Practice Problems for Fractions, Decimals, & Percents

Simplify: 8(3)(x^2)(3)/6x

8(3)(x^2)(3)/6x= 8(x^2)(3)/2x= 4(x^2)(3)/x= 4(x)(3)= 12x

Initially, the men and women in a room were in the ratio of 5:7. Six women leave the room. If there are 35 men in the room, how many women are left in the room?

Men = 5x Women = 7x 5x=35 x=7 Women= 7(7)= 49 If 6 women leave the room, there are 49-6 or 43, women left.

Express the following as percents: 25/8

Or convert the fraction to a decimal and shift the decimal point two places to the right: 25/8= 3 1/8= 3.125= 312.5%

Express the following as fractions and simplify: 8%

Write it over a denominator of 100 and simplify: 8/100= 2/25

Express the following as fractions and simplify: 0.008

Write it over the appropriate power of 10 and simplify: 0.008= 8/1000= 1/125

x is 40% of y. 50% of y is 40. 16 is what percent of x?

You can translate the first two sentences directly into equations: x is 40% of y --> x= (40/100)y 50% of y is 40 --> (50/100)y=40 You can solve the second equation for Y: (50/100)y=40 (1/2)y=40 y=80 Now you can replace y with 80 in the first equation to solve for x: x= (40/100)(80) x= 4/10 x 80 x= 4x8=32 Be careful now. The question asks, "16 is what percent of x?" You know that x=32, so this question is really asking, "16 is what percent of 32?" Create a new variable (z) to represent the unknown value in the question and solve: 16= z/100x 32 16 x 100/32= z 1x 100/2= z 50=z

A stereo was marked down by 30% and sold for $84. What was the presale price of the stereo?

You know the new price of the stereo, so you can use the following formula: New Percent= New Value/ Original Value The new value of the stereo is $84. If the price of the stereo was marked down 30%, then the new percent is 100- 30= 70%. Finally, the original value is the value you've asked for, so you can replace it with x. 70/100= 84/x= 7/10= 84/x = 7x=840 x= 120. Alternatively, you could rephrase the given info to say the following: $84 is 70% of the original price of the stereo. You could then translate this statement into an equation and solve: 84= (70/100)x 84= (7/10)x 840=7x 120=x

What is 40% of 30?

100%= 30 10%=3 40%= (4)(10%)= (4)(3)= 12

What is 7% of 50?

100%= 50 5%= 2.5 (10%=5, so 5%= half of that) 1%= 0.5 7%= 5%+1%+1% = 2.5 +0.5 +0.5= 3.5

A car loan is offered at 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?

Although this looks like an interest problem, you can think of it as a percent change problem. The percent change is 8%, and the change in value is $240. Percent Change= Change in Value/Original Value 8/100= 240/x 8x=24,000 x=3000. Alternatively, you could rephrase the given information to say the following: $240 is 8% of the total loan. Then translate this statement into an equation and solve: 240= (8/100)x 24,000= 8x 3,000=x

Decide whether the given operation will cause the original value to increase, decrease, or stay the same: Multiply a positive, proper fraction by 3/8.

Decrease: Multiplying a positive number by a proper fraction decreases the number.

What is 75% of 20?

Don't forget about your fraction-conversion skills! Sometimes, it's easier to convert to fractions and cancel: 75%= 3/4. 3/4(20)= (3)(5)= 15

simplify: (4 x 10^-2) - (2.5 x 10^-3)

First, rewrite the numbers in standard notation by shifting the decimal point. Then, add zeroes, line up the decimal points, and subtract: 0.0400 - 0.0025 = 0.0375

What number is 62.5% of 192?

If you simply recognize that 62.5%= 0.625= 5/8, this problem will be a lot easier. 5/8 x 192= 5/1x24= 120. (Multiplying 0.625 x 192 will take much longer to complete)

Which integer values of b would give the number: 2002/ 10^-b a value between 1 and 100?

In order to give 2002 a value between 1 and 100, you must shift the decimal point to change the number to 2.002 or 20.02. This requires a shift of either two or three places to the left. Remember that while multiplication shifts the decimal point to the right, division shifts it to the left. To shift the decimal point 2 places to the left, you would divide by 10^2. To shift 3 places to the left, you would divide by 10^3. Therefore, the exponent -b is equal to {2,3}, and b is equal to {-2, -3}.

Decide whether the given operation will cause the original value to increase, decrease, or stay the same: Add 1 to the numerator of a positive, prover fraction and subtract 1 from its denominator.

Increase: As the numerator of a positive, proper fraction increases, the value of the fraction also increases. Both actions will work to increase the value of the fraction.

Decide whether the given operation will cause the original value to increase, decrease, or stay the same: Divide a positive, proper fraction by 3/13.

Increase: Dividing a positive number by a positive, proper fraction increases the number.

Decide whether the given operation will cause the original value to increase, decrease, or stay the same: Multiply the numerator of a positive, proper fraction by 3/2.

Increase: Multiplying the numerator of a positive fraction by a number greater than 1 increases the numerator. As the numerator of a positive, proper fraction increases, its value increases.

Simplify: 0.00081/0.09

Shift the decimal point 2 spaces to eliminate the decimal point in the denominator: 0.00081/0.09= 0.081/9 Now divide. First, drop the 3 decimal places : 81/9= 9. Then put the 3 decimal places back: 0.009.

Express the following as decimals: 12 8/3

Simplify the mixed number first, if needed: 12 8/3= 12+ 2 2/3= 14 2/3= 14.6

2x:y is equivalent to 4x: 8500. What is y?

Simplify the ratio on the right-hand sign of the equation to match the one on the left. 2x/y= 2x/4,250 Since the numerators are identical, y must equal 4,250.

48:2x is equivalent to 144:600. What is x?

Simplify the ratios and cancel factors horizontally across the equals sign. 48/2x= 144/600 = 24/x= 6/25 = 4/x= 1/25 Then cross-multiply- x=100

Decide whether the given operation will cause the original value to increase, decrease, or stay the same: Multiply both the numerator and denominator of a positive, proper fraction by 3 1/2.

Stay the same: multiplying or dividing the numerator and denominator of a fraction by the same number will not change the value of the fraction.

200 is 16% of what number?

This is a percent vs. decimal conversion problem. If you simply recognize that 16%= 0.16= 16/100= 4/25, this problem will be a lot easier: (4/25)x= 200, so x= 200 x 25/4= 50 x 25= 1,250. (Dividing out 200/0.16 will prob take longer to complete.

Express the following as fractions and simplify: 2.45

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify: 2.45= 2 45/100= 2 9/20 (mixed)= 49/20(improper)

Express the following as percents: 1000/10

To convert a fraction to a percent, rewrite the fraction with a denominator of 100: 1000/10= 10,000/100= 10,000%

Express the following as decimals: 1 27/4

To convert a mixed number to a decimal. simplify the mixed number first, if needed: 1 27/4= 1+ 6 3/4= 7.75

Express the following as fractions and simplify: 420%

To convert a percent to a fraction, write it over a denominator of 100 and simplify: 420%= 420/100= 21/5= 4 1/5