# Prealgebra

## Educators

DK

Problem 1

In the following exercises, name the fraction of each figure that is shaded.

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Problem 2

In the following exercises, name the fraction of each figure that is shaded.

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Problem 3

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{1}{2}$$

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Problem 4

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{1}{3}$$

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Problem 5

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{3}{4}$$

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Problem 6

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{2}{5}$$

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Problem 7

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{5}{6}$$

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Problem 8

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{7}{8}$$

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Problem 9

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{5}{8}$$

DK
Danny K.

Problem 10

In the following exercises, shade parts of circles or squares to model the following fractions.
$$\frac{7}{10}$$

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Problem 11

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.
3 thirds

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Problem 12

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

8 eighths

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Problem 13

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

7 sixths

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Problem 14

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

4 thirds

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Problem 15

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

7 fifths

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Problem 16

In the following exercises, use fraction circles to make wholes, if possible, with the following pieces.

7 fourths

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Problem 17

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

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Problem 18

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

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Problem 19

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

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Problem 20

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{3}{3}$$

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Problem 21

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{4}{4}$$

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Problem 22

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{7}{4}$$

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Problem 23

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{5}{3}$$

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Problem 24

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{11}{6}$$

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Problem 25

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{13}{8}$$

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Problem 26

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{10}{3}$$

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Problem 27

In the following exercises, draw fraction circles to model the given fraction.
$$\frac{9}{4}$$

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Problem 28

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{3}{2}$$

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Problem 29

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{5}{3}$$

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Problem 30

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{11}{4}$$

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Problem 31

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{13}{5}$$

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Problem 32

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{25}{6}$$

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Problem 33

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{28}{9}$$

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Problem 34

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{42}{13}$$

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Problem 35

In the following exercises, rewrite the improper fraction as a mixed number.
$$\frac{47}{15}$$

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Problem 36

In the following exercises, rewrite the mixed number as an improper fraction.
$$1 \frac{2}{3}$$

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Problem 37

In the following exercises, rewrite the mixed number as an improper fraction.
$$1 \frac{2}{5}$$

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Problem 38

In the following exercises, rewrite the mixed number as an improper fraction.
$$2 \frac{1}{4}$$

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Problem 39

In the following exercises, rewrite the mixed number as an improper fraction.
$$2 \frac{5}{6}$$

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Problem 40

In the following exercises, rewrite the mixed number as an improper fraction.
$$2 \frac{7}{9}$$

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Problem 41

In the following exercises, rewrite the mixed number as an improper fraction.
$$2 \frac{5}{7}$$

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Problem 42

In the following exercises, rewrite the mixed number as an improper fraction.
$$3 \frac{4}{7}$$

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Problem 43

In the following exercises, rewrite the mixed number as an improper fraction.
$$3 \frac{5}{9}$$

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Problem 44

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many sixths equal one third?

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Problem 45

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many twelfths equal one third?

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Problem 46

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many eighths equal three-fourths?

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Problem 47

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many twelfths equal three-fourths?

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Problem 48

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many fourths equal three-halves?

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Problem 49

In the following exercises, use fraction tiles or draw a figure to find equivalent fractions.

How many sixths equal three- halves?

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Problem 50

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{1}{4}$$

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Problem 51

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{1}{3}$$

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Problem 52

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{3}{8}$$

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Problem 53

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{5}{6}$$

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Problem 54

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{2}{7}$$

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Problem 55

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
$$\frac{5}{9}$$

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Problem 56

In the following exercises, plot the numbers on a number line.
$$\frac{2}{3}, \frac{5}{4}, \frac{12}{5}$$

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Problem 57

In the following exercises, plot the numbers on a number line.
$$\frac{1}{3}, \frac{7}{4}, \frac{13}{5}$$

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Problem 58

In the following exercises, plot the numbers on a number line.
$$\frac{1}{4}, \frac{9}{5}, \frac{11}{3}$$

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Problem 59

In the following exercises, plot the numbers on a number line.
$$\frac{7}{10}, \frac{5}{2}, \frac{13}{8}, 3$$

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Problem 60

In the following exercises, plot the numbers on a number line.
$$2 \frac{1}{3},-2 \frac{1}{3}$$

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Problem 61

In the following exercises, plot the numbers on a number line.
$$1 \frac{3}{4},-1 \frac{3}{5}$$

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Problem 62

In the following exercises, plot the numbers on a number line.
$$\frac{3}{4},-\frac{3}{4}, 1 \frac{2}{3},-1 \frac{2}{3}, \frac{5}{2},-\frac{5}{2}$$

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Problem 63

In the following exercises, plot the numbers on a number line.
$$\frac{2}{5},-\frac{2}{5}, 1 \frac{3}{4},-1 \frac{3}{4}, \frac{8}{3},-\frac{8}{3}$$

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Problem 64

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-1_{-}-\frac{1}{4}$$

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Problem 65

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-1_{-}-\frac{1}{3}$$

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Problem 66

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-2 \frac{1}{2}-3$$

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Problem 67

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-1 \frac{3}{4}--2$$

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Problem 68

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-\frac{5}{12}--\frac{7}{12}$$

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Problem 69

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$-\frac{9}{10}--\frac{3}{10}$

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Problem 70

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-3_{-}-\frac{13}{5}$$

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Problem 71

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$
$$-4_{-}\frac{23}{6}$$

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Problem 72

Music Measures A choreographed dance is broken into counts. A $\frac{1}{1}$ count has one step in a count, a $\frac{1}{2}$ count has two steps in a count and a $\frac{1}{3}$ count has three steps in a count. How many steps would be in a $\frac{1}{5}$ count? What type of count has four steps in it?

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Problem 73

Music Measures Fractions are used often in music. In $\frac{4}{4}$ time, there are four quarter notes in one measure.
(a) How many measures would eight quarter notes make?
(b) The song "Happy Birthday to You" has 25 quarter notes. How many measures are there in
"Happy Birthday to You?"

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Problem 74

Baking Nina is making five pans of fudge to serve after a music recital. For each pan, she needs $\frac{1}{2}$ cup of walnuts.
(a) How many cups of walnuts does she need for five pans of fudge?
(b) Do you think it is easier to measure this amount when you use an improper fraction or a mixed number? Why?

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Problem 75

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

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Problem 76

Explain how you locate the improper fraction $\frac{21}{4}$ on a number line on which only the whole numbers from 0 through 10 are marked.

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