Question

homework: fractions as multiples of unit fractions

1. decompose \\(\frac{2}{12}\\) into unit fractions. then, describe \\(\frac{2}{12}\\) as a multiple of the unit fraction using the blanks to the right.

\\(\frac{2}{12}\\) is a multiple of \\(\frac{box}{box}\\)
because
\\(box \times \frac{box}{box} = \frac{2}{12}\\)

1. decompose \\(\frac{8}{8}\\) into unit fractions. then, describe \\(\frac{8}{8}\\) as a multiple of the unit fraction using the blanks to the right.

\\(\frac{box}{box}\\) is a multiple of \\(\frac{box}{box}\\)
because
\\(box \times \frac{box}{box} = \frac{box}{box}\\)

1. decompose \\(\frac{5}{5}\\) into unit fractions. then, describe \\(\frac{5}{5}\\) as a multiple of the unit fraction using the blanks to the right.

\\(\frac{box}{box}\\) is a multiple of \\(\frac{box}{box}\\)
because
\\(box \times \frac{box}{box} = \frac{box}{box}\\)

Explanation:

Problem 1: Decompose $\boldsymbol{\frac{2}{12}}$ into Unit Fractions and Describe as a Multiple

Step 1: Recall Unit Fraction Definition

A unit fraction has a numerator of 1. For $\frac{2}{12}$, the unit fraction with the same denominator is $\frac{1}{12}$.

Step 2: Determine the Multiple

To find how many times $\frac{1}{12}$ fits into $\frac{2}{12}$, we solve $n \times \frac{1}{12} = \frac{2}{12}$. Here, $n = 2$ because $2 \times \frac{1}{12} = \frac{2}{12}$.

Step 1: Identify the Unit Fraction

The unit fraction with denominator 8 is $\frac{1}{8}$.

Step 2: Find the Multiplier

We need $n$ such that $n \times \frac{1}{8} = \frac{6}{8}$. Solving for $n$, we get $n = 6$ (since $6 \times \frac{1}{8} = \frac{6}{8}$).

Step 1: Determine the Unit Fraction

The unit fraction with denominator 5 is $\frac{1}{5}$.

Step 2: Calculate the Multiplier

We find $n$ where $n \times \frac{1}{5} = \frac{5}{5}$. Simplifying $\frac{5}{5} = 1$, and $n \times \frac{1}{5} = 1$ implies $n = 5$ (since $5 \times \frac{1}{5} = 1 = \frac{5}{5}$).

Answer:

$\frac{2}{12}$ is a multiple of $\frac{1}{12}$ because $2 \times \frac{1}{12} = \frac{2}{12}$. The blanks are filled as: $\frac{2}{12}$ is a multiple of $\frac{\boldsymbol{1}}{\boldsymbol{12}}$ because $\boldsymbol{2} \times \frac{\boldsymbol{1}}{\boldsymbol{12}} = \frac{\boldsymbol{2}}{\boldsymbol{12}}$.

Problem 2: Decompose $\boldsymbol{\frac{6}{8}}$ into Unit Fractions and Describe as a Multiple