Multiplying 23.4 and 2.53, you get 59.202. Ensure the decimal is in the correct position.
To compare decimals, check the tenths place first. If two numbers have the same value in the tenths place, then check the hundredths place, and then the thousandths place if necessary
Divide 96 by 128 to get 0.75, which is equivalent to 75%
Write the three terms vertically and be sure to line them up so that the decimal points are all directly above each other. For the first two terms, you can fill in additional zeroes so that there are three digits to the right of the decimal.
The interior angles of a triangle sum to 180 degrees. We know one angle is 30 degrees, so subtracting that from 180, we know the sum of the remaining two angles is 150. The problem then says that the larger remaining angle is twice the measure of the smaller one. From here, we can set up an equation to solve for a smaller angle x: 2x+x=150 Then combine the terms with x: 2x+x=3x 3x=150 Divide both sides by 3 isolate x: 3x⁄2 = 150⁄3 x = 150 Therefore, the measure of the smaller angle is 50.
The least common denominator of 2⁄3 and 1⁄4 is 12, so convert fractions to have a denominator of 12 and you will get 8⁄12 and 3⁄12. Then, and the fractions and add the whole numbers to get 1111⁄12.
To divide by a fraction, multiply by the reciprocal. The problem 6⁄7 ÷ 1⁄8 then becomes 6⁄7 * 8⁄1 = 48⁄7. To simplify the answer, divide 48 by 7. 48 ÷ 7 = 6 because 7 * 6 = 42 48 - 42 = 6 so there are 6 left over, which equals 6⁄7 We arrive at the answer, 6 6⁄7.
The greatest common factor of 16 and 64 is 16, so divide the numerator and denominator by 16 to get 1⁄4.
25 x 10 = 250, so the product of the two given numbers will be a bit above 250 with the decimals included. The only other number that is close is 200, but it should be clear that 200 is too low.
6 3⁄4 - 3 1⁄3 = The least common multiple of 3 and 4 is 12, so convert both fractions to 12ths: 6 9⁄12 - 3 4⁄12. Then, subtract the whoe numbers and the numerators of the fractions to get 3 5⁄12.
Divide 8 into 5 by putting a decimal and extra zeroes at the end of the 5 (such as 5.000). When you get the first two decimal places, you don’t need to go any further since none of the other answers are possible choices any longer.
This one is a bit tricky but it can be helpful to translate the fractions into actual numbers. Starting with the colors, half are blue, 1⁄ are green, and the rest are yellow. There are 30 marbles total, so this means 15 are blue, 10 are green, and 5 are yellow. Regarding textures, 2⁄3 are smooth and the rest are rough, so there are 20 smooth marbles and 10 rough marbles. Half of the rough marbles are green, so there are 5 rough green marbles, and 5⁄30 reduces to 1⁄6 .
We know 1⁄3 of 240 is 80, so 1⁄3 of 250 is slightly more. The next closest answer is 70, but if it is not clear 70 is too small, divide 250 by 3 to see that 85 is closer to the actual number.
First, convert the fractions into slices of the pie: 1⁄2 * 8 = 4 slices (pepperoni) 3⁄8 * 8 = 3 slices (mushroom) 1⁄4 * 8 = 2 slices (pepperoni and mushroom) Right away, it looks like there have to be 9 slices total, since the fractional parts in the question add up to 9⁄8 . But this is inconsistent with the total of 8 slices given in the question, and the customer’s specification that 1/2 (or 4 slices) of the pie must contain pepperoni and 3/8 (or 3 slices) must contain mushroom. Going back to the 4 slices containing pepperoni, it does not say “pepperoni only.” So, some of the 4 slices must contain both pepperoni and mushroom. This is the same for the 3 slices containing mushroom, it does not say “mushroom only.”
The less common multiple of 7 and 4 is 28, convert both fractions so that they have 28 in the denominator. Multiplying the first fraction by 4⁄4 and the second by 7⁄7, we get 24⁄28 and 35⁄28. Adding the numerators gives 59⁄28. Note: Often, you will be required to change an improper fraction, like this answer, to a mixed number. However, 59⁄28 is correct and it is the only correct choice given for this question. Some modern tests consider improper fractions to be correct, especially those with “fill-in” responses.
To divide by a fraction, multiply by its reciprocal. The question then becomes 3⁄5 * 4⁄2, which equals 12⁄10. We can reduce this to 6⁄5, and then to the mixed numbers 1 1⁄5.
3⁄4 x 6⁄6 = 18⁄24, so the two fractions are equivalent.
