# Praxis Mathematics Exam 1

#### If Todd can type 60 word a minute, how long will it take him to type a 15,000 word document?

Divide the length of the document by the number of words per minute to find the number of minutes it will take. The number of minutes can then be divided by the number of minutes in an hour. 250 minutes is equivalent to 4 hours and 10 minutes.

#### Solve and simplify: 2/3 x 3/5 x 5/10 x 6/8

Fractions are multiplied by multiplying numerators by numerators and denominators by denominators. Some of the fractions in this problem can be simplified.

#### Three people divide up a large pizza. If the first person gets half and the second person gets half as much as the first person, how much is left for the third person?

The first person gets ½, the second gets ¼, leaving ¼ for the third person.

#### Albert is driving at 80 miles per hour. How far will he go in 45 minutes?

45 minutes is three-quarters of an hour, which can be rewritten as the decimal 0.75. Multiply this decimal by his speed.

#### If Dave drives at a steady speed of 50 miles per hour, how long will it take him to drive 10 miles?

Since there are 60 minutes in an hour, this problem can be solved with the following equation: 50/60 = 10/x

#### On a real number line, x =-4 and y = 7. What is the length of the line XY?

Measure the length of the line by adding the respective distances of each value from zero.

#### Rex is four times as old as Ted. If the sum of their ages is 30, how old is Ted?

The ratio of Rex’s age to Ted’s age is 4:1; the sum of their ages can be divided by the total number of units in this ratio, 5. This indicates that Rex is 24 and Ted is 6.

#### Which of the following units would be most appropriate foe measuring the length of a pen?

All of the other units are either much too big or much too small.

#### 54 is 75% of what number?

Multiply 54 by 100 and then divide by 75.

#### If Ted runs at 8 miles an hour,which computation would you use to determine how far Ted runs in 15 minutes?

Fifteen minutes is a quarter-hour, which is equivalent to the decimal 0.25.

#### Gerald received the following test scores in math class: 76, 86, 89, 81, and 99. What was Gerald's average test score, rounded to the nearest point?

Add all of the scores together and divide by the number of scores.

#### Solve for x: (7x/5) +9 = 23

In order to find x, you must subtract 9 from 23, then multiply the difference by 5, and finally divide the product by 7.

#### If x=3 and y = -1, then 3x squared + 2xy - 5 =?

Substitute the given values into the equation, and then remember to observe the order of operations.

#### Which of the following numbers has the greatest absolute value: 17, -9, 15.5, -20, 19?

Absolute value is the number of integers away from zero, so the absolute value of -20 is greater than the absolute value of 19 by one unit.

#### John's sock drawer contains 4 pairs of green socks, 7 pairs of black socks, and 7 pairs of red socks. If John reaches into the drawer at random, what are his chances of NOT selecting a pair of green socks?

14 of the 18 pairs of socks are not green; the fraction 14/18 can be simplified as 7/9.

#### Randy got the following test scores in science class: 76,98,78,80 and 54. What is the median test score?

The median is the piece of data that is in the middle position when the entire set is placed in order from least to greatest.

#### 3/8 + 1/3 + 1/8 =

Convert the fractions so that they have a common denominator of 24.

#### If John scores 20% of his team's oint in a basketball game, how many points does the team score if John scores 14 points?

20% is one-fifth, so multiply John’s point total by 5.

#### Regie has enough flour to last for days. If he increases his use of flour by 25%, however, how many day's worth of flour will he have?

Reggie will be using flour at 5/4 the normal rate. Since the amount of flour used is inversely proportional to the amount of time it takes to go through the flour, the duration can be found by multiplying 40 by the inverse of 5/4, or 4/5.

#### 9 / 20 =

Multiply both 9 and 20 by 5.

#### 8.26 x 76.8

Remember that since the terms of the problem have three units to the right of the decimal point, the answer will as well.

#### John will be x in 7 years. How old was he last year?

The target age can be found by subtracting first seven and then one year from x.

#### 3/27

Divide numerator and denominator by 3.

#### Find the slope: 4x - 5y =20

The equation form for slope is y = mx + b, in which m is slope.

#### 4 2/3 - 2 ½

Convert both fractions so that they have a common denominator of 6.

#### 8.5 x 9.07 =

Remember that since the terms of the problem have three units to the right of the decimal point, the answer will as well.

#### If x= -5, then l x - 7 l =

Remember that absolute value is the distance from zero on a real number line, and therefore cannot be zero.

#### Written in scientific notation, the number 173,000,000,000 is:

Place a decimal point at the end of the number and then move it eleven places to the left, until it creates a number between one and ten.

#### A number is multiplied by 6 and then has 4 subtracted from it. The answer is 14. Which of the following equations matches these statements?

In this equation, the order of operations will dictate that the multiplication takes place before the subtraction.

#### If a recipe for cookies calls for ¾ of a cup of sugar, and you want to quadruple the recipe, how many cups of sugar will you need?

The fraction ¾ is equivalent to the decimal 0.75. Multiply this decimal by 4.

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