Unit 7: Adding and Subtracting Fractions
Why fractions need a common denominator before they can be added or subtracted, worked out piece by piece.
5 topics · 21 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Adding Fractions with the Same Denominator
- How it worksWalk me through adding 3 eighths of a chocolate bar and 4 eighths of the same bar by counting pieces.
- Common mistakeWhy doesn't adding 2 fourths and 1 fourth give you 3 eighths?
- Worked exampleFind the sum of 3 tenths of a bag of marbles and 4 tenths of the same bag.
- Worked exampleFind how many sixths you have if you eat 2 sixths of a pizza and then 3 more sixths.
- Going furtherWhat happens if you add 5 sixths and 4 sixths and end up with more than one whole pizza?
Your turn1 of 2
Maya drank 3 over 10 of a bottle of juice and Tom drank 4 over 10 of the same size bottle. Added together, what is the new numerator (the denominator stays 10)?Adding Fractions with Different Denominators
- How it worksWalk me through turning 1 third and 1 fourth into twelfths so you can add them together.
- Worked exampleFind the sum of 2 fifths of a bag of stickers and 1 half of the same bag.
- Common mistakeWhy isn't 1 third plus 1 fourth equal to 2 sevenths?
- Ties togetherHow does finding a common denominator connect to finding common multiples of two numbers?
Your turn1 of 2
Nina walked 3 fifths of a mile, then walked one half of a mile more. Using tenths as the common denominator, what is the new numerator (over a denominator of 10)?Subtracting Fractions with Different Denominators
- Worked exampleFind the difference between 3 fourths of a chocolate bar and 1 sixth of the same bar.
- Common mistakeWhy isn't 1 half minus 1 third equal to zero just because both tops are 1?
- Going furtherWhat changes if you use a bigger common denominator than you actually need, like twenty-fourths instead of twelfths?
Your turn1 of 2
Leo had 3 fourths of a candy bar and gave away 6 over 12 of it (3 fourths is the same as 9 twelfths). What is the new numerator of what's left?Adding and Subtracting Mixed Numbers
- How it worksWalk me through adding 2 and 1 third pizzas to 1 and 1 half pizzas by combining wholes and parts.
- Common mistakeWhy doesn't adding 2 and 1 half to 1 and 1 half just give you 3 and 2 halves as the final answer?
- Worked exampleFind the total if you eat 1 and 3 fourths chocolate bars and then 2 and 1 fourth more chocolate bars.
- Going furtherWhat changes if you add 1 and 1 third to 2 and 1 fourth, where the fraction parts don't match?
- Ties togetherHow does adding mixed numbers connect to adding fractions with different denominators?
Your turn1 of 2
Maya drank 7 and 2 fourths of a bottle of juice. Tom drank 8 and 1 fourths. How much did they drink altogether?Subtracting Mixed Numbers with Regrouping
- How it worksWalk me through turning 5 and 1 fourth pizzas into 4 and 5 fourths pizzas so there's enough to subtract 3 fourths.
- How it worksHow do you finish subtracting 2 and 3 fourths pizzas once you've regrouped 5 and 1 fourth into 4 and 5 fourths?
- Worked exampleFind the answer to 6 and 1 sixth chocolate bars minus 2 and 5 sixths chocolate bars.
- Common mistakeWhy isn't the answer to 6 and 1 sixth minus 2 and 5 sixths equal to 4 and 4 sixths?
Your turn1 of 2
A recipe calls for 8 and 1 sixths cups of flour. Priya has already used 3 and 4 sixths cups. How many cups of flour does she have left to use?