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  • Fractions and Mixed Numbers

Prealgebra

Charles P. McKeague

Chapter 3

Fractions and Mixed Numbers - all with Video Answers

Educators


Section 1

The Meaning and Properties of Fractions

Problem 1

Name the numerator of each fraction.
$$\frac{1}{3}$$

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Problem 2

Name the numerator of each fraction.
$$\frac{1}{4}$$

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Problem 3

Name the numerator of each fraction.
$$\frac{2}{3}$$

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Problem 4

Name the numerator of each fraction.
$$\frac{2}{4}$$

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Problem 5

Name the numerator of each fraction.
$$\frac{x}{8}$$

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Problem 6

Name the numerator of each fraction.
$$\frac{y}{10}$$

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Problem 7

Name the numerator of each fraction.
$$\frac{a}{b}$$

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Problem 8

Name the numerator of each fraction.
$$\frac{x}{y}$$

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Problem 9

Name the denominator of each fraction.
$$\frac{2}{5}$$

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Problem 10

Name the denominator of each fraction.
$$\frac{3}{5}$$

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Problem 11

Name the denominator of each fraction.
$$6$$

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Problem 12

Name the denominator of each fraction.
$$2$$

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Problem 13

Name the denominator of each fraction.
$$\frac{a}{12}$$

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Problem 14

Name the denominator of each fraction.
$$\frac{b}{14}$$

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Problem 15

Complete the following tables.
$$
\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Numerator } \\
\text { a }
\end{array} & \begin{array}{c}
\text { Denominator } \\
b
\end{array} & \begin{array}{c}
\text { Fraction } \\
\frac{a}{b}
\end{array} \\
\hline 3 & 5 & \\ \hline
1 & & \frac{1}{7} \\
\hline & y & \frac{x}{y} \\ \hline
x+1 & x & \\ \hline
\end{array}$$

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Problem 16

Complete the following tables.
$$
\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Numerator } \\
\text { a }
\end{array} & \begin{array}{c}
\text { Denominator } \\
b
\end{array} & \begin{array}{c}
\text { Fraction } \\
\frac{a}{b}
\end{array} \\
\hline 2 & 9 & \\ \hline
& 3 & \frac{4}{3} \\
\hline 1 & & \frac{1}{x} \\ \hline
x & & \frac{x}{x+1} \\ \hline
\end{array}$$

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Problem 17

For the set of numbers $\left\{\frac{3}{4}, \frac{6}{5}, \frac{12}{3}, \frac{1}{2}, \frac{9}{10}, \frac{20}{10}\right\},$ list all the proper fractions.

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Problem 18

For the set of numbers $\left(\frac{1}{8}, \frac{7}{9}, \frac{6}{3}, \frac{18}{6}, \frac{3}{5}, \frac{9}{8}\right),$ list all the improper fractions.

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Problem 19

Indicate whether each of the following is True or False.
Every whole number greater than 1 can also be expressed as an improper fraction.

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Problem 20

Indicate whether each of the following is True or False.
Some improper fractions are also proper fractions.

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Problem 21

Indicate whether each of the following is True or False.
Adding the same number to the numerator and the denominator of a fraction will not change its value.

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Problem 22

Indicate whether each of the following is True or False.
The fractions $\frac{3}{4}$ and $\frac{9}{16}$ are equivalent.

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Problem 23

Divide the numerator and the denominator of each of the following fractions by 2 .
$$\frac{6}{8}$$

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Problem 24

Divide the numerator and the denominator of each of the following fractions by 2 .
$$\frac{10}{12}$$

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Problem 25

Divide the numerator and the denominator of each of the following fractions by 2 .
$$\frac{86}{94}$$

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Problem 26

Divide the numerator and the denominator of each of the following fractions by 2 .
$$\frac{106}{142}$$

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Problem 27

Divide the numerator and the denominator of each of the following fractions by 3.
$$\frac{12}{9}$$

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Problem 28

Divide the numerator and the denominator of each of the following fractions by 3.
$$\frac{33}{27}$$

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Problem 29

Divide the numerator and the denominator of each of the following fractions by 3.
$$\frac{39}{51}$$

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Problem 30

Divide the numerator and the denominator of each of the following fractions by 3.
$$\frac{57}{69}$$

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Problem 31

Write each of the following fractions as an equivalent fraction with denominator 6.
$$\frac{2}{3}$$

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Problem 32

Write each of the following fractions as an equivalent fraction with denominator 6.
$$\frac{1}{2}$$

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Problem 33

Write each of the following fractions as an equivalent fraction with denominator 6.
$$\frac{55}{66}$$

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Problem 34

Write each of the following fractions as an equivalent fraction with denominator 6.
$$\frac{65}{78}$$

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Problem 35

Write each of the following fractions as an equivalent fraction with denominator 12.
$$\frac{2}{2}$$

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Problem 36

Write each of the following fractions as an equivalent fraction with denominator 12.
$$\frac{5}{6}$$

