# Dividing decimals

CCSS Math: 5.NBT.B.7
We'll start with simple problems like 3 / 2 and build to more complex problems like 4.5 / 0.15.
In this article, you'll learn how to divide decimals by jumping in and giving it a try without being shown how to do it first.
The problems go from easier to more difficult. Along the way there are examples and explanations to help you out if you get stuck. If you get a little confused, just think of it as a chance to learn!
Let's start by dividing whole numbers to get a decimal.
Example: $9 \div 4$
One way to solve this problem is to think in terms of hundredths:
$\phantom{=}9 \div 4$
$=9.00 \div 4$
$= 900$ hundredths $\div ~4$
$= 225$ hundredths
$= 2.25$
Another way is to convert the division problem to a fraction with a denominator of 100:
$9 \div 4 = \dfrac{9}{4}~~~~\small\gray{\text{Rewrite the division problem as a fraction.}}$
$= \dfrac{9 \times 25}{4 \times 25}~~~~\small\gray{\text{Multiply the top and bottom by 25.}}$
$= \dfrac{225}{100}$
$= 2.25$

### Problem set 1:

Problem 1a
$3 \div 2 =$

Beautiful, let's move on to dividing larger whole numbers.
Example: $19 \div 2$
$\phantom{=} 19\div 2$
$= \dfrac{19}{2}$
$=\dfrac{18 + 1}{2}~~~~~~~~\small\gray{\text{Split 19 into 18 and 1}.}$
$=\dfrac{18}{2} + \dfrac{1}{2} ~~~~~~~~\small\gray{\text{Break into two fractions.}}$
$=9 + \dfrac12~~~~~~~~\small\gray{\text{Simplify.}}$
$=9 + 0.5$
$=9.5$

### Problem set 2:

Problem 2a
$27 \div 4 =$

Great, now we'll work on dividing a decimal by a whole number.
Example: $4.2 \div 6$
Let's think in terms of tenths:
$\phantom{=}4.2 \div 6$
$= 42$ tenths $\div ~ 6$
$= 7$ tenths

### Problem set 3:

Problem 3a
$2.5 \div 5 =$

Nice! Let's move onto working with slightly bigger numbers.
Example: $9 \div 60$
Let's break 60 down:
$9 \div 60 = 9 \div 6 \div 10~~~~~~~~\small\gray{\text{Break 60 into 6 and 10.}}$
$\phantom{9 \div 60} = (9 \div 6) \div 10$
$\phantom{9 \div 60} = 1.5 \div 10$
$\phantom{9 \div 60} = 0.15$

### Problem set 4:

Problem 4a
$9 \div 30 =$

Sweet! Next up are even bigger numbers!
Example: $20 \div 80$
Let's rewrite this equation as a fraction and factor out multiples of 10:
$20 \div 80 = \dfrac{20}{80}~~~~~~~~\small\gray{\text{Rewrite the division problem as a fraction.}}$
$\phantom{20 \div 80} = \dfrac{2 \times 10}{8 \times 10}~~~~~~~~\small\gray{\text{Factor out multiples of 10.}}$
$\phantom{20 \div 80} = \dfrac{2}{8} \times \dfrac{10}{10}~~~~~~~~\small\gray{\text{Break into two fractions.}}$
$\phantom{20 \div 80} = \dfrac{1}{4} \times 1~~~~~~~~\small\gray{\text{Simplify.}}$
$\phantom{20 \div 80} = 0.25 \times 1$
$\phantom{20 \div 80} = 0.25$

### Problem set 5:

Problem 5a
$50 \div 40 =$

Baller. Now we'll divide decimals by decimals.
Example: $0.9 \div 0.3$
One way to solve this problem is to think in terms of tenths:
$\phantom{=}0.9 \div 0.3$
$= 9$ tenths $\div ~3$ tenths
$= 3$
Another way is to convert the division problem to a fraction, then multiply the top and bottom of the fraction by 10 so that you can work with whole numbers:
$0.9 \div 0.3 = \dfrac{0.9}{0.3}$
$\phantom{0.9 \div 0.3} = \dfrac{0.9 \times 10}{0.3 \times 10}$
$\phantom{0.9 \div 0.3} = \dfrac{9}{3}$
$\phantom{0.9 \div 0.3} = 3$

### Problem set 6:

Problem 6a
$0.8 \div 0.2 =$

Awesome! Let's try a few that are a bit harder.
Example: $7.6 \div 0.1$
One way to solve this problem is to think in terms of tenths:
$\phantom{=}7.6 \div 0.1$
$= 76$ tenths $\div ~1$ tenth
$= 76$
Another way is to convert the division problem to a fraction, then multiply the top and bottom of the fraction by 10 so you can work with whole numbers:
$7.6 \div 0.1 = \dfrac{7.6}{0.1}$
$\phantom{7.6 \div 0.1} = \dfrac{7.6 \times 10}{0.1 \times 10}$
$\phantom{7.6 \div 0.1} = \dfrac{76}{1}$
$\phantom{7.6 \div 0.1} = 76$

### Problem set 7:

Problem 7a
$4.5 \div 0.1=$

Great, we'll finish with a few more challenging problems.
Example: $5.4 \div 0.9$
One way to solve this problem is to think in terms of tenths:
$\phantom{=}5.4 \div 0.9$
$= 54$ tenths $\div ~9$ tenths
$= 6$
Another way is to convert the division problem to a fraction, then multiply the top and bottom of the fraction by 10 so you can work with whole numbers:
$5.4 \div 0.9 = \dfrac{5.4}{0.9}$
$\phantom{5.4 \div 0.9} = \dfrac{5.4 \times 10}{0.9 \times 10}$
$\phantom{9.4 \div 0.9} = \dfrac{54}{9}$
$\phantom{5.4 \div 0.9} = 6$

### Problem set 8:

Problem 8a
$12 \div 0.5 =$