Simple Division (No Remainder)

Convert $\frac{1}{2}$ to a decimal.

Set up the division: $1 \div 2$ = Numerator divided by denominator

Perform the division: $1 \div 2 = 0.5$ = $0.5$

Verify your answer: $0.5 \times 2 = 1$ ✓ = Correct!

Answer: $\frac{1}{2} = 0.5$

Converting Quarters

Convert $\frac{3}{4}$ to a decimal.

Set up the division: $3 \div 4$ = 3 divided by 4

Divide: $3.00 \div 4 = 0.75$ = Add zeros after decimal point to continue dividing

Read the result: $3 \div 4 = 0.75$ = $0.75$

Answer: $\frac{3}{4} = 0.75$

Tenths Are Easy!

Convert $\frac{7}{10}$ to a decimal.

Recognize the pattern: Denominator is 10 = This is a tenth

Apply the shortcut: Tenths go in the first decimal place = $0.7$

Verify with division: $7 \div 10 = 0.7$ ✓ = Confirmed!

Answer: $\frac{7}{10} = 0.7$

Fifths Conversion

Convert $\frac{2}{5}$ to a decimal.

Set up the division: $2 \div 5$ = 2 divided by 5

Perform the division: $2.0 \div 5 = 0.4$ = 5 goes into 20 exactly 4 times

Alternative method: $\frac{2}{5} = \frac{4}{10} = 0.4$ = Multiply top and bottom by 2 to get tenths

Answer: $\frac{2}{5} = 0.4$

Eighths Conversion

Convert $\frac{5}{8}$ to a decimal.

Set up the division: $5 \div 8$ = 5 divided by 8

Add decimal places and divide: $5.000 \div 8$ = Keep dividing until it terminates

Complete the division: $5 \div 8 = 0.625$ = 8 goes into 50 six times (48), remainder 2; 8 goes into 20 twice (16), remainder 4; 8 goes into 40 five times (40), no remainder

Answer: $\frac{5}{8} = 0.625$

Mistake: Dividing the denominator by the numerator instead

Why: Students sometimes reverse the division: doing $4 \div 3$ instead of $3 \div 4$ for $\frac{3}{4}$.

Correct: Always divide the TOP number (numerator) by the BOTTOM number (denominator). Think: the fraction bar means 'divided by'.

Mistake: Forgetting to add zeros when dividing

Why: When $3 \div 4$ doesn't work as a whole number, students get stuck.

Correct: Add a decimal point and zeros: $3.00 \div 4 = 0.75$. You can always add zeros after a decimal point.

Mistake: Stopping the division too early

Why: Students might write $\frac{5}{8} = 0.6$ instead of completing the division to get $0.625$.

Correct: Keep dividing until there's no remainder OR you see a repeating pattern.

Mistake: Confusing decimal places with fraction parts

Why: Writing $\frac{3}{4}$ as $0.34$ by just placing the numbers.

Correct: You must DIVIDE! $\frac{3}{4} = 3 \div 4 = 0.75$, not $0.34$.

Shopping Discounts

Stores often express discounts as fractions, but calculators use decimals.

A jacket costs 80 dollars with $\frac{1}{4}$ off. Since $\frac{1}{4} = 0.25$, the discount is $80 \times 0.25 = 20$ dollars.

Cooking Measurements

Recipes use fractions, but digital scales show decimals.

A recipe needs $\frac{3}{4}$ cup of flour. Your digital measuring cup shows this as 0.75 cups.

Test Scores

Teachers often convert fraction scores to decimals for calculating grades.

Getting $\frac{18}{20}$ correct means $18 \div 20 = 0.9$ or 90%.

Q: What if the division never ends?

A: Some fractions create repeating decimals. For example, $\frac{1}{3} = 0.333...$ (the 3 repeats forever). We write this as $0.\overline{3}$. You'll learn more about this in the next lesson!

Q: Is there a shortcut for tenths and hundredths?

A: Yes! For tenths, put the numerator in the tenths place: $\frac{7}{10} = 0.7$. For hundredths, put the numerator in the hundredths place: $\frac{23}{100} = 0.23$.

Q: Why should I learn this if I can use a calculator?

A: Understanding WHY division works helps you estimate, check your calculator results, and recognize patterns. Plus, knowing common conversions like $\frac{1}{4} = 0.25$ saves time!