Core Focus on Decimals & Fractions Dividing Decimals by Decimals Lesson 2.6

Warm-Up Find the value of: ÷ ÷ ÷

Dividing Decimals by Decimals Find quotients of expressions where decimals are divided by decimals. Lesson 2.6

Good to Know! Dividing requires you to look at how many groups of one number fit into another number. When dividing by decimals, the same approach applies. Example 24  6 can be read as, “How many groups of 6 fit in the number 24?” 2.4  0.6 can be read as, “How many groups of 0.6 fit in the number 2.4?” Base-ten blocks can be used to model decimal division. The model below shows the expression 2.4  0.6 in base-ten blocks. 2.4 There are 4 groups of 0.6 in the number 2.4.

Dividing Decimals by Decimals 1.Change the divisor into a whole number by moving the decimal to the right. 2.Move the decimal point in the dividend the same number of places to the right as was moved in the divisor. 3.Divide the dividend by the divisor. 4.Move the decimal point into the quotient directly above the decimal point in the dividend. 5.Insert zeros, if necessary, to hold place values.

Example 1 Thuyet purchased 3.2 pounds of fertilizer for $4.48. To determine how much he paid per pound you must find $4.48 ÷ 3.2. Rewrite the problem. When dividing by a decimal the divisor needs to be a whole number. Do this by moving the decimal point to the right in the divisor first. Divisor 3.2. The decimal point in the dividend must be moved the same number of places to the right as in the divisor. DivisorDividend The decimal point was moved one place to the right. Move the decimal point one place to the right.

Example 1 Continued… Thuyet purchased 3.2 pounds of fertilizer for $4.48. To determine how much he paid per pound you must find $4.48 ÷ 3.2. Find the quotient using the new44.8 ÷ 32 dividend and divisor. Thuyet’s fertilizer cost $1.40 per pound.

Example 2 Find the value of 67.2 ÷ 0.56 Change the divisor into a whole number and move the decimal point the same number of places to the right in both the divisor and the dividend. Divide the dividend by the divisor as if both were whole numbers. Move the decimal point into the quotient directly above the decimal point in the dividend ÷ 0.56 = 120 Insert a zero on the end of the dividend to hold place-value when the decimal point is moved. Zero is the last digit in the quotient because 0  56 = 0

Example 3 Joe makes $8.30 per hour. Macie makes $12.45 per hour. How many times greater is Macie’s hourly pay than Joe’s hourly pay? To find how many times greater Macie’s hourly pay is, write a multiplication equation. Use division to find the missing number. Change the divisor into a whole number. Move the decimal point the same number of places to the right in both the divisor and the dividend. $8.30  _____ = $12.45 $12.45  $8.30 Remember 8.30 is the same as 8.3.

Example 3 Continued… Joe makes $8.30 per hour. Macie makes $12.45 per hour. How many times greater is Macie’s hourly pay than Joe’s hourly pay? Divide the dividend by the divisor as if both were whole numbers. Move the decimal point into the quotient directly above the decimal point in the dividend. Macie makes 1.5 times the amount per hour that Joe makes.

Example 4 Landon put gallons of gas into his car last week. This week he put in gallons of gas. How many times greater was the amount of gasoline last week than this week? Round to the nearest tenth. Change the divisor into a whole number. Move the decimal point the same number of places to the right in both the divisor and the dividend. Divide the dividend by the divisor as if both were whole numbers. Stop dividing when you have one more place- value position in the quotient than needed.

Example 4 Continued… Landon put gallons of gas into his car last week. This week he put in gallons of gas. How many times greater was the amount of gasoline last week than this week? Round to the nearest tenth. Move the decimal point into the quotient directly above the decimal point in the dividend. Round to the nearest tenth. Last week’s fill-up was approximately 1.1 times more than this week’s fill-up.

Communication Prompt What is the most challenging part about dividing with decimals for you?

Find the value of: ÷ ÷ Jennifer spent $ at the mall. Sally spent $ How many times greater is the amount that Jennifer spent than the amount that Sally spent? Find the value of the following expressions. Round to the nearest hundredth, if necessary ÷ Michel bought 2.3 pounds of deli-meat for $9.09. How much did the meat cost per pound? Exit Problems times greater $3.95 per pound