Math

• Relating decimals to fractions are the same because of there numbers and etc.
• 0.1 if turn to fraction is 1/10, but if 0.38 turn it to fraction it will be 38/100
• Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.
• Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.
• Divide decimals by multiplying both numbers by a factor of 10 so the divisor no longer has a decimal value. Then, use long division to divide as normal. Place the decimal point in the quotient directly above the decimal point in the dividend. Multiply both by 100 to get rid of the decimal part in the divisor.
• How to simplify. Example, 2/10, we can still simplify that. We have to find the GCF/Greatest common factor. 2-1,2 10-1,2,5,10, so 2 is the GCF and we divide that it will become 1/5
• To add or subtract fractions with different denominators, we need to make them equal. This process is called finding the least common multiple (LCM). First, write down all the denominators. Find the LCM of those denominators. Now, change one of the fractions into an equivalent fraction using the LCM as the new denominator. Add or subtract the fractions as usual. Finally, reduce your answer if possible.
• Multiplying Fractions: When multiplying fractions, simply multiply the numerators together and then multiply the denominators together. Reduce the resultant fraction if necessary.
• Fractions x Decimal: If you want to multiply a fraction by a decimal, just treat the decimal like any other whole number. So, instead of multiplying the numerator and denominator separately, multiply the entire fraction by the decimal.
• Addition of Decimals: To add decimals, align the decimal points vertically and add up the corresponding digits. If there are more zeros at the end than needed, remove them. If there aren't enough zeros, fill in the missing places with zeroes.
• Subtraction of Decimals: To subtract decimals, line up the decimal points vertically and borrow from the next place over when subtracting a larger number from a smaller number. Remember to always carry over the borrowed amount.
• A mixed number is made up of a whole number plus a fraction. It’s important to remember that when adding or subtracting mixed numbers, you must always keep the whole number separate from the fraction. You cannot combine the whole number and the fraction until the very end of the problem.
• Decimals x Decimal: To multiply two decimals, follow these steps: Write out the multiplication problem. Move the decimal points in the numbers being multiplied so they are aligned on the right side. Multiply the corresponding digits from left to right. After the last digit, move the decimal point back to its original position.
• Fractions are numbers between zero and one. They represent parts of a whole. A fraction consists of a numerator (the top number), which represents how many parts there are, and a denominator (the bottom number), which tells us what kind of parts they are. For instance, ½ means half of something; ¼ means a quarter of something; ⅛ means eighth of something.
• The product of a fraction and a whole number is found by multiplying the numerator of the fraction by the whole number and leaving the denominator unchanged. If the resulting product is not already a whole number, leave it as a mixed number.
• A mixed number is made up of a whole number and a proper fraction. It is also sometimes called a compound fraction. Mixed numbers are used when there is more than one whole unit involved. They are often seen in real life situations such as measuring time, distance, weight, etc.
• Multiplication of Decimals: To multiply two decimals, follow these steps: 1. Align the decimal points vertically. 2. Multiply the corresponding digits. 3. Count the total number of decimal places in the product. The decimal point goes in this many positions to the right of the last nonzero digit. 4. Write the decimal point in the correct location and complete the multiplication.
• Division of Decimals: To divide two decimals, follow these steps: 1. Flip the second decimal around so that it becomes a fraction. 2. Perform the division problem. 3. Check whether the result is a terminating decimal or repeating decimal. If it is neither, continue adding trailing zeros until the result is a terminating decimal. 4. Remove the extra zeros from the result.
• Multiplication of Decimals: Multiplying two numbers with decimals involves moving the decimal point to the right in both numbers until they are no longer decimals, performing the multiplication, and then moving the decimal point back to its original position.
• Subtraction of Decimals: To subtract decimals, first ensure that they have the same number of decimal places. If not, move the decimal place(s) over until they match. Subtract the smaller digit from the larger digit and carry out the operation on the remaining digits. Move the decimal back to its original position.
• When adding or subtracting mixed numbers, first convert both mixed numbers to improper fractions. Then, perform addition/subtraction on these fractions. Afterwards, return the sum/difference back to its original form as a mixed number.
• Order of Operations: The correct sequence of operations is Parentheses, Exponents, Multiplication & Division, Addition & Subtraction. Always follow this rule to get the correct answers.
• Multiplication of Mixed Numbers: Multiplying mixed numbers involves converting the mixed numbers to improper fractions, multiplying the two fractions, and returning the product to its original form as a mixed number.
• Fractions can be added by finding their least common multiple (LCM).
• Subtraction of Fractions: When subtracting fractions, find their least common denominator (LCD), write them as equivalent fractions under LCD, subtract numerators, and reduce if necessary.
• The LCM is found using prime factorization - identify the factors of each denominator and write down only those that appear more than once.
• Dividing Fractions: Invert the second fraction and flip it around so that the dividend becomes the numerator and the divisor becomes the denominator. Then, multiply the resulting fraction.
• Once we have our LCM, we create an equivalent fraction for each term by multiplying it by the ratio of the new denominator over the old one.
• Multiplying Fractions: To multiply fractions, simply multiply the numerators together and then multiply the denominators together.
• When adding or subtracting fractions, make sure they share a common denominator.
• To add or subtract fractions with different denominators, first find the lowest common denominator (LCD) of all the fractions involved.
• Division of Decimals: Divide the digits on top by the digits below, then move the decimal point one place to the left for every digit divided.
• Adding/subtracting decimals with different places requires moving decimal points until they are aligned.
• We do this by finding the lowest common multiple (LCM) of all the denominators involved.
• Multiplying Decimals: To multiply decimals, move the decimal point one place to the right for every digit multiplied.
• Addition of Fractions with Different Denominators: Find the LCM of denominators, change all fractions into an equivalent fraction using the LCM, add up the new numerator values, then simplify the resultant fraction.
• To add fractions with different denominators, we need to make sure they have the same denominator so that they are like terms.
• Multiply the numerator of each fraction by the LCM and add them together.
• The LCM will always be one of the remaining factors.