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Problem 37

Write each of the following fractions as an equivalent fraction with denominator 12.
$$\frac{56}{84}$$

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Problem 38

Write each of the following fractions as an equivalent fraction with denominator 12.
$$\frac{143}{156}$$

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Problem 39

Write each fraction as an equivalent fraction with denominator $12 x .$
$$\frac{1}{6}$$

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Problem 40

Write each fraction as an equivalent fraction with denominator $12 x .$
$$\frac{3}{4}$$

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Problem 41

Write each number as an equivalent fraction with denominator $24 a$.
$$2$$

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Problem 42

Write each number as an equivalent fraction with denominator $24 a$.
$$1$$

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Problem 43

Write each number as an equivalent fraction with denominator $24 a$.
$$5$$

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Problem 44

Write each number as an equivalent fraction with denominator $24 a$.
$$8$$

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Problem 45

One-fourth of the first circle below is shaded. Use the other three circles to show three other ways to shade one-fourth of the circle.
(Figure cant copy)

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Problem 46

The objects below are hexagons, six-sided figures. One-third of the first hexagon is shaded. Shade the other three hexagons to show three other ways to represent one-third.
(Figure cant copy)

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Problem 47

Simplify by dividing the numerator by the denominator.
$$\frac{3}{1}$$

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Problem 48

Simplify by dividing the numerator by the denominator.
$$\frac{3}{3}$$

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Problem 49

Simplify by dividing the numerator by the denominator.
$$\frac{6}{3}$$

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Problem 50

Simplify by dividing the numerator by the denominator.
$$\frac{12}{3}$$

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Problem 51

Simplify by dividing the numerator by the denominator.
$$\frac{37}{1}$$

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Problem 52

Simplify by dividing the numerator by the denominator.
$$\frac{37}{37}$$

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Problem 53

For each square below, what fraction of the area is given by the shaded region?
a. (Figure cant copy)
b. (Figure cant copy)
c. (Figure cant copy)
d. (Figure cant copy)

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Problem 54

For each square below, what fraction of the area is given by the shaded region?
a. (Figure cant copy)
b. (Figure cant copy)
c. (Figure cant copy)
d. (Figure cant copy)

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Problem 55

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{1}{4}$$

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Problem 56

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{1}{8}$$

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Problem 57

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{1}{16}$$

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Problem 58

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{5}{8}$$

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Problem 59

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{3}{4}$$

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Problem 60

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{15}{16}$$

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Problem 61

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{3}{2}$$

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Problem 62

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{5}{4}$$

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Problem 63

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{31}{16}$$

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Problem 64

The number line below extends from 0 to 2, with the segment from 0 to 1 and the segment from 1 to 2 each divided into 8 equal parts. Locate each of the following numbers on this number line.
$$\frac{15}{8}$$

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Problem 65

Write each fraction as an equivalent fraction with denominator 100 . Then write them in order from smallest to largest.
$$\frac{3}{10} \quad \frac{1}{20} \quad \frac{4}{25} \quad \frac{2}{5}$$

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Problem 66

Write each fraction as an equivalent fraction with denominator $30 .$ Then write them in order from smallest to largest.
$$\frac{1}{15} \quad \frac{5}{6} \quad \frac{7}{10} \quad \frac{1}{2}$$

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Problem 67

The chart shows the average rainfall for Death Valley in the given months. Write the rainfall for January as an equivalent fraction with denominator 12 .
(Chart cant copy)

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Problem 68

The chart shows the average rainfall for Death Valley in the given months. Write the rainfall for April as an equivalent fraction with denominator 75 .
(Chart cant copy)

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Problem 69

The pie chart below shows the fraction of workers who responded to a survey about sending non work-related e-mail from the office. Use the pie chart to fill in the table.
(Pie chart cant copy)
$$\begin{array}{|ccc|}
\hline\begin{array}{c}
\text { How Often Workers Send } \\
\text { Non-Work-Related E-Mail } \\ \text { From the Office}
\end{array} & \begin{array}{c}
\text { } \\
\text { } \\
\end{array} & \begin{array}{c}
\text { From the Office } \\
\text { Respondents } \\
\text {Saying Yes}
\end{array} \\
\hline \text {never} \\
\hline \text {1 to 5 times a day}\\
\hline \text {5 to 10 times a day} \\
\hline \text {more than 10 times a day} \\
\hline \end{array}$$

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Problem 70

The pie chart below shows the fraction of workers who responded to a survey about viewing non-
work-related sites during working hours. Use the pie chart to fill in the table.
(Pie chart cant copy)
$$\begin{array}{|ccc|}
\hline\begin{array}{c}
\text { How Often Workers Send } \\
\text { Non-Work-Related E-Mail } \\ \text { From the Office}
\end{array} & \begin{array}{c}
\text { } \\
\text { } \\
\end{array} & \begin{array}{c}
\text { From the Office } \\
\text { Respondents } \\
\text {Saying Yes}
\end{array} \\
\hline \text {never} \\
\hline \text {a few times a week}\\
\hline \text {a few times a day} \\
\hline \text {constantly} \\
\hline \end{array}$$

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Problem 71

If there are 3 girls in a family with 5 children, then we say that $\frac{3}{5}$ of the children are girls. If there are 4 girls in a family with 5 children, what fraction of the children are girls?