The least common multiple of 5 and 3 is 15, so multiply the first fraction by 3⁄3 and the second by 5⁄5 so that both have 15 in the denominator. Then, subtract the numerators to get 17⁄15. OR, try this method: The least common multiple of 5 and 3 is 15. Sinnce you multiplied the 5 in the fraction 9⁄5 by 3 to get 15 in the denominator, you have to multiply 9 by 3, as well. So, the first fraction becomes 27⁄15. Similarly, multiply the 2 in the fraction 2⁄3 by 5 since you multiplied the 3 in that fraction by 5 to get the denominator of 15. This second fraction becomes 10⁄15. The resulting problem is 27⁄15 - 10⁄15 and the answer is 17⁄15.
First, let’s solve for x: 2 1⁄4 + x = 5 1⁄8 x = 5 1⁄8 - 2 1⁄4 x = (4+8⁄8 + 1⁄8) - 2 2⁄8 x = 4 9⁄8 - 2 2⁄8 x = 2 7⁄8 xx is clearly “greater than 2 and less than 3”, the correct answer.
7⁄8 of 400 is 350, so Sally will use 350 feet of fencing and have 50 feet left over.
Convert the second number from a mixed number to an improper fraction. Then, multiply the numerators and denominators to get 48⁄45. This fraction can be reduced by dividing the numerator and denominator by 3 to get 16⁄15, which is the correct answer.
Write the numbers on top of each other and line up the decimal points. If it is helpful, you can put zeroes after the decimals so that all of the numbers have the same amount of digits to the right of the decimal.
Write the numbers on top of each other and line up the decimal points. If it is helpful, you can put zeroes after the decimals so that all of the numbers have the same amount of digits to the right of the decimal.
Write the numbers on top of each other and line up the decimal points. Put a zero after the first number so both numbers have two digits to the right of the decimal. Then, subtract as usual and ensure the decimal point stays in the correct spot.
Write the numbers on top of one another. Multiply the numbers and make sure to put the decimal point three places in from the right, because there are a total of 3 decimal places in the 2 numbers being multiplied.
To get 75% of 190, multiply 0.75 x 190. The correct answer is 142.5, and 140 is the closest choice.
This problem can be approached in a few ways. First, we know 1⁄4 = 25, and 1⁄8 is half of 1⁄4, so 1⁄8 = 12.5. Then, multiply 12.5 to get 5⁄8 = 62.5. Alternatively, you can just divide 5 by 8 to get the decimal 0.625, which is equivalent to 62.5%.
When dividing by decimals, you want to start by making the divisor a whole number. To do this, shift the decimal one place to the right. Ensure you also move the decimal in the dividend (one place to the right). Your problem is now 360÷15, which will give you an answer of 24.
Write the numbers on top of each other, lining up the decimal points. Then, multiply them and ensure the decimal point goes over four places from the right in your final answer.
Write the numbers on top of each other, lining up the decimal points (put a decimal point to the right of the 10). Then, put three zeroes to the right of the decimal point, so 10 becomes 10.000. Finally, subtract the numbers, borrowing all the way from the left.
Start by estimating, multiplying 45 x 8 to get 360. This narrows it down to the two choices 365 and 385. Based on the estimation, 365 seems like the better choice. To be certain, we can estimate again by rounding both of our original numbers up and multiplying 46 by 8 to get 368. Since our higher estimation is only just above 365 and our first estimation was 360, we know the best choice is 3
Convert 35% to a decimal (0.35). Then, multiply 0.35 by 26.2 to get 9.17.
When comparing decimals, start with the tenths place. Only 0.058 has a zero in the tenths place, so it must be the smallest. Then, compare the hundredths place of the remaining three decimals to arrive at the correct answer.
First, it is clear that 0.5 is the smallest. Next, converting 65% to a decimal, we see that 0.65 > 0.605. All that remains is 7/8, so either divide 7 by 8 to get 0.875, or we know that 6/8 = 3/4 = 0.75, and 7/8 must be greater than that, so 7/8 must be the greatest number given.
First, find the area of the carpet by multiplying 8.5 by 10 to get 85. Then, because the room is 20% larger than the carpet, find 20% of 85 by converting 20% to the equivalent decimal number, .20 and multiplying it by 85. The answer is 17. Add this number to the area of the carpet to get the total area of the room, which is 102 square feet.
