How to add, subtract, multiply and divide fractions and mixed numbers Fractions Review: How to add, subtract, multiply and divide fractions and mixed numbers Compiled and adapted by Lauren McCluskey from several power points by Monica Yuskaitis

This power point would not have been possible without Monica Yuskaitis.

Parts of a Fraction 3 = numerator = denominator 4 3 = dividend = divisor 4 Which means…3÷4

¾ looks like 1/4 1/4 1/4 Or 75% of the whole If you think about money, ¾ of a dollar equals $0.75 or 75 cents.

1/4 1/4 1/4 ¾ looks like Or 75% of the whole If the rectangle is 1 foot high, then each section is 0.25 ft.

How much of 4 is 3? To find how big a portion you have, divide the numerator by the denominator. 3÷4 = 0.75 or 75% So ¾ = 75%

How many quarters are in a whole? 4 1= 4/4 1/4 1/4 1÷4 = 1/4 1÷ ¼ = 4

How many quarters are in a half? ½ ÷1/4 = 2 1/4 2 1/4 Or: 2 quarters equals ½ dollar.

1 2 = 2 4 Equivalent Fractions Name the same amount but have different numerators and denominators. Or: Half a dollar = 2 quarters. 1 2 1 1 = 4 2 4 2 1 4

Equivalent Fraction Models ¼=2/8 1/8 1/8 1/4 1/4 1/8 1/8 1/8 1/4 1/8 1/4 1/8 So if you have 3 times as much, you have… 3 6 = 4 8

To Find Equivalent Fractions Multiply the numerator and the denominator by the same number. Or… 1 3 3 x = 3 3 9

To Find Equivalent Fractions Divide the numerator and the denominator by the same number. 4 4 1 ÷ = 12 4 3

Adding Like Denominators Only add the numerators 1/4 1/4 3 1 4 + = 4 4 4 1/4 1/4

Subtracting Like Denominators Only subtract the numerators 1/4 1/4 4 1 3 - = 4 4 4 1/4 1/4

To Add or Subtract Fractions with Unlike Denominators: 1/3 + 1/6 = ? 1/3 + 1/9 = ? Rewrite each fraction using the least common multiple.

Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42 Common Multiple A number that is a multiple of two or more numbers. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42

Shortcut for Finding the Least Common Denominator or Least Common Multiple Check to see if the smaller denominator divides evenly into the larger denominator. 1 3 1 3 will divide evenly into 9, so 9 is your LCD or LCM. + 9

To Add or Subtract Fractions With Unlike Denominators Rewrite the fractions using the least common denominator or least common multiple. 1 = 5 1 = + 10

To Add or Subtract Fractions With Unlike Denominators Now just add the numerators. 1 x 2 = 5 10 x 2 = Remember when adding fractions you never add the denominators. 1 1 + 10 10 10

Subtract these Fractions Use the short cut to find the Least Common Denominator (LCD). 1 2 1 - 8

Mixed Numbers Mixed numbers are whole numbers and fractions together. 1 3 1 1 1 = ½ 2

Shortcut for Finding the Least Common Denominator Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD or LCM. 1 3 2 1 1 + 2 will divide evenly into 8, so 8 is your LCD or LCM. 8

To Add Mixed Numbers With Unlike Denominators Find the multiples of each denominator. 1 3 4 = 4, 8, 12, 16, 20, 30 1 1 + 10 = 10, 20, 30, 40, 50

Compare the lists of multiples Compare the lists of multiples. Circle the common multiples between the two lists. 1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + = 10, 20, 30, 40, 50 10

1 3 4 20 1 1 + 10 20 x 5 = Ask yourself what you multiply 4 by Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. Ask yourself what you multiply 4 by to get 20. 1 3 4 20 x 5 = 1 1 + 10 20

To Subtract Two Mixed Numbers with Unlike Denominators Borrow 1 whole. Rename. Add to what you already had, then subtract. 2 answer= 1 / 1 = 5 20 = 25 + 20 20 20 4 - 1 8 4 8 = 20 10 20 17 20

Try it! 1 3 - 1 Answer= ? 2 3 5

Answer= 1 9/10 How did you do?

When would you multiply a fraction by a fraction? Your family eats 1/8 of 1/2 of a left-over wedding cake. 1/8 of 1/2 or 1/8 x 1/2 1/8* ½ = ?

