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Math, from the beginning

Fractions & Decimals

The bridge most of us missed, finally explained.

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What this covers

Every lesson is short enough to finish in one sitting and ends with questions that make you use what you just read.

  1. What a Fraction Really IsFrom pizza slices to the number line5 min
  2. Equivalent FractionsSame amount, different outfit5 min
  3. Comparing FractionsWhich is bigger, and how to tell fast5 min
  4. Adding and Subtracting FractionsWhy you need matching pieces first6 min
  5. Multiplying Fractions"Of" means times5 min
Show all 14 lessonsShow fewer lessons
  1. Dividing FractionsThe flip trick, finally demystified6 min
  2. Decimals Are Fractions in DisguisePlace value does the heavy lifting5 min
  3. Rounding and EstimatingClose enough, on purpose5 min
  4. Converting Between Fractions and DecimalsTwo languages, one translator6 min
  5. Fractions in Real LifeRecipes, measurements, and splitting the bill6 min
  6. Ratios and ProportionsWhere fractions stop being homework and start being useful8 min
  7. Mixed Numbers in Real ArithmeticThe form recipes and tape measures actually use8 min
  8. Order of Operations With FractionsWhen a problem has more than one step7 min
  9. Fractions Timed Simulation: Set A30 items, 30 minutes, exam mode30 min

A whole lesson, start to finish

Not a sample and not a summary. This is all of lesson 2, exactly as it reads in the app.

Lesson 2 of 14 · about 5 min

Equivalent Fractions

Same amount, different outfit

Here is a fact that feels like a magic trick the first time: 1/2, 2/4, 3/6, and 50/100 are all the exact same amount. Same spot on the number line, same amount of pizza. They are one number wearing different outfits.

Why it works

Take half a sandwich and cut each half into 2. Now you have 2 pieces out of 4 total. You did not gain or lose any sandwich, you just made more, smaller pieces. Cutting every piece into the same number of smaller pieces changes the labels but not the amount.

The one rule

Multiply (or divide) the top and bottom by the same number, and the fraction's value does not change. 1/2 with top and bottom times 3 becomes 3/6. Same amount, smaller pieces, more of them.

Going the other direction is called simplifying. If top and bottom share a common factor, divide both by it. 6/8: both divide by 2, giving 3/4. Simplifying does not shrink the amount, it just uses the fewest pieces possible. 3/4 is easier to picture than 75/100, and they are identical.

The strategy

To find an equivalent fraction, ask: "What did the bottom get multiplied or divided by?" Then do the exact same thing to the top. Bottom went from 4 to 12? That is times 3, so the top gets times 3 too.

Now answer the question that follows it

This is one of 4 questions on that lesson. Pick an answer and it will tell you.

Which fraction is equal to 1/2?

Terms you will own

Cards come back on a schedule built from how well you knew them last time, so the ones you keep missing show up more.

More in math, from the beginning

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