Unit 6: Understanding Fractions
What a fraction actually is, seen as pieces being cut, compared, simplified, and rewritten as mixed numbers.
8 topics · 31 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.
What a Fraction Actually Is
- How it worksHow do the top and bottom numbers of a fraction each describe a different part of a cut pizza?
- Worked exampleFind what fraction of a pizza is left if you eat 3 out of 8 slices.
- Common mistakeWhy doesn't 5 twelfths have to be bigger than 3 fourths just because 5 is bigger than 3?
- Going furtherWhat happens to the size of each slice if you cut the same pizza into 12 pieces instead of 8?
Your turn1 of 2
A pizza is cut into 10 equal slices. Maya eats 2 of them. What fraction of the pizza is left?Fractions on a Number Line
- How it worksHow do you split the space between 0 and 1 into fifths to plot 3 fifths on a number line?
- Worked exampleFind where 5 sixths belongs on a number line between 0 and 1.
- Common mistakeWhy doesn't plotting 3 fourths mean counting 3 spaces on a number line marked off in halves?
Your turn1 of 2
A ribbon that is one metre long is marked off into 9 equal parts. What is the length, in metres, of 2 of those parts put end to end?Equivalent Fractions: the Same Amount, Cut Differently
- How it worksHow does cutting a pizza's halves in half again turn 1 half into 2 fourths without changing how much you get?
- How it worksHow does cutting a chocolate bar into twice as many pieces turn 3 fourths into 6 eighths?
- Worked exampleFind an equivalent fraction for 2 thirds by cutting each third into 2 smaller pieces.
- Common mistakeWhy doesn't cutting a pizza into more pieces mean you end up with more pizza to eat?
- Going furtherWhat happens to the amount of chocolate bar you have if you keep cutting it into more and more pieces?
Your turn1 of 2
Nina has 2 over 7 of a chocolate bar. If each piece is cut into 6 smaller pieces, what is the new numerator for the same amount of chocolate?Simplifying Fractions to Lowest Terms
- How it worksHow do you divide both the top and bottom of 9 over 12 by their greatest common factor to simplify it?
- Common mistakeWhy doesn't simplifying a fraction change how much of the pizza you actually have?
- Worked exampleFind the simplest form of 12 over 16.
- Going furtherWhat happens if you try to simplify a fraction like 7 over 15 that has no common factors?
Your turn1 of 2
Leo's fraction of a garden simplifies to 2 thirds after dividing both the numerator and denominator by their greatest common factor, 9. What was the original numerator before simplifying?Comparing Fractions with the Same Denominator
- How it worksHow do you compare 4 ninths and 7 ninths by counting how many equal-sized pieces each one has?
- Common mistakeWhy don't you need to find a common denominator before comparing 5 eighths and 2 eighths?
- Going furtherWhat happens to the comparison between 3 tenths and 7 tenths if you double both top numbers?
Your turn1 of 2
Ben ate 5 over 11 of a pie and Zoe ate 7 over 11 of an identical pie. What is the bigger of the two numerators, 5 or 7?Comparing Fractions with Different Denominators
- How it worksHow do you turn 2 thirds and 3 fourths into twelfths so you can compare them directly?
- Worked exampleFind which is bigger, 3 fifths or 7 tenths, by rewriting them with the same denominator.
- Worked exampleFind which is bigger, 5 sixths or 2 thirds, by comparing them on a number line.
- Common mistakeWhy isn't 1 eighth bigger than 1 half just because 8 is a bigger number than 2?
- Going furtherWhat happens to your comparison method if the two denominators, like 4 and 9, share no common factors?
Your turn1 of 2
Sam drank 3 fifths of a bottle of juice. Rewrite that amount with a denominator of 10 instead of 5. What is the new numerator?Mixed Numbers and Improper Fractions
- How it worksHow do whole pizzas and leftover slices combine to make a mixed number like 2 and 3 fourths?
- Worked exampleFind how many whole pizzas and leftover slices are in 11 fourths of a pizza.
- Going furtherWhat happens to a mixed number if the leftover part is exactly a whole pizza's worth of slices?
- Ties togetherHow does an improper fraction like 9 fourths connect to the division problem 9 divided by 4?
Your turn1 of 2
Nina has an improper fraction of pizzas equal to 4 times 8, plus 4, all over 8. What is the whole number part when she writes it as a mixed number?Converting Between Mixed Numbers and Improper Fractions
- How it worksHow do you turn 3 and 2 fifths into an improper fraction by multiplying and adding?
- Going furtherWhat changes in the steps if the whole number part is much bigger, like 12 in 12 and 3 fourths?
- Ties togetherHow does turning an improper fraction back into a mixed number connect to finding a quotient and remainder?
Your turn1 of 2
Amara baked 7 and 2 over 7 cakes. Turn that into an improper fraction. What is the new numerator?