For most floors, one or two gallons of water will suffice. If you need to clean a larger area, you can add an extra couple of gallons incrementally. The warmer the water, the better it will be for loosening stuck-on dirt and grime.  Before you start mopping, make sure you've cleared the floor of all removable furniture, appliances and other objects that might get in the way or be damaged by water. If the bucket is too big to fit under the sink, try filling it your bathtub. Aim for a ratio of roughly ½ to 1 cup of vinegar for every gallon of water. Swish the vinegar solution gently to make sure it’s blended. Vinegar is mildly acidic, which makes it useful for dissolving hardened residue.   Diluting the vinegar will prevent it from bleaching the color or wearing down the finish of your floor tiles. Other high-potency types of vinegar, such as apple cider vinegar, will also get the job done. Work your way across the tiles, mopping in a circular or side-to-side direction. Make sure to spread the vinegar over the entire surface of the floor. Don’t forget to run the mop beneath nearby furniture and along the baseboards.  As you mop, you should be able to see the results of the vinegar right away.  Be careful not to saturate bordering wood or carpet flooring with the vinegar solution. Empty the bucket and refill it with clean, warm water. Go back over the floor once more, wringing out and rewetting the mop every few feet. This will help clear the tiles of loose residue and any remaining traces of vinegar. Soak up excess water with the mop, a squeegee or an absorbent towel, then allow it to air dry completely.  If you skip the rinsing step, the dingy water will dry on the floor, leaving behind streaks and splotches.  Making sure that the grout has a chance to dry out is essential for preventing the growth of mold and mildew, which thrive in warm, moist spaces.
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One-sentence summary -- Fill a bucket with hot water. Add a cup of distilled white vinegar. Mop the tiles with the vinegar solution. Rinse the floor with fresh water.


All numbers in the 30s start with the word for the number 30, followed by the correct word for the digit in the ones place (numbers 1 through 9). This is the same pattern you saw for the French words for numbers in the 20s. Don't forget to add an et between the digits for 31 – trente et un (trahnt ay uh). While the t at the end of vingt is silent, the t is pronounced in trente and other French number words when it is followed by an e. So, for example, you would say trahnt-katr for 24. Continuing with the same pattern, start with 40 and then add the correct word for the digit in the ones place (numbers 1 through 9). Add an et between the digits for 41 – quarante et un (kah-rohnt ay uh). The word quarante is a good opportunity to practice your French r. Pull the sound from the back of your throat, as though you are gargling. Cinquante means 50 in French, but there's no need to stop there. As before, you can simply add the correct word for the digit in the ones place (numbers 1 through 9) to the word cinquante. Not only can you count to 50, you can easily count to 59 using number words you already know.   Cinquante has two vowels that are followed by an n, signaling a nasal pronunciation. This makes it a good word for you to practice making French nasal vowel sounds. Remember that 51 would be cinquante et un (sank-ohnt ay uh).
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One-sentence summary -- Say trente (trahnt) for the number 30. Use quarante (kah-rohnt) to count from 40 to 49. Learn cinquante (sank-ohnt) to finish counting to 50.


To find the greatest common factor (GCF) between two or more numbers, you need to start by breaking down each number into its prime number factors. You can use the factor tree method to do this.  You will need to create a separate factor tree for each number. The process required for making a factor tree is the same as described in the “Making a Factor Tree” section. The GCF between two or more numbers is the largest prime number factor that is shared between all of the given numbers in the problem. This number must divide evenly into all of the original numbers in the problem.  Example: Find the GCF of 195 and 260.  ......195 ....../....\ ....5....39 ........./....\ .......3.....13 The prime factors of 195 are: 3, 5, 13 .......260 ......./.....\ ....10.....26 .../...\ …/..\ .2....5...2...13 The prime factors of 260 are: 2, 2, 5, 13 Look at all of the factor trees created for your original values. Identify the prime factors of each original number, then highlight or write down all of the factor numbers that both lists have in common  If there are no common factors between the numbers, the GCF is the number 1.  Example: As noted previously, the factors of 195 are 3, 5, and 13; the factors of 260 are 2, 2, 5, and 13. The common factors between both numbers are 5 and 13. When two or more numbers have more than one common factor between them, you must find the GCF by multiplying all of the shared factors together.  If there is only one shared factor between two or more numbers, however, the GCF is simply that single shared factor.  Example: The common factors between 195 and 260 are 5 and 13. The product of 5 multiplied by 13 is 65. 5 * 13 = 65 The problem is now complete, and you should have your answer ready.  You can double-check your work, if desired, by dividing each of your original numbers by the GCF you calculated. If the GCF goes into each number evenly, the solution should be accurate.  Example: The greatest common factor (GCF) of 195 and 260 is 65.  195 / 65 = 3 260 / 65 = 4
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One-sentence summary --
Create a factor tree for each number in the set. Identify all of the common factors. Multiply the common factors together. Write your answer.