Question

frankie’s fractions & decimals page 2 of 2
6
frankie wrote this equation on her paper during math class: ( 1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} )
a is frankie’s equation true?

b write three more equations for ( 1 \frac{2}{3} ) that are all true and all different. any fractions you use must have a denominator of 3. include at least one multiplication equation.
( 1 \frac{2}{3} = )
( 1 \frac{2}{3} = )
( 1 \frac{2}{3} = )
7
frankie and lori have two different - sized grids. their teacher said, “no matter the size of your grid, it has a value of 1. please shade in exactly ( \frac{1}{4} ) of your grid.”
a here are the grids frankie and lori have. shade in exactly ( \frac{1}{4} ) of each grid.

Explanation:

Step1: Analyze the target value

We need to write equations equal to \(1\frac{2}{3}\) (which is \(\frac{5}{3}\)) with different fractions, at least one multiplication, and denominators of 3.

Step2: Equation 1 (Addition)

Let's use addition. We know \(1\frac{2}{3}=\frac{3}{3}+\frac{2}{3}\), and \(\frac{3}{3} = 1\), so \(1+\frac{2}{3}=1\frac{2}{3}\).

Step3: Equation 2 (Another Addition)

We can split the whole number part differently. \( \frac{4}{3}+\frac{1}{3}=\frac{5}{3}=1\frac{2}{3}\) (since \(\frac{4}{3}=1\frac{1}{3}\) and \(1\frac{1}{3}+\frac{1}{3}=1\frac{2}{3}\)).

Step4: Equation 3 (Multiplication + Addition)

For a multiplication equation, let's use \(2\times\frac{2}{3}+\frac{1}{3}\). Calculate \(2\times\frac{2}{3}=\frac{4}{3}\), then \(\frac{4}{3}+\frac{1}{3}=\frac{5}{3}=1\frac{2}{3}\).

Answer:

1. \(1+\frac{2}{3}=1\frac{2}{3}\)
2. \(\frac{4}{3}+\frac{1}{3}=1\frac{2}{3}\)
3. \(2\times\frac{2}{3}+\frac{1}{3}=1\frac{2}{3}\)