frac{2}{3}$. Convert $\frac{1}{2}$ to sixths: $\frac{1}{2}=\frac{3}{6}$, and $1=\frac{6}{6}$. $\frac{3}{6}<\frac{4}{6}=\frac{2}{3}<\frac{6}{6}$, so $\frac{2}{3}$ also works. The key is that the numerator is greater than half of the denominator (for the lower bound) and less than the denominator (for the upper bound, since it's less than 1).

Step1: Simplify the fractions

First, simplify $\frac{4}{6}$. The greatest common divisor (GCD) of 4 and 6 is 2. So $\frac{4\div2}{6\div2}=\frac{2}{3}$.

Step2: Compare the fractions

Jared mowed $\frac{2}{5}$ of the yard, and Abby claims he mowed $\frac{4}{6}=\frac{2}{3}$. Now, compare $\frac{2}{5}$ and $\frac{2}{3}$. To compare fractions with the same numerator, the one with the smaller denominator is larger. Since $5 > 3$, $\frac{2}{5}<\frac{2}{3}$. So $\frac{2}{5}
eq\frac{2}{3}$, which means $\frac{2}{5}
eq\frac{4}{6}$.

Step1: Recall equivalent fractions

To find an equivalent fraction using division, we divide both the numerator and the denominator by their GCD.

Step2: Find GCD of 9 and 12

The factors of 9 are 1, 3, 9. The factors of 12 are 1, 2, 3, 4, 6, 12. The GCD of 9 and 12 is 3.

Step3: Divide numerator and denominator

Divide the numerator 9 by 3: $9\div3 = 3$. Divide the denominator 12 by 3: $12\div3 = 4$. So $\frac{9\div3}{12\div3}=\frac{3}{4}$. This shows how to use division (dividing numerator and denominator by their GCD) to find an equivalent fraction.

Answer:

A possible fraction is $\frac{3}{4}$ (or $\frac{2}{3}$, $\frac{5}{8}$, etc.). Explanation: For $\frac{3}{4}$, $\frac{1}{2}=\frac{2}{4}$ and $1 = \frac{4}{4}$, and $\frac{2}{4}<\frac{3}{4}<\frac{4}{4}$, so it's more than $\frac{1}{2}$ and less than 1.

Question 3