Think of the multiples of each denominator. For the first fraction, some multiples of 2 are 2, 4, 6, 8, and 10. For the second fraction, some multiples of 4 are 4, 8, 12. Find the smallest multiple each denominator has in common. In this case, the smallest multiple is 4. Rewrite one or both fractions as equivalent fractions, so that they have the same denominator. Use the smallest common multiple. In this case, 4. For the first fraction, 12=24{\displaystyle {\frac {1}{2}}={\frac {2}{4}}}, so you can rewrite the problem as 24+24{\displaystyle {\frac {2}{4}}+{\frac {2}{4}}}. Add the numerators. Keep the common denominator: 24+24=44{\displaystyle {\frac {2}{4}}+{\frac {2}{4}}={\frac {4}{4}}}.
For example, to divide 4÷13{\displaystyle 4\div {\frac {1}{3}}}, you would find 14×3=112{\displaystyle {\frac {1}{4\times 3}}={\frac {1}{12}}}.
For example, to divide 15)3045¯{\displaystyle 15{\overline {)3045}}}, your first step is to divide 15 into 30. Since 30÷15=2{\displaystyle 30\div 15=2}, you would write a 2 above the 0. Next, multiply 15×2=30{\displaystyle 15\times 2=30}. Subtract 30−30=0{\displaystyle 30-30=0}. Bring down the 4. Since you can’t divide 15 into 4, place a 0 above the 4. Multiply 15×0=0{\displaystyle 15\times 0=0}. Subtract 4−0=4{\displaystyle 4-0=4}. Bring down the 5. Divide 45÷15=3{\displaystyle 45\div 15=3}. Write the 3 above the 5. Multiply 15×3=45{\displaystyle 15\times 3=45}. Subtract 45−45=0{\displaystyle 45-45=0}. So, 3045÷15=203{\displaystyle 3045\div 15=203}, with no remainder.
For example, to add 10. 25+8. 5{\displaystyle 10. 25+8. 5} rewrite the numbers so that they are on top of each other, with the decimal points lined up. Then, add a 0 to 8. 5, so that it becomes 8. 50. Next, you can add the number like you normally would. You get 1875. When you drop down the decimal point into your answer, you get 18. 75.
For example, to multiply 3. 25×1. 75{\displaystyle 3. 25\times 1. 75}, begin by multiplying 325×175=56875{\displaystyle 325\times 175=56875}. Then, since there are 2 places behind the decimal point in 3. 25, and 2 places behind the decimal point in 1. 75, you would count 4 places from the right in your answer. So 56875 becomes 5. 6875.
You can measure the volume of a shape by counting the number of unit cubes that fit inside the shape. For example, if you have a box that is 2 cubes long, 3 cubes wide, and 1 cube high, you can fit one layer of 6 cubes inside of it. This means the volume is 6 cubic units. If the box is 2 cubes high, you can fit 2 layers of 6 cubes inside of it. So that means the volume is 12 cubic units. You can find the volume of shape by using a formula. A formula is like a recipe that tells you how to find something. The formula for the volume of a cube is volume=length×width×height{\displaystyle {\text{volume}}={\text{length}}\times {\text{width}}\times {\text{height}}}. For the box that is 2 cubes long, 3 cubes wide, and 2 cubes high, you would multiply 2×3×2=12{\displaystyle 2\times 3\times 2=12}. So the volume is 12 cubic units.
So, 37% equals 37100{\displaystyle {\frac {37}{100}}}, as 37 goes on the numerator, and the percent goes on the denominator.
For example, consider the problem 234{\displaystyle 2{\tfrac {3}{4}}} + 114{\displaystyle 1{\tfrac {1}{4}}}. Firstly, convert the mixed numbers to improper fractions. 234{\displaystyle 2{\tfrac {3}{4}}} equals 114{\displaystyle {\frac {11}{4}}}, as you multiply the whole number by the denominator and add the numerator to get the improper fraction. Subsequently, 114{\displaystyle 1{\tfrac {1}{4}}} equals 54{\displaystyle {\frac {5}{4}}}. Then, add 114{\displaystyle {\frac {11}{4}}} and 54{\displaystyle {\frac {5}{4}}}. The total is 164{\displaystyle {\frac {16}{4}}}, which equals 4.
For dividing decimals, move the decimal for the dividend if necessary. If you moved the decimal for the divisor, you also need to move the decimal for the dividend. Move it the same number of places. This may mean that you’ll need to add zeroes if necessary. For example, for 4. 5 ÷ 0. 05, move the decimal to the right 2 times to make the dividend a whole number. You’ll also need to move the decimal two times for the divisor. The problem becomes 450 ÷ 5. Then, divide as usual. First, pretend that the decimal points aren’t there. Multiply each digit as usual. After you’ve multiplied two layers of numbers and added them up, see how many numbers are behind the decimal in the original problem. For example, in 0. 12 x 0. 02, 12 and 02 are behind the decimal points, so you move the decimal point from the very right to 4 places in front of the last digit. You may have gotten 24, but you need to move the decimal from behind 4 to 4 places in front of it. This equals 0. 0024.