Think of the total number of pens contained in the box as a whole number, or a value equal to 1. Represent 1 as a fraction with a denominator common to the given fractions. The fraction 40⁄40 is a good choice because each of the denominators evenly divides into 40. Convert 1⁄4 for the green pens to fortieths, and we have 10⁄40. Convert 1⁄8 for the red pens to fortieths, and we have 5⁄40. Subtract the amount of green and red pens from the total: 40⁄40 - 5⁄40 - 10⁄40 = 25⁄40 black and blue pens. Since 1⁄5 of the remaining pens (25⁄40, which reduces to 5⁄8) are black, we compute the fraction of black pens by multiplying 1⁄5 with 5⁄8: 1⁄5 * 5⁄8 = 1⁄8 = 5⁄40 represents the fraction of black pens in the box. Solving for the fraction representing the blue pens, we subtract the amount of black pens from the total of blue and black pens: 25⁄40 - 5⁄40 = 20⁄40 = 1⁄2 of the box are blue pens.
Multiply 530 gallons/hour by 2.5 hours to get 1,325 gallons.
Multiply .45 (the decimal for 45%) by 240 to find that 108 is 45% of 240. Subtract 108 from 240 to get the number of books in English, which is 132.
A triangle has 180 degrees. If one angle is 90 degrees and one is 60 degrees, the remaining angle would be 30 degrees. Since the second angle is at least 60, the largest the third angle could be is 30 degrees.
The tank is 6 feet x 2 feet x 5 feet, so its total volume is 60 cubic feet. If 20 cubic feet are filled, 40 cubic feet are not, and 40⁄60 = 2⁄3.
We are trying to calculate 40% of 50, which is how many golf balls went past the 150-yard mark. To do that, change 40% into a decimal (.40) so we can multiply it by the number of balls, 50. The resulting problem is .40 x 50 = 20 (Remember to move the decimal point in the answer to the left the number of decimal places in the numbers being multiplied.)
1⁄3 of the animals are cats and1⁄9 are dogs, 1⁄3 x 45 = 15 cats 1⁄9 x 45 = 5 dogs Subtracting these 20 animals, there are 25 remaining.
Each curtain is 4 x 2 = 8 square feet. She needs 6 of them, so that makes 6 x 8 = 48 square feet of material total. Each square foot costs $14.00, so the total she spends will be $14.00 x 48 = $672.
The front and back of the shed measure 10 feet x 8 feet = 80 square feet each, times 2 of them = 160 square feet. The sides measure 12 feet x 8 feet = 96 square feet each, times 2 sides = 192 square feet. The total surface area of the shed is then 160 + 192 = 352 square feet. Each bucket of paint covers 50 square feet, so dividing, we see John needs 352÷50=7.04352÷50=7.04 buckets of paint. Since he can only buy whole buckets, and he needs more than 7, he will need to buy 8 buckets of paint.
This plain-language question actually translates directly to a mathematical statement or equation. It says: 75 is 60% of what number. In math, that is: 75=0.60⋅x Take note: “is” translates to “equals”; “of” translates to “times or multiply”; the unknown number can be assigned any letter (here we used x). Continuing with the equation, we divide both sides by 0.60 and get: 125=x Of course, it looks nicer with the sides swapped: x=125
Linda initially has a 2⁄3 -full bag of candies. She gives away 1⁄4 of 2⁄3: 2⁄3 - (1⁄4 * 2⁄3) = 2⁄3 - 1⁄6 Coverting 2⁄3 to its equivalent fraction of 4⁄6, and continuing to solve: 4⁄6 - 1⁄6 = 3⁄6 = 1⁄2
tudent tickets are sold at 30% discount from the regular price of $8.50: 8.50−(8.50⋅0.30)=8.50−2.55=5.95 8.50−(8.50⋅0.30)=8.50−2.55=5.95 A discounted student ticket will cost $5.95.
Let’s call the original price P, and write a problem to solve. We want to restate the information we have in order to solve for P, the answer to the question. The easiest way to do this is to set up ratios, then a proportion to solve. If the discount was 25%, we know that the sale price is 75% of the original price, P, which is 100%: 75⁄100 We know that this ratio equals the sale price (we know), compared to P, which we don’t know: 48⁄P To form the proportion to solve, set these 2 ratios equal to each other: 75⁄100 = 48⁄P (You would read this, “75 is to 100 as 48 is to P”) To solve a proportion, cross-multiply and you have: 75P=4800 75P=4800 To isolate the P and get the answer, divide both sides by 75: P=64
Amanda earned a total of $34.00 + $54.00 = $88.00 over 6 + 4 = 10 hours. Therefore, her average hourly wage was $88.00/10 = $8.80 per hour.
His final average was 86 over 5 tests, so letting x be the score on his final test, we know that: (84+78+72+96+x⁄5) = 86. Multiplying both sides of the equation by 5, we get: 330+x=430 x=100
