Fractions, Decimals & % Math · Noduly
Lesson

Three names for the same number

A fraction, a decimal and a percent can all describe the same value. Learning to slide between them makes a huge slice of math feel calmer.

12=0.5=50% 34=0.75=75%

Fractions

The top number, the numerator, says how many parts you have. The bottom number, the denominator, says how many equal parts the whole is divided into.

3/4 means: split a thing into 4 equal parts and take 3 of them.

Decimals

A decimal extends place value past the ones place. The first digit after the dot is tenths, the next is hundredths, and so on.

0.75 = 7 tenths + 5 hundredths = 75/100.

Percentages

Percent means “out of 100.” A percent is just a fraction with denominator 100, written with a % sign.

75% = 75/100 = 0.75.

How to convert

Fraction → Decimal: divide top by bottom.
Decimal → Percent: multiply by 100, add %.
Percent → Fraction: drop the %, put it over 100, simplify.

Common equivalents to memorize

One half
1/2 = 0.5 = 50%
One third
1/3 ≈ 0.333… ≈ 33.3%
Two thirds
2/3 ≈ 0.666… ≈ 66.7%
One quarter
1/4 = 0.25 = 25%
Three quarters
3/4 = 0.75 = 75%
One fifth
1/5 = 0.2 = 20%
One eighth
1/8 = 0.125 = 12.5%
One tenth
1/10 = 0.1 = 10%

Hands-on tools

Pick a tool, drag a slider, and watch the numbers update.

Compare two fractions

Slide either fraction. The longer bar is the larger value.

0.500 · 50%
0.750 · 75%

Pie slicer

A pie chart of 1/4 — see the same fraction as a decimal and a percent.

Reads as: one quarter — 0.250 — 25%

Triple converter

Type into any one of the three boxes. The other two update with worked steps.

Discount & tip playground

Try a coupon, a sales tax, or a tip — see the math broken down.

Add two fractions

Different denominators? The tool finds a common one and shows every step.

+ = 7/12

Quiz

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Flashcards

Tap a card to flip. Use ← / → keys to step through.

Numerator
NumeratorThe top number of a fraction; how many parts you have.
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For teachers

Print-ready worksheet, answer key, teaching tips and standards alignment. Generate a fresh worksheet whenever you need one.

Teaching tips

    Standards alignment

      Reference

      Formula sheet plus a small photo gallery from Wikipedia.

      Formula sheet

      Add / subtract
      a/b ± c/d = (ad ± bc) / bd
      Multiply
      a/b × c/d = ac / bd
      Divide
      a/b ÷ c/d = ad / bc
      Decimal → percent
      d × 100 = p%
      Percent → decimal
      p ÷ 100 = d
      Percent of N
      (P / 100) × N
      Percent change
      (new − old) / old × 100%
      Simplify
      a/b ÷ gcd(a,b)

      Photo gallery

      Images sourced from Wikipedia.

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