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:

$\frac{1}{4},\frac{1}{2},\frac{3}{4}$

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 :

$\begin{gathered} 1)\frac{1}{4}=\frac{2\cdot1}{2\cdot4}=\frac{2}{8} \\ 2)\frac{1}{4}=\frac{3\cdot1}{3\cdot4}=\frac{3}{12} \end{gathered}$

The two fractions equivalent to 1/2:

$\begin{gathered} 1)\frac{1}{2}=\frac{2\cdot1}{2\cdot2}=\frac{2}{4} \\ 2)\frac{1}{2}=\frac{3\cdot1}{3\cdot2}=\frac{3}{6} \end{gathered}$

The two fractions equivalent to 3/4:

$\begin{gathered} 1)\frac{3}{4}=\frac{2\cdot3}{2\cdot4}=\frac{6}{8} \\ 2)\frac{3}{4}=\frac{3\cdot3}{3\cdot4}=\frac{9}{12} \end{gathered}$

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