For example, 0. 5 equals 510{\displaystyle {\frac {5}{10}}}. The 5 is in the tenths place, so you multiply the five by 110{\displaystyle {\frac {1}{10}}}. Similarly, 0. 34 equals 310{\displaystyle {\frac {3}{10}}} + 4100{\displaystyle {\frac {4}{100}}}. The 3 is in the tenths place, so it is multiplied by 110{\displaystyle {\frac {1}{10}}}. The 4 is in the hundredths place, so it is multiplied by 1100{\displaystyle {\frac {1}{100}}}.
Consider the number 15. What numbers multiply to get 15? 3 and 5 do, and so do 15 and 1. So, 1, 3, 5, and 15 are all factors of 15. Another example would be factoring 84. Since 84’s an even number, you know that it has 2 as one of its factors. 84 divided by 2 would be 42, so 42 is also a factor of 84. 4 is also a factor of 84; 21 x 4 = 84. Because 4 x 21 is 84, 21 is another factor of 84. If you’ve memorized your times tables up to 12, you know that 7 x 12 is 84, so 7 and 12 are additional factors of 84. As 8 and 4 added together equals 12 (which is a factor of 3), it is also a factor of 3! 3 x 28 is 84, so 3 and 28 are factors of 84 too. 6 and 14 are more examples of 84’s factors. Lastly, 84 and 1 (the number itself and 1) are naturally factors of 84, so they are added to the factor list of 84. Now, order all of the factors of 84 from least to greatest. The factors of 84 are 1, 2, 3, 4, 6, 12, 14, 21, 28, 42, and 84.
Consider the number 15. What numbers multiply to get 15? 3 and 5 do, and so do 15 and 1. So, 1, 3, 5, and 15 are all factors of 15. Another example would be factoring 84. Since 84’s an even number, you know that it has 2 as one of its factors. 84 divided by 2 would be 42, so 42 is also a factor of 84. 4 is also a factor of 84; 21 x 4 = 84. Because 4 x 21 is 84, 21 is another factor of 84. If you’ve memorized your times tables up to 12, you know that 7 x 12 is 84, so 7 and 12 are additional factors of 84. As 8 and 4 added together equals 12 (which is a factor of 3), it is also a factor of 3! 3 x 28 is 84, so 3 and 28 are factors of 84 too. 6 and 14 are more examples of 84’s factors. Lastly, 84 and 1 (the number itself and 1) are naturally factors of 84, so they are added to the factor list of 84. Now, order all of the factors of 84 from least to greatest. The factors of 84 are 1, 2, 3, 4, 6, 12, 14, 21, 28, 42, and 84.
Consider the number 15. What numbers multiply to get 15? 3 and 5 do, and so do 15 and 1. So, 1, 3, 5, and 15 are all factors of 15. Another example would be factoring 84. Since 84’s an even number, you know that it has 2 as one of its factors. 84 divided by 2 would be 42, so 42 is also a factor of 84. 4 is also a factor of 84; 21 x 4 = 84. Because 4 x 21 is 84, 21 is another factor of 84. If you’ve memorized your times tables up to 12, you know that 7 x 12 is 84, so 7 and 12 are additional factors of 84. As 8 and 4 added together equals 12 (which is a factor of 3), it is also a factor of 3! 3 x 28 is 84, so 3 and 28 are factors of 84 too. 6 and 14 are more examples of 84’s factors. Lastly, 84 and 1 (the number itself and 1) are naturally factors of 84, so they are added to the factor list of 84. Now, order all of the factors of 84 from least to greatest. The factors of 84 are 1, 2, 3, 4, 6, 12, 14, 21, 28, 42, and 84.
If you make a mistake, stay calm. Learn from it, and try again.
Cool Math is a great web site that has many free math games. [9] X Research source Make sure you know the password to math games you play at school, like ST Math (JiJi) or iReady, so that you can play at home or when you have a substitute teacher. Play math board games the right way. Follow the directions. If you don’t follow the directions, the game might not be helping you use math. Some board games you need to use math to play include Pay Day, Ticket to Ride, or Sumoku. You can also find many variations of math bingo and Monopoly.
A friend can also be very helpful. If you don’t know how to do a problem, your friend might. You might be able to do some problems your friend can’t.
Even if your teacher doesn’t check your agenda every day, write down your math homework. This way, when you get home, you can remember what you are supposed to do.
Completing all of your work will also help you get a good grade in math. Even a few missed assignments can hurt your grade. In fifth grade, the most important thing is that you do your work. Teachers usually give you full credit for assignments if you try your best. If you don’t turn in your work at all, you won’t earn any points.
You should have a folder that is just for math work. Keep your classwork and graded work in this folder. You should also have a folder that is just for homework. When you complete your homework, put it in your homework folder. Put your homework folder in your bookbag right away. This way, you won’t forget to take it to school the next day.
Teachers are very busy. Even if your teacher does not have extra time to help you, don’t get upset. Ask your teacher if you can work with a partner who can help you learn the topics you are struggling with. Try to be specific when you ask for help. For example, don’t say, “I don’t get fractions. " Instead, ask, “Can you explain again how to change fractions so they have the same denominator?” If the teacher knows that you have a specific problem, it will be easier to take the time to stop and help.
Some good sites with written lessons are Cool Math[11] X Research source and Math is Fun. [12] X Research source A very popular site with videos is Khan Academy. [13] X Research source
Your parents can find you a tutor through websites like WyzAnt[15] X Research source or Varsity Tutors[16] X Research source . Most tutors will meet with you in person, but you can also find a tutor who will work with you online through the computer.
