Mathematics Knowledge – Test 4

The easiest way to start is to multiply each term by 10. This will eliminate all of the denominators.

We now have 60/5 x + 4x = 320/10

12x + 4x = 32

16x = 32

x = 2.

Rewrite each fraction with a denominator of 20 and the sum of the fractions must equal one

8/20 (freshmen)+5/20 (sophomores)+2/20(juniors)+x=20/20

15/20+x=20/20

x=5/20=1/4

if her batting average is .320 that means, out of 100 times at bat, she would have hit the ball 32 times. Thus your ratio is 32/100 = .320. Now we want to know how many hits out of 25? Could look at this a couple ways:

1. 25 is equal 1/4 of 100 (denominator).... thus take 1/4 of the numerator (32) to get 8.

2. Set up and cross multiply the following:

32/100 = x / 25. Thus 25 * 32 = 800, then divide by 100 to get 8.

Either way works. Thus, she would get 8 hits.

Division of fractions - flip the second and multiply.

-3/8 * 32/27 = -1/8 * 32/9

-1/1 * 4/9

-4/9

8/17 ÷ 15/17

= 8/17 x 17/15

= (8 x 17)/(17 x 15)

= 8/15

Get the y expressions on one side and numbers on the other side.

- 8 - 5y = 12 - 9y

9y - 5y - 8 = 12 (by adding 9y to both sides)

4y - 8 = 12

4y = 20 (by adding 8 to both sides)

y = 5 (because 4 x 5 = 20)

x = an unknown integer.

Since they are consecutive, it would go as follows: x, x + 1, x + 2, x + 3, x + 4

5x + 10 = 225

Since we have to multiply the sum by 5 ----> 5(5x + 10) = 225

Answer: Since you get 7, then just plug it in, 7, 7 + 1, 7 + 2, 7 + 3, 7 + 4

So it would be 11

7 3/10 - 4 4/5 (convert mixed numbers into improper fractions)

73/10 - 24/5 (find LCD, which is 10; multiply second fraction by 2/2)

73/10 - 24/5*2/2

73/10 - 48/10 (subtract numerators)

25/10 (reduce)

5/2 or 2 1/2

Divide the monthly fee by the difference in price:

$15 / ($2.35-$2.05) = $15/$0.30 = 50

50 gallons.

We know that every triangle is made up of three angles totaling 180 degees. We know to find out what the measure of angle 2 is, that we need to figure out what x is.

Step one: set the problem up so adding all the measures together is equal to 180 degrees.

(4x)+(3x+10)+(2x+17)=180.

Step two: Add like variable and numbers.

4x+3x+2x=9x

10+17=27

9x+27=180

Step three: Subtract 27 from both sides.

9x +27-27= 180-27

9x=153

Step four: Divide both sides by 9.

x=17.

Step five: Now that we know that x=17, we can substitute it back into the measure of angle two to solve the problem.

3(17)+10=

51+10=

61.

The measure of angle two = 61 degrees.

3 1/4 - 1 5/6 (convert mixed numbers into improper fractions)

13/4 - 11/6 (find LCD, which is 24; multiply first fraction by 6/6 and second by 4/4)

13/4*6/6 - 11/6*4/4

78/24 - 44/24 (subtract numerators)

34/24 (reduce)

17/12 or 1 5/12

Let length = L & width = W

Total floor area = LW

Tiled area = 3/5 L * 2/4 W = 3/10 LW

the fraction of the floor that has been covered by tiles

= ( 3/10 LW) / ( LW)

= 3/10

Since multiplication and division happen at the same time in order of operations, you just work left to right.

8/1 divided by 1/4 is 32

32 times 3 times 4/6 divided by 3/8 times 14/16 divided by 7/8 times 5/12 times 9/12 divided by 10/24

32 times 3 is 96

96 times 4/6 divided by 3/8 times 14/16 divided by 7/8 times 5/12 times 9/12 divided by 10/24

96 times 4/6 is 64

64 divided by 3/8 times 14/16 divided by 7/8 times 5/12 times 9/12 divided by 10/24

64 divided by 3/8 is 512/3

512/3 times 14/16 divided by 7/8 times 5/12 times 9/12 divided by 10/24

512/3 times 14/16 is 448/3

448/3 divided by 7/8 times 5/12 times 9/12 divided by 10/24

448/3 divided by 7/8 is 512/3

512/3 times 5/12 times 9/12 divided by 10/24

512/3 times 5/12 is 640/9

640/9 times 9/12 divided by 10/24

640/9 times 9/12 is 160/3

160/3 divided by 10/24

160/3 divided by 10/24 is 128.

Your answer is 128.

Every foot is equal to 12 inches.

The area of a square is one side times the other. So you have 12 inches x 12 inches. That comes out to 144 square inches per square foot.

Now you only have to multiply 144 (square inches) by 6.25 (the square feet) and you get: 900 square inches.

let x = jen's age now

x - 6 = sue's age now

x + 4 = 2((x-6) - 5)

x + 4 = 2(x - 11)

x + 4 = 2x - 22

x - 2x = -22 - 4

-x = -26

x = 26 -------------------> jen's age now

x - 6 = 20 --------------> sue's age now