Question

1. in her science class, monica watched an insect crawl 6 1/2 inches in one minute. the next minute the insect crawled 3 2/3 inches. how far did the insect crawl in total? 3. what is the missing number that makes the fractions equal? 3/12 = 9/x

Explanation:

Step1: Simplify the given fraction

Simplify $\frac{3}{12}$ to $\frac{1}{4}$ by dividing both numerator and denominator by 3.

Step2: Find the equivalent fraction

We want $\frac{3}{12}=\frac{z}{9}$. Since $\frac{3}{12}=\frac{1}{4}$, we set up the proportion $\frac{1}{4}=\frac{z}{9}$. Cross - multiply: $4z = 9\times1$.

Step3: Solve for z

$z=\frac{9}{4}= 2.25$

Step4: Solve the second problem (insect crawling)

The insect crawled $6\frac{1}{2}$ inches in one minute and $3\frac{2}{3}$ inches in the next minute. First, convert the mixed numbers to improper fractions. $6\frac{1}{2}=\frac{13}{2}$ and $3\frac{2}{3}=\frac{11}{3}$.

Step5: Find a common denominator

The common denominator of 2 and 3 is 6. $\frac{13}{2}=\frac{13\times3}{2\times3}=\frac{39}{6}$ and $\frac{11}{3}=\frac{11\times2}{3\times2}=\frac{22}{6}$.

Step6: Add the fractions

$\frac{39}{6}+\frac{22}{6}=\frac{39 + 22}{6}=\frac{61}{6}=10\frac{1}{6}$ inches.

Answer:

For the first problem, $z = 2.25$. For the second problem, the insect crawled $10\frac{1}{6}$ inches in total.