Question

For each question, write a divisionexpression and then find the answer.a. How many 1/4-inch segmentsare in a length of 3 1/2 inches?b. How many 1/4-inch segmentsare in a length of 2 1/4 inches?

Answer 1

a) 14 segments

b) 9 segements

Step-by-step explanation

a)How many 1/4-inch segments are in a length of 3 1/2 inches

Step 1

convert the mixed numbers in fractions

`\begin{gathered} (1)/(4)=(1)/(4) \\ 3\text{ }(1)/(2)=((3\cdot2)+1)/(7)=(7)/(2) \end{gathered}`

Now, to find how many 1/4 inch segments are in 7/2 of inches use a division

`\begin{gathered} Number\text{ of segments=}(7)/(2)divided\text{ by }(1)/(4) \\ N=(7)/(2)\colon(1)/(4)=(7\cdot4)/(2\cdot1)=(28)/(2)=14 \end{gathered}`

b) How many 1/4-inch segmentsare in a length of 2 1/4 inches?​

Step 1

convert the mixed numbers in fractions

`2\text{ }(1)/(4)=((2\cdot4)+1)/(4)=(9)/(4)`

Now, to find how many 1/4 inch segments are in 9/4 of inches use a division

`\begin{gathered} \text{Number of segments}_2=(9)/(4)\colon(1)/(4) \\ N_b=(9\cdot4)/(4\cdot1)=(36)/(4)=9 \end{gathered}`

i hope this helps you