AM 3Review Patterson

Which two points have opposite locations on a number line? -2/5 and 0.25 OR -2/5 and 4/10

-2/5 and 4/10...because -2/5 = -0.40 and 4/10 = 0.40

What is the multiplicative inverse of -1/4?

-4/1 because a number and its multiplicative inverse should have a product of 1. -1/4 * -4/1 = 4/4 = 1

What is -8/15 written as a decimal? Use bar notation to show a repeating decimal if necessary.

-8/15 = 0.533333... 0.53 with a bar over the 3.

Shawn made 15 out of 20 free throws during the game. What is Shawn's success rate at the free throw line?

15/20 = 0.75, so his success rate is 0.75 or 3/4 of the time.

Of the 800 students at HWMS, 4/5 of them are successful in math class. How many students are successful in math class?

4/5 * 800/1 = 3200/5, which reduces down to 640 students.

What is the value of 5mq if m = -1/4 and q = 5/8.

5/1 * -1/4 * 5/8 = -25/32

Which symbol ( <, >, or = ) completes the following inequality? 5/8 _____ 0.63

< ....because 5/8 = 0.625, which is less than 0.63

How many hair bows can be made from 30 yards of ribbon if each bow is 1 1/2 yards long?

Change 1 1/2 into an improper fraction first, which would be 3/2. The process needed is division, so 30/1 divided by 3/2. Division changes to multiplication and the 3/2 is flipped (multiplicative inverse). The new problem becomes 30/1 * 2/3 = 60/3, which reduces to 20. So 20 bows can be made.

A room needs to be divided into 5 equal sections. If the wall of the room is 12 2/5 feet long, how wide should each section be to the nearest half a foot?

Change 12 2/5 into an improper fraction then change 5 into 1/5 because division changes to multiplication using the multiplicative inverse. 62/5 * 1/5 = 62/25, which cannot be simplified but it can be changed to a mixed fraction of 2 12/25. Each section should be approximately 2.5 or 2 1/2 feet wide.

Shane ran 5 8/9 laps around the track yesterday. Today he ran 5 times that amount. How many laps did Shane run today?

Change 5 8/9 into an improper fraction then multiply. 53/9 * 5/1 = 477/9, which reduces to 53. So Shane ran 53 laps around the track today.

What is the value of m - n if m = -2/5 and n = -1 2/7?

First change m - n into an addition problem... m + (-n)...then change -1 2/7 from a mixed fraction into an improper, -9/7... so -2/5 + -(-9/7) becomes -2/5 + 9/7. Addition and subtraction require a common denominator for 5 and 7, which would be 35. The new fractions would be -14/35 + 45/35, which equals 31/35.

What is the perimeter of a rectangle with a length of 2 1/3 feet and a width of 3 2/5 feet? Write your answer as a fraction and a decimal.

Perimeter means to add up all the sides. 2 1/3 + 2 1/3 + 3 2/5 + 3 2/5...Add up the whole numbers 2 + 2 + 3 + 3 = 10...add up the fractions 1/3 + 1/3 + 2/5 + 2/5 = 2/3 + 4/5...find a common denominator of 15, so 10/15 + 12/15 = 22/15 or 1 7/15...add the whole number to it to become 11 7/15. The decimal would be 11.46 with a bar over the 6.

What is the quotient of 3m/n and 5m/n?

Quotient means to divide so it is easier to change it to multiplication. The first fraction stays the same and the second is flipped (multiplicative inverse). 3m/n * n/5m = 3mn/5mn...since top and bottom both have an mn, they cancel each other out and you are left with 3/5 as the final answer.

What is the area of a rectangle with a length of 2 1/3 feet and a width of 3 2/5 feet? Write your answer as a fraction and a decimal.

Since area means length multiplied by width, the mixed fractions need to be converted to improper fractions and then multiplied. 7/3 * 17/5 = 119/15 or 7 14/15 feet or 7.93 with a bar over the 3.

What is 0.54 as a reduced fraction?

The 4 in 0.54 is in the hundredths place value, so the fraction would be 54/100, which reduces to 27/50.