Fractions Fact Sheet



1.02 Fractions Fact Sheet

|Fractions show parts of a whole. |

|The denominator (number on the bottom) shows how many pieces are in the whole thing. |

|The numerator (number on the top) shows how many pieces someone or something has. |

|For example: ¾ or 3/4 of a candy bar |

|3 is the numerator, and you have 3 pieces of the candy bar |

|4 is the denominator and there are 4 pieces in the whole candy bar |

|A mixed number is a whole number and a fraction. It means you have a whole portion and part of another portion. |

|For example: 3½ or 3 1/2 of a pizza |

|3 is the whole number and ½ is the fraction. You have 3 whole pizzas plus another half of a pizza. |

| An improper fraction is a fraction where the numerator is larger than the denominator. It can be changed into a mixed number. |

|For example: 7/4 of a pie |

|There are 4 pieces in a whole pie. You have 7 pieces, so you have enough to make one whole pie and have 3 pieces left over. |

|You have 1¾ or 1 3/4 pies. 7/4 is the same as 1¾. |

|To add fractions, the fractions must have the same denominator. Add the numerators and keep the denominator the same. |

|For example: 4/6 + 1/6 = 5/6 |

|If the denominators are not the same, you must make them the same or find common denominators. The easiest way to do this is to look at the highest of the |

|denominators. |

| |

|For example: 2/3 + 2/6 = _____ |

|6 is the highest denominator. |

|To change the 3 (the other denominator) into a 6, you must multiply it by 2. |

|If you multiply the denominator by a number, you must multiply the numerator by the same number. So, multiply the numerator 2 by 2. (2 x 2 = 4) |

|The fraction is now 4/6 and the denominators are the same. |

|Add numerators, 4 + 2 = 6, and keep the denominators the same. 6/6 or 1 whole. |

|Remember: You must multiply the numerator and denominator by the same number. |

|To subtract fractions, the fractions must have the same denominator. Subtract the numerators and keep the denominator the same. |

|For example: 4/6 - 1/6 = 3/6 |

|If the denominators are not the same, you must make them the same or find common denominators. The easiest way tot do this is to look at the highest of the |

|denominators. |

|For example: 9/12 – 1/3 = _____ |

|12 is the highest denominator. |

|To change the 3 to a 12 you must multiply it by 4. |

|If you multiply the denominator by a number, you must multiply the numerator by the same number. So, multiply the numerator 1 by 4. (1 x 4 = 4) |

|The fraction is now 4/12 and the denominators are the same. |

|Subtract numerators, 9 – 4 = 5. and keep the denominators the same, 5/12. |

|Remember: You must multiply the numerator and denominator by the same number. |

|Any fraction that has the same numerator and denominator is equal to 1 whole. |

|For example: 3/3 = 1 whole 7/7 = 1 whole 20/20 = 1 whole |

|To simplify a fraction, you make the numerator and denominator as small as possible by dividing by the same number. |

|For example: 3/12 |

|Both the numerator and denominator can be divided by 3, so the fraction can be reduced. |

|3 ( 3 = 1 (numerator) and 12 ( 3 = 4 (denominator) so 3/12 can be reduced to ¼. |

| |

|You can simplify any fraction that has an even number for both the numerator and denominator. Divide each number by 2 and continue until it cannot be divided |

|by 2 evenly. |

|For example: 10/16 |

|10 ( 2 = 5 and 16 ( 2 = 8, so 10/16 can be reduced to 5/8. |

|Another example: 12/16 |

|12 ( 2 = 6 and 16 ( 2 = 8 to equal 6/8. Both numbers are still even, so they can be divided by 2 again. |

|6 (2 = 3 and 8 ( 2 = 4 to equal ¾. 3 is an odd number, so it cannot be reduced any further. |

|You need to be able to make conversions between these fraction families: |

|halves, fourths, and eights (1/2, 1/4, 1/8) |

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|thirds, sixths, and twelfths (1/3, 1/6, 1/12) |

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|fifths, tenths, hundredths, and thousandths (1/5, 1/10, 1/100, 1/1000) |

| |

|When converting a fraction to a decimal, divide the numerator by the denominator. |

|For example: ¾ = 3 ( 4 = .75 |

|When converting a decimal to a fraction, say the fraction aloud. |

|If there is one number after the decimal, the denominator is 10. |

|If there are two numbers after the decimal, the denominator is 100. |

|If there are three numbers after the decimal, the denominator is 1,000. |

|The numerator is the original number without any decimals. |

| |

|For example: .72 is seventy-two hundredths |

|the denominator is 100 |

|the numerator is 72 |

|the fraction is 72/100 |

| |

|Another example: .4 is four tenths |

|the denominator is 10 |

|the numerator is 4 |

|the fraction is 4/10 ( and it can be reduced to 2/5 by dividing each number by 2) |

| |

|Another example: .395 is three hundred ninety five thousandths |

|the denominator is 1000 |

|the numerator is 395 |

|the fraction is 395/1000 |

|When comparing fractions, it is easiest to change them into decimals by dividing the numerator by denominator. Fix the calculator to 2 places if you have a |

|TI-15. |

|For example: Place the fractions in ascending order (smallest to largest) |

|1/2 3/12 5/6 3/8 |

|1(2 = .50 3(12= .25 5(6= .83 3(8=.37 |

| |

|Think about money when you compare the numbers with decimals. |

|The smallest amount is .25 or 25 cents, which is 3/12, so it is first. |

|The next smallest amount is .37 or 37 cents, which is 3/8. |

|The next smallest amount is .50 or 50 cents, which is 1/2. |

|The largest amount is .83 or 83 cents, which is 5/6. |

|In ascending order the fractions are 3/12, 3/8, 1/2, and 5/6. |

| |

|To put the fractions in descending order (largest to smallest) you follow the same steps, but put the largest numbers first and end with the smallest number,. |

| |

|Hint: ascending starts with a, like the alphabet, so you start at the beginning and go up. |

|descending starts with d, so you start with the biggest number and go down |

|To compare fractions without a calculator, think about halves and compare each fraction to a half. |

|For example: Place the fractions is ascending order (smallest to largest) |

| |

|2/8 |

|1/2 |

|8/9 |

|4/7 |

| |

|half of eight would be four, so 2/8 is less than half |

|this is exactly one half |

|if there were nine slices and I had eight of them, I would only be one slice away from having the whole thing, so 8/9 is more than half |

|half of seven would be 3½ and I have 4 so I have just a little bit more than half |

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|Now I know that 2/8 is less than half, ½ is exactly half, 4/7 is just a little bit more than half and 8/9 is almost the whole thing, so I can put the fractions|

|in order. |

|ascending order would be 2/8, 1/2, 4/7, 8/9 |

|You can also use the clock to help you compare fractions. Always start at 12 and go to the center before you go to the next number. |

|Draw a line from the 12 to the 3 and you have ¼ of the clock. |

|Draw a line from 12 to 6 and you have ½ of the clock. |

|Draw a line from the 12 to the 9 and you have ¾ of the clock. |

|Draw a line from the 12 to the 4 and you have 1/3 of the clock. |

|Draw a line from the 12 to the 8 and you have 2/3 of the clock. |

|Draw a line from the 12 to the 2 and you have 1/6 of the clock. |

|Draw a line from the 12 to the 4 and you have 2/6 or 1/3 of the clock. |

|Draw a line from the 12 to the 6 and you have 3/6 or ½ of the clock. |

|Draw a line from the 12 to the 8 and you have 4/6 or 2/3 of the clock. |

|Draw a line from the 12 to the 10 and you have 5/6 of the clock. |

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