Fraction Operations
Lessons in this chapter
About Fraction Operations
Fraction Operations is two lessons because by 6th grade almost everything about fractions is already in place; what remains is making division secure.
Divide Fractions revisits invert-and-multiply with the explanation that makes it stick. Dividing by three quarters asks how many three-quarters fit into the amount, and since four quarters fit in each whole, the answer scales by four thirds, which is exactly the reciprocal.
This is also the moment to settle the result that most unsettles kids: dividing by a number less than one makes the answer bigger. 6 ÷ one half is 12, because twelve halves fit into six, and a child who checks that against a drawing stops distrusting it.
Solve Applied Problems on Fraction Operations covers all four operations in context, where the real work is choosing. Two thirds of a quantity is multiplication, splitting two thirds among people is division, and only the sentence distinguishes them.
Fraction fluency matters more here than it looks, because 6th grade algebra is full of fractional coefficients. A child shaky on dividing fractions will stall in the Linear Equations chapter for reasons that have nothing to do with equations.
Both lessons in Fraction Operations open as 6th grade math worksheets inside the page. Divide Fractions and Solve Applied Problems on Fraction Operations give practice questions worked one at a time and marked as you go, so the word problems get as much attention as the arithmetic. Free to try, with no login needed for your first 3.
Frequently asked questions
Two lessons. Divide Fractions carries the new idea: dividing by a fraction asks how many of it fit into the other number, which is why the answer is often larger than what you started with and why inverting and multiplying works at all. Solve Applied Problems on Fraction Operations then mixes all four operations into word problems, where the harder decision is usually which operation the situation calls for rather than the computation itself. The chapter sits in the Common Core domain The Number System (6.NS).
Because dividing asks how many of the divisor fit into the amount. Dividing by three quarters scales by four thirds, which is the reciprocal, and flipping and multiplying does exactly that.
Because you are dividing by something less than one, so more of them fit. 6 ÷ one half is 12, since there are twelve halves in six.
Taking a fraction of an amount is multiplication. Splitting an amount into fractional parts, or asking how many fit, is division.
Because adding, subtracting and multiplying fractions were all covered in 4th and 5th grade. 6th grade only needs to secure division and apply the lot.
Because 6th grade equations are full of fractional coefficients. A child who stalls on dividing fractions will stall on equations for reasons unrelated to equations.