Lesson 45: Dividing by a Decimal Number

New Concept

To perform division with a decimal divisor, we create an equivalent problem where the divisor is a whole number by shifting the decimal point.

To divide by a decimal number, we move the decimal point in the divisor to the right to make the divisor a whole number. Then we move the decimal point in the dividend the same number of places to the right.

What’s next

This is the foundational method. Next, you'll apply this technique in worked examples, from simple equations to practical word problems.

Property

To divide by a decimal number, move the decimal point in the divisor to the right to make it a whole number. Then, move the decimal point in the dividend the same number of places to the right.

Examples

$3.35 \div 0.05$ is equivalent to $335 \div 5 = 67$
$0.144 \div 0.8$ is equivalent to $1.44 \div 8 = 0.18$
$21 \div 0.5$ is equivalent to $210 \div 5 = 42$

Explanation

Think of it as a currency swap! Dividing 2.00 dollars by 0.25 dollars is tricky. So, just convert it to 200 cents divided by 25 cents. By shifting the decimal point in both numbers, you get an easier problem with the exact same answer. It's a perfectly legal math cheat code!

Property

You can create an equivalent division problem by multiplying the dividend and divisor by the same number. It's the same principle as multiplying a fraction by a form of 1, like $\frac{10}{10}$.

Examples

$\frac{1.36}{0.4}$ becomes $\frac{1.36 \times 10}{0.4 \times 10}$ = $\frac{13.6}{4}$
$\frac{7}{0.35}$ becomes $\frac{7.00 \times 100}{0.35\times100}$ = $\frac{700}{35}$ = 20

Explanation

This is the secret power behind our decimal trick! Multiplying the top and bottom of a division problem by 10 or 100 doesn't change the final answer. It just cleverly transforms the problem into a friendlier version that gets rid of the pesky decimal in the number you're dividing by.

Property

To solve a one-step equation like $0.07x = 5.6$, isolate the variable by dividing the constant term by the decimal coefficient.

Examples

• Solve: $0.07x$ = $5.6 \rightarrow x$ = $5.6 \div 0.07 \rightarrow x$ = $560 \div 7$ = $80$
• Solve: $0.4y$ = $20 \rightarrow y$ = $20 \div 0.4 \rightarrow y$ = $200 \div 4$ = $50$

Explanation

Don't let decimals in your algebra problems intimidate you! To find the mystery value of x, just use your new division superpower. Divide the number on its own by the number hanging out with x. Just remember to slide those decimal points in both numbers before you solve!