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Problem 72

If 3 out of every 7 people who apply to medical school actually get accepted, what fraction of the people who apply get accepted?

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Problem 73

The new iPod $^{\text TM}$ Shuffle will hold up to 500 songs. You load 311 of your favorite tunes onto your iPod. Represent the number of songs on your iPod as a fraction of the total number of songs it can hold.

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Problem 74

In a survey of 1,000 cell phone subscribers it was determined that 160 subscribers owned more than one cell phone and used different carriers for each phone. Represent the number of cell phone subscribers with more than one carrier as a fraction.

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Problem 75

Recently the men's basketball team at the University of Maryland won 19 of the 33 games they played. What fraction represents the number of games won?

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Problem 76

Test Your math teacher grades on a point system. You take a test worth 75 points and score a 67 on the test. Represent your score as a fraction.

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Problem 77

A circle measures 360 degrees, which is commonly written as $360^{\circ} .$ The shaded region of each of the circles below is given in degrees. Write a fraction that represents the area of the shaded region for each of these circles.
a. (Figure cant copy)
b. (Figure cant copy)
c. (Figure cant copy)
d. (Figure cant copy)

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Problem 78

All living things contain a small amount of carbon- 14, which is radioactive and decays. The half-life of carbon-14 is 5,600 years. During the lifetime of an organism, the carbon- 14 is replenished, but after its death the carbon- 14 begins to disappear. By measuring the amount left, the age of the organism can be determined with surprising accuracy. The line graph below shows the fraction of carbon- 14 remaining after the death of an organism. Use the line graph to complete the table.

$$\begin{array}{|cc|}
\hline \text { Colicenticlion of cellionsits } \\
\hline \begin{array}{c}
\text { Nears firce braitin } \\
\text { of oxeulsin }
\end{array} & \begin{array}{c}
\text { Rectron os cellivisite } \\
\text { ifeuctifitio }
\end{array} \\
\hline & 1 \\
\hline 11,200 & \frac{1}{2} \\
\hline 16,800 & \\
\hline & \frac{1}{16} \\
\hline
\end{array}$$
(Graph cant copy)

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Problem 79

Which of the following fractions is closest to the number 0?
a. $\frac{1}{2}$
b. $\frac{1}{3}$
c. $\frac{1}{4}$
d. $\frac{1}{5}$

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Problem 80

Which of the following fractions is closest to the number 1?
a. $\frac{1}{2}$
b. $\frac{1}{3}$
c. $\frac{1}{4}$
d. $\frac{1}{5}$

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Problem 81

Which of the following fractions is closest to the number 0?
a. $\frac{1}{8}$
b. $\frac{3}{8}$
c. $\frac{5}{8}$
d. $\frac{7}{8}$

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Problem 82

Which of the following fractions is closest to the number 1?
a. $\frac{1}{8}$
b. $\frac{3}{8}$
c. $\frac{5}{8}$
d. $\frac{7}{8}$

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Problem 83

Multiply.
$$2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$$

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Problem 84

Multiply.
$$2^{2} \cdot 3^{3}$$

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Problem 85

Multiply.
$$2^{2} \cdot 3 \cdot 5$$

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Problem 86

Multiply.
$$2 \cdot 3^{2} \cdot 5$$

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Problem 87

Divide.
$$12 \div 3$$

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00:33

Problem 88

Divide.
$$15 \div 3$$

Heather Zimmers
Heather Zimmers
Numerade Educator

Problem 89

Divide.
$$20 \div 4$$

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Problem 90

Divide.
$$24 \div 4$$

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00:30

Problem 91

Divide.
$$42 \div 6$$

Kerry Thornton-Genova
Kerry Thornton-Genova
Numerade Educator
00:17

Problem 92

Divide.
$$72 \div 8$$

Christopher Stanley
Christopher Stanley
Numerade Educator

Problem 93

Divide.
$$102 \div 2$$

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Problem 94

Divide.
$$105 \div 7$$

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Problem 95

Simplify.
$$3+4 \cdot 5$$

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Problem 96

Simplify.
$$20-8 \cdot 2$$

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Problem 97

Simplify.
$$5 \cdot 2^{4}-3 \cdot 4^{2}$$

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Problem 98

Simplify.
$$7 \cdot 8^{2}+2 \cdot 5^{2}$$

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Problem 99

Simplify.
$$4 \cdot 3+2(5-3)$$

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Problem 100

Simplify.
$$6 \cdot 8+3(4-1)$$

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Problem 101

Simplify.
$$18+12 \div 4-3$$

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Problem 102

$$20+16 \div 2-5$$

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