Jose had already read 1/2 of his novel Jose had already read 1/2 of his novel. Today he read 1/12 of the 1/2 left. How much of the book has he read? 1/12 of 1/2 or 1/12 x 1/2

Multiplying Fractions When you multiply two fractions that are between 0 and 1 the product is smaller than both fractions. ½ x ¾ = 3/8 Look at the diagram on the next slide to understand why.

Multiplying Fractions ½ x ¾ = 3/8 ½ of ¼ = 1/8 ¼ ¼ ¼ ¼ 1/8 1/8 1/8

How to Find a Fraction of a Fraction: When you see a fraction problem with the word “of”, multiply. 1 4 x of 2 9

Multiply your numerators straight across. 1 x 4 4 = 2 9

Then multiply your denominators straight across. 1 x 4 4 = 2 9 18

Simplify your answer. In this case we reduce. 1 x 4 4 2 2 ÷ = = 2 9 18 2 9 ÷

When would you multiply a fraction and a whole number? You walk a 4 mile route halfway. ½ of 4 or ½ x 4 You walk a ¾ mile route twice. 2 x ¾

A $12 ticket to the magic show is on sale for 2/3 of the original price. 2/3 of $12 or 2/3 x 12

How to Find the Fraction of a Whole Number The first thing to remember is “of” means multiply in mathematics. of = X (times)

Multiply. 1 x of 46 2

Change your whole number to a fraction by adding a one underneath. 1 x 46 2 1

Multiply your numerators straight across. 1 x 46 46 = 2 1

Multiply your denominators straight across. 1 x 46 46 = 2 1 2

Simplify your answer. In this case we change an improper fraction to a mixed number or a whole number. 23 1 x 46 46 2) = 46 2 1 2

Cross Simplifying: 46 1 = 1 2 23 = 1 2 X 1 X 1 X 46 Sometimes you can cross simplify before you multiply instead of afterwards. 46 1 = X 1 2 23 1 X 46 46÷2= 23 = 1 2 X 1 2÷2 = 1

When would you multiply a mixed number by a fraction? In a car race, the track is 2 ¼ miles long. If the car breaks down ½ way through the course, how far did you go? 1/2 of 2 1/4 or 1/2 x 2 1/4

Multiplying Fractions When you multiply a positive mixed number by a fraction between 0 and 1 the product is less than the mixed number. 1¼ x ½ = 5/8 Look at the diagram on the next slide to understand why.

Multiplying Fractions 1¼ x ½ = 5/8 ½ of ¼= 1/8 ¼ ¼ ¼ ¼ 1/8 1/8 1/8 1/8 ¼ ¼ ¼ ¼ 1/8

How to Find a Fraction of a Mixed Number The first thing to remember is “of” means multiply in mathematics. X (times) of =

When you see a fraction problem with the word “of” in it, you multiply. 1 4 x of 3 2 9

First change the mixed number to an improper fraction. 27 + 4 1 4 31 + x 3 2 9 9 x 27

Then multiply the numerators straight across. 1 31 31 x = 2 9

Next multiply the denominators straight across. 1 31 31 x = 2 9 18

Lastly simplify your answer Lastly simplify your answer. In this case change the improper fraction to a mixed number. 13 1 18 1 31 31 18) 31 x = 2 9 18 18 13

Dividing Mixed Numbers 2½ ÷ ¾ = ? ½ of ¼ = 1/8 ¼ ¼ ¼ ¼ 1/4 1/4 ¼ 1/4 1/4 1/4 1/4 1/4 1/4

2½ ÷ ¾ = ? Answer= There are 3 1/3 (¾’s) in 2 ½.

Dividing Mixed Numbers and Fractions Multiply the first number by the reciprocal of the second number. (To find the reciprocal flip it!) 5 ¼ ÷ ¼ = ? (The reciprocal is 4/1…) Change 5 ¼ into an improper fraction: 5 = 20/4 20/4 + ¼ = 21/4 21/4 * 4/1 = 84/4 Simplify: 21

Try it! 3 ¾ ÷ ¾ = ?

Answer= 5

Credits Monica Yuskaitis and Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/ clipgallerylive/default.asp