Fractions that have the same value Equivalent fractions out of 100 In both of the shapes 2/5 of the shape is shaded. You can see that if the shape is divided into 5 equal parts, then 2 of those parts are shaded. If the shape is divided into 100 equal parts, then 40 parts are shaded. These are equivalent fractions as in both cases the same amount has been shaded. Tip! If the denominator (the bottom number) of a fraction divides into 100 then the fraction can be written as an equivalent fraction out of 100.
Using this method other fractions can be written as equivalent fractions out of 100 (percents). Here are some examples: =
The word percentage means out of 100. We use the % sign to show percentage. 10 squares out of 100 are shaded. This could be written as 10%. Writing this as a fraction you could say that 10 squares out of 100 are shaded. 10% = which can be simplified to.. We then divide the numerator by the denominator of the fraction to get the decimal, or divide the percent by 100, or use proportions. There are many ways to convert! To write a percentage as a fraction put the number over 100 and simplify if possible. PRACTICE- 45% = = 72% = = 3% = = Changing Percentages to Fractions and Decimals
Changing fractions to decimals using division To change a fraction to a decimal you can do it by a division. You can think of a fraction like 1/2 as meaning 1 ÷ 2 If you work out 1 ÷ 2 you get it as a decimal. 1 ÷ 2 = 0.5 so 1/2 = 0.5 In the same way 3/4 is 3 ÷ 4 so 3/4 = 3 ÷ 4 = 0.75 And 1/10 is 1 ÷ 10 so 1/10 = 1 ÷ 10 = 0.1 Changing fractions to decimals using division To change a fraction to a decimal you can do it by a division. You can think of a fraction like 1/2 as meaning 1 ÷ 2 If you work out 1 ÷ 2 you get it as a decimal. 1 ÷ 2 = 0.5 so 1/2 = 0.5 In the same way 3/4 is 3 ÷ 4 so 3/4 = 3 ÷ 4 = 0.75 And 1/10 is 1 ÷ 10 so 1/10 = 1 ÷ 10 = 0.1
Top tip! Here's a quick method for changing decimals to fractions. Look at the decimal and work out which number has the smallest value. For example in the decimal 0.75 the number 5 has the smallest value as 5/100. Write the decimal over hundredths: 75/ = which can be simplified to ¾ Here's another example. With the decimal the number 5 has the smallest value as. Write the decimal over thousandths: = which can be simplified to 7/ 200
Changing decimals to percentages using multiplication The quick way to change a decimal into a percentage is to multiply it by 100 For example to write 0.75 as a percentage multiply it by x 100 = 75 so 0.75 as a percentage is 75% - remember to add the % sign.
Changing percentages to decimals using division The quick way to turn a percentage into a decimal is to divide it by 100. For example to change 90% to a decimal do 90 ÷ ÷ 100 = 0.9 so 90% is the same as 0.9 In the same way divide 5% by 100 to make it into a decimal. 5 ÷ 100 = 0.05 so 5% = 0.05
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The word for ratios is Jane had 4 eggs and Tom had 10 eggs. What is the ratio of Tom’s eggs to Jane’s eggs? /4 can be simplified to 5/2
Practice Ratios DaQuan had 18 home runs and Olivia had 12 home runs. What is the ratio of Daquan’s homeruns to all the homeruns? Tamia made 20 bracelets and Chantel made 15. What is the ratio of bracelets Chantel made to the bracelets Tamia made? Skyler ate 16 skittles and Toree ate 24. What is the ratio of Skittles Skyler ate to the Skittles Toree ate?
…..and some more! What is the ratio of suns to hearts? What is the ratio of bolts to hearts? What is the ratio of bolts to all the shapes? What is the ratio of suns to bolts? What is the ratio of hearts and bolts to suns?
I Greatest Common Factor I’ve discovered the key to simplifying List the factors for each number and find the greatest one they have in common. To simplify a fraction, divide the numerator and denominator by their GCF
LCM That would be the least common multiple. List the multiples for each number and the first one that matches is IT!
Okay, that covers most of it! Study everything!