Question

Using the benchmark fractions 1/4, 1/2, and 3/4 model these on number lines, model two fractions that are equivalent using additional number lines. Create a story problem to go with your equivalent fractions.

Answer 1

Given the fractions:

`(1)/(4),(1)/(2),(3)/(4)`

The fraction on the numbers lines will be as shown in the following picture:

We will write two fractions equivalent to each given fraction:

The two fractions equivalent to 1/4 :

`\begin{gathered} 1)(1)/(4)=(2\cdot1)/(2\cdot4)=(2)/(8) \\ 2)(1)/(4)=(3\cdot1)/(3\cdot4)=(3)/(12) \end{gathered}`

The two fractions equivalent to 1/2:

`\begin{gathered} 1)(1)/(2)=(2\cdot1)/(2\cdot2)=(2)/(4) \\ 2)(1)/(2)=(3\cdot1)/(3\cdot2)=(3)/(6) \end{gathered}`

The two fractions equivalent to 3/4:

`\begin{gathered} 1)(3)/(4)=(2\cdot3)/(2\cdot4)=(6)/(8) \\ 2)(3)/(4)=(3\cdot3)/(3\cdot4)=(9)/(12) \end{gathered}`

A story problem to go with your equivalent fractions.​

A student has 6 cards of fractions

2/8, 3/6, 3/12, 6/8, 3/12, 9/12, 2/4

And want to make 3 boards, each board contains the equivalent fractions, what are the fractions of each board?

The answer will be:

The student will make three boards:

Board (1): will contain the fractions equivalent to 1/4 which are 2/8 and 3/12

Board (2): will contain the fractions equivalent to 1/2 which are 2/4 and 3/6

Board (3): will contain the fractions equivalent to 3/4 which are 6/8 and 9/12