4.1 Visualize Fractions

Before you get started, take this readiness quiz.

Simplify: $5 \cdot 2 + 1 .$
If you missed this problem, review the reference.

Fill in the blank with $<$ or $>: −2 \underset{__}{ } −5$
If you missed this problem, review the reference.

Convert the improper fraction to a mixed number: $\frac{13}{7} .$

Convert the improper fraction to a mixed number: $\frac{14}{9} .$

Convert the improper fraction to a mixed number: $\frac{23}{7} .$

Convert the improper fraction to a mixed number: $\frac{48}{11} .$

Convert the mixed number to an improper fraction: $3 \frac{5}{7} .$

Convert the mixed number to an improper fraction: $2 \frac{7}{8} .$

Convert the mixed number to an improper fraction: $4 \frac{6}{11} .$

Convert the mixed number to an improper fraction: $11 \frac{1}{3} .$

Use fraction tiles to find equivalent fractions: How many eighths equal one-fourth?

Use fraction tiles to find equivalent fractions: How many twelfths equal one-fourth?

Find three fractions equivalent to $\frac{3}{5} .$

Find three fractions equivalent to $\frac{4}{5} .$

Find a fraction with a denominator of $21$ that is equivalent to $\frac{6}{7} .$

Find a fraction with a denominator of $100$ that is equivalent to $\frac{3}{10} .$

Order each of the following pairs of numbers, using $<$ or $>:$

1. ⓐ $- \frac{1}{3} \underset{__}{ } - 1$
2. ⓑ $−1 \frac{1}{2} \underset{__}{ } - 2$
3. ⓒ $- \frac{2}{3} \underset{__}{ } - \frac{1}{3}$
4. ⓓ $−3 \underset{__}{ } - \frac{7}{3}$

Order each of the following pairs of numbers, using $<$ or $>:$

1. ⓐ $−3 __ - \frac{17}{5}$
2. ⓑ $−2 \frac{1}{4} __ −2$
3. ⓒ $- \frac{3}{5} \underset{__}{ } - \frac{4}{5}$
4. ⓓ $−4 \underset{__}{ } - \frac{10}{3}$

Rewrite the improper fraction as a mixed number.

$\frac{5}{3}$

Rewrite the improper fraction as a mixed number.

$\frac{13}{5}$

Rewrite the improper fraction as a mixed number.

$\frac{28}{9}$

Rewrite the improper fraction as a mixed number.

$\frac{47}{15}$

Rewrite the mixed number as an improper fraction.

$1 \frac{2}{5}$

Rewrite the mixed number as an improper fraction.

$2 \frac{5}{6}$

Rewrite the mixed number as an improper fraction.

$2 \frac{5}{7}$

Rewrite the mixed number as an improper fraction.

$3 \frac{5}{9}$

Use fraction tiles or draw a figure to find equivalent fractions.

How many twelfths equal one-third?

Use fraction tiles or draw a figure to find equivalent fractions.

How many twelfths equal three-fourths?

Use fraction tiles or draw a figure to find equivalent fractions.

How many sixths equal three-halves?

Find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{1}{3}$

Find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{5}{6}$

Find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{5}{9}$

Order each of the following pairs of numbers, using $<$ or $>.$

$−1 \underset{__}{ } - \frac{1}{3}$

Order each of the following pairs of numbers, using $<$ or $>.$

$−1 \frac{3}{4} \underset{__}{ } - 2$

Order each of the following pairs of numbers, using $<$ or $>.$

$- \frac{9}{10} \underset{__}{ } - \frac{3}{10}$

Order each of the following pairs of numbers, using $<$ or $>.$

$−4 \underset{__}{ } - \frac{23}{6}$

Music Measures Fractions are used often in music. In $\frac{4}{4}$ time, there are four quarter notes in one measure.

1. ⓐ How many measures would eight quarter notes make?
2. ⓑ The song “Happy Birthday to You” has $25$ quarter notes. How many measures are there in “Happy Birthday to You?”

Give an example from your life experience (outside of school) where it was important to understand fractions.