Comparing Fractions and Decimals

Lesson Objectives 4.NF.2 Compare fractions and decimals to the thousandths place. Essential Question: How can you compare decimals and fractions?

Vocabulary Words Least common denominator Least common multiple Equivalent Decimal

Definitions Least common denominator is the lowest common multiple of the denominators. The smallest number into which both of the denominators will divide exactly. Least common multiple is the smallest number that is the multiple of two of more numbers. Equivalent fractions are fractions with the same value. Decimal is a number in a number system based on 10, also known as the base 10 system.

Let’s Review Comparing fractions Comparing decimals

Comparing Fractions In order to compare fractions, the denominators for each fraction need to be the same. Find the Least Common Multiple Make equivalent fractions

Comparing Fractions 3 2 7 4 , 5 , 20 4: 4, 8, 12, 16, 20 5: 5, 10, 15, 20, 25 20: 20 LCM = 20

Now order these fractions from least to greatest. Comparing Fractions 3 15 2 8 7 7 4 20 5 20 20 20 Now order these fractions from least to greatest. = = = 7 20 2 5 3 4

Comparing Fractions Order these fractions 6 10 1 2 4 5 6 10 4 5 1 2

Comparing Decimals When comparing decimals, you have to look at the whole numbers. If the whole numbers are the same, then look at the decimal in the tenths place. Keep looking at the digits until you can identify which is the greatest or least.

Practice Time! Order from least to greatest Comparing Decimals Practice Time! Order from least to greatest Answers Problems 1.134, 1.341, 1.103 1.103, 1.134, 1.341 14.072, 14.172, 14.07 14.07, 14.072, 14.172 3.963, 3.63, 3.93 3.63, 3.93, 3.963

Converting Fractions to Decimals Think about how you say the fraction. .6 6 10 How many TENTHS are there? The 6 goes in the TENTHS place. = 8 100 .08 How many HUNDREDTHS are there? The 8 goes in the HUNDREDTHS place. =

Converting Fractions to Decimals If the denominator is not a tenth or hundredth, you will need to make an equivalent fraction using a 10 or 100 as the denominator. 4 5 8 10 = = .8

Converting Fractions to Decimals Let’s try a few! 3 4 75 100 = = .75 4 20 20 100 = = .20 10 25 40 100 .40 = =

Converting Decimals to Fractions Converting decimals to fractions is the opposite of converting fractions to decimals. Once again, read the fraction. What do you hear? Tenths or hundredths?

Converting Decimals to Fractions Think about how you say the decimal. .6 Read the decimal. The 6 is in the TENTHS place, so the denominator is 10. 6 10 = .08 8 100 What place is the 8 in? The HUNDREDTHS place. The denominator is 100. =

Converting Decimals to fractions Let’s try a few! 6 10 60 100 .60 = or 16 100 .16 = 40 100 4 10 .40 = or

Comparing Fractions and Decimals In order to compare fractions and decimals, you have to use all of the skills you have learned and reviewed in this session. You can not compare fractions and decimals. You have to convert them all to either fractions or all to decimals.

Comparing Fractions and Decimals Compare and order these fractions and decimals. 4 10 4 20 .60 1 2 .